Daily Papers

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

Large language models have transformed the comprehension and generation of natural language tasks, but they come with substantial memory and computational requirements. Quantization techniques have emerged as a promising avenue for addressing these challenges while preserving accuracy and making energy efficient. We propose CPTQuant, a comprehensive strategy that introduces correlation-based (CMPQ), pruning-based (PMPQ), and Taylor decomposition-based (TDMPQ) mixed precision techniques. CMPQ adapts the precision level based on canonical correlation analysis of different layers. PMPQ optimizes precision layer-wise based on their sensitivity to sparsity. TDMPQ modifies precision using Taylor decomposition to assess each layer's sensitivity to input perturbation. These strategies allocate higher precision to more sensitive layers while diminishing precision to robust layers. CPTQuant assesses the performance across BERT, OPT-125M, OPT-350M, OPT-1.3B, and OPT-2.7B. We demonstrate up to 4x compression and a 2x-fold increase in efficiency with minimal accuracy drop compared to Hugging Face FP16. PMPQ stands out for achieving a considerably higher model compression. Sensitivity analyses across various LLMs show that the initial and final 30% of layers exhibit higher sensitivities than the remaining layers. PMPQ demonstrates an 11% higher compression ratio than other methods for classification tasks, while TDMPQ achieves a 30% greater compression ratio for language modeling tasks.

This paper introduces an information-aware quantization framework that adaptively compresses the key-value (KV) cache in large language models (LLMs). Although prior work has underscored the distinct roles of key and value cache during inference, our systematic analysis -- examining singular value distributions, spectral norms, and Frobenius norms -- reveals, for the first time, that key matrices consistently exhibit higher norm values and are more sensitive to quantization than value matrices. Furthermore, our theoretical analysis shows that matrices with higher spectral norms amplify quantization errors more significantly. Motivated by these insights, we propose a mixed-precision quantization strategy, KV-AdaQuant, which allocates more bit-width for keys and fewer for values since key matrices have higher norm values. With the same total KV bit budget, this approach effectively mitigates error propagation across transformer layers while achieving significant memory savings. Our extensive experiments on multiple LLMs (1B--70B) demonstrate that our mixed-precision quantization scheme maintains high model accuracy even under aggressive compression. For instance, using 4-bit for Key and 2-bit for Value achieves an accuracy of 75.2%, whereas reversing the assignment (2-bit for Key and 4-bit for Value) yields only 54.7% accuracy. The code is available at https://tinyurl.com/kv-adaquant

Video large language models (VideoLLMs) have demonstrated the capability to process longer video inputs and enable complex reasoning and analysis. However, due to the thousands of visual tokens from the video frames, key-value (KV) cache can significantly increase memory requirements, becoming a bottleneck for inference speed and memory usage. KV cache quantization is a widely used approach to address this problem. In this paper, we find that 2-bit KV quantization of VideoLLMs can hardly hurt the model performance, while the limit of KV cache quantization in even lower bits has not been investigated. To bridge this gap, we introduce VidKV, a plug-and-play KV cache quantization method to compress the KV cache to lower than 2 bits. Specifically, (1) for key, we propose a mixed-precision quantization strategy in the channel dimension, where we perform 2-bit quantization for anomalous channels and 1-bit quantization combined with FFT for normal channels; (2) for value, we implement 1.58-bit quantization while selectively filtering semantically salient visual tokens for targeted preservation, for a better trade-off between precision and model performance. Importantly, our findings suggest that the value cache of VideoLLMs should be quantized in a per-channel fashion instead of the per-token fashion proposed by prior KV cache quantization works for LLMs. Empirically, extensive results with LLaVA-OV-7B and Qwen2.5-VL-7B on six benchmarks show that VidKV effectively compresses the KV cache to 1.5-bit and 1.58-bit precision with almost no performance drop compared to the FP16 counterparts.

Deploying neural networks on microcontroller units (MCUs) presents substantial challenges due to their constrained computation and memory resources. Previous researches have explored patch-based inference as a strategy to conserve memory without sacrificing model accuracy. However, this technique suffers from severe redundant computation overhead, leading to a substantial increase in execution latency. A feasible solution to address this issue is mixed-precision quantization, but it faces the challenges of accuracy degradation and a time-consuming search time. In this paper, we propose QuantMCU, a novel patch-based inference method that utilizes value-driven mixed-precision quantization to reduce redundant computation. We first utilize value-driven patch classification (VDPC) to maintain the model accuracy. VDPC classifies patches into two classes based on whether they contain outlier values. For patches containing outlier values, we apply 8-bit quantization to the feature maps on the dataflow branches that follow. In addition, for patches without outlier values, we utilize value-driven quantization search (VDQS) on the feature maps of their following dataflow branches to reduce search time. Specifically, VDQS introduces a novel quantization search metric that takes into account both computation and accuracy, and it employs entropy as an accuracy representation to avoid additional training. VDQS also adopts an iterative approach to determine the bitwidth of each feature map to further accelerate the search process. Experimental results on real-world MCU devices show that QuantMCU can reduce computation by 2.2x on average while maintaining comparable model accuracy compared to the state-of-the-art patch-based inference methods.

Mixed-Precision Quantization~(MQ) can achieve a competitive accuracy-complexity trade-off for models. Conventional training-based search methods require time-consuming candidate training to search optimized per-layer bit-width configurations in MQ. Recently, some training-free approaches have presented various MQ proxies and significantly improve search efficiency. However, the correlation between these proxies and quantization accuracy is poorly understood. To address the gap, we first build the MQ-Bench-101, which involves different bit configurations and quantization results. Then, we observe that the existing training-free proxies perform weak correlations on the MQ-Bench-101. To efficiently seek superior proxies, we develop an automatic search of proxies framework for MQ via evolving algorithms. In particular, we devise an elaborate search space involving the existing proxies and perform an evolution search to discover the best correlated MQ proxy. We proposed a diversity-prompting selection strategy and compatibility screening protocol to avoid premature convergence and improve search efficiency. In this way, our Evolving proxies for Mixed-precision Quantization~(EMQ) framework allows the auto-generation of proxies without heavy tuning and expert knowledge. Extensive experiments on ImageNet with various ResNet and MobileNet families demonstrate that our EMQ obtains superior performance than state-of-the-art mixed-precision methods at a significantly reduced cost. The code will be released.

Edge applications, such as collaborative robotics and spacecraft rendezvous, demand efficient 6D object pose estimation on resource-constrained embedded platforms. Existing 6D pose estimation networks are often too large for such deployments, necessitating compression while maintaining reliable performance. To address this challenge, we introduce Modular Quantization-Aware Training (MQAT), an adaptive and mixed-precision quantization-aware training strategy that exploits the modular structure of modern 6D pose estimation architectures. MQAT guides a systematic gradated modular quantization sequence and determines module-specific bit precisions, leading to quantized models that outperform those produced by state-of-the-art uniform and mixed-precision quantization techniques. Our experiments showcase the generality of MQAT across datasets, architectures, and quantization algorithms. Remarkably, MQAT-trained quantized models achieve a significant accuracy boost (>7%) over the baseline full-precision network while reducing model size by a factor of 4x or more.

Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (ALRS) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HASB) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We also validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task. Our codes are available at https://github.com/haiduo/Double-Rounding.

The pre-trained language models have achieved great successes in various natural language understanding (NLU) tasks due to its capacity to capture the deep contextualized information in text by pre-training on large-scale corpora. In this technical report, we present our practice of pre-training language models named NEZHA (NEural contextualiZed representation for CHinese lAnguage understanding) on Chinese corpora and finetuning for the Chinese NLU tasks. The current version of NEZHA is based on BERT with a collection of proven improvements, which include Functional Relative Positional Encoding as an effective positional encoding scheme, Whole Word Masking strategy, Mixed Precision Training and the LAMB Optimizer in training the models. The experimental results show that NEZHA achieves the state-of-the-art performances when finetuned on several representative Chinese tasks, including named entity recognition (People's Daily NER), sentence matching (LCQMC), Chinese sentiment classification (ChnSenti) and natural language inference (XNLI).

The burgeoning computational demands for training large language models (LLMs) necessitate efficient methods, including quantized training, which leverages low-bit arithmetic operations to reduce costs. While FP8 precision has shown potential, leveraging FP4 remains challenging due to inherent quantization errors and limited representation capability. Based on the Transformer architecture, we present an FP4 training scheme for LLMs, overcoming these obstacles through mixed-precision quantization strategies tailed for different modules and training stages. This allows us to apply the precision level suitable to distinct components within the model, ensuring that multi-head attention and linear layers are handled appropriately. Our pretraining recipe ensures stability in backpropagation by incorporating fine-grained quantization methods with a target precision training schedule. Experimental results demonstrate that our FP4 training scheme achieves accuracy comparable to BF16 and FP8, with smaller theoretical computational cost. With the advent of next-generation hardware supporting FP4, our method sets the foundation for efficient ultra-low precision training.

Post-Training Quantization (PTQ) is pivotal for deploying large language models (LLMs) within resource-limited settings by significantly reducing resource demands. However, existing PTQ strategies underperform at low bit levels < 3 bits due to the significant difference between the quantized and original weights. To enhance the quantization performance at low bit widths, we introduce a Mixed-precision Graph Neural PTQ (MG-PTQ) approach, employing a graph neural network (GNN) module to capture dependencies among weights and adaptively assign quantization bit-widths. Through the information propagation of the GNN module, our method more effectively captures dependencies among target weights, leading to a more accurate assessment of weight importance and optimized allocation of quantization strategies. Extensive experiments on the WikiText2 and C4 datasets demonstrate that our MG-PTQ method outperforms previous state-of-the-art PTQ method GPTQ, setting new benchmarks for quantization performance under low-bit conditions.

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical evaluation across models ranging from 10M to 1B parameters, we demonstrate that quantization can achieve up to 68% reduction in model size while maintaining performance within 6% of full-precision baselines when utilizing our proposed scaling factor {\gamma}. Our experiments show that INT8 quantization delivers a 40% reduction in computational cost and power consumption, while INT4 quantization further improves these metrics by 60%. We introduce a novel theoretical framework for mixed-precision quantization, deriving optimal bit allocation strategies based on layer sensitivity and weight variance. Hardware efficiency evaluations on edge devices reveal that our quantization approach enables up to 2.4x throughput improvement for INT8 and 3x for INT4, with 60% power reduction compared to full-precision models.

In this paper, we explore FP8 low-bit data formats for efficient training of large language models (LLMs). Our key insight is that most variables, such as gradients and optimizer states, in LLM training can employ low-precision data formats without compromising model accuracy and requiring no changes to hyper-parameters. Specifically, we propose a new FP8 automatic mixed-precision framework for training LLMs. This framework offers three levels of FP8 utilization to streamline mixed-precision and distributed parallel training for LLMs. It gradually incorporates 8-bit gradients, optimizer states, and distributed learning in an incremental manner. Experiment results show that, during the training of GPT-175B model on H100 GPU platform, our FP8 mixed-precision training framework not only achieved a remarkable 42% reduction in real memory usage but also ran 64% faster than the widely adopted BF16 framework (i.e., Megatron-LM), surpassing the speed of Nvidia Transformer Engine by 17%. This largely reduces the training costs for large foundation models. Furthermore, our FP8 mixed-precision training methodology is generic. It can be seamlessly applied to other tasks such as LLM instruction tuning and reinforcement learning with human feedback, offering savings in fine-tuning expenses. Our FP8 low-precision training framework is open-sourced at {https://github.com/Azure/MS-AMP}{aka.ms/MS.AMP}.

Post-training quantization of Large Language Models (LLMs) has proven effective in reducing the computational requirements for running inference on these models. In this study, we focus on a straightforward question: When aiming for a specific accuracy or perplexity target for low-precision quantization, how many high-precision numbers or calculations are required to preserve as we scale LLMs to larger sizes? We first introduce a critical metric named the quantization ratio, which compares the number of parameters quantized to low-precision arithmetic against the total parameter count. Through extensive and carefully controlled experiments across different model families, arithmetic types, and quantization granularities (e.g. layer-wise, matmul-wise), we identify two central phenomenons. 1) The larger the models, the better they can preserve performance with an increased quantization ratio, as measured by perplexity in pre-training tasks or accuracy in downstream tasks. 2) The finer the granularity of mixed-precision quantization (e.g., matmul-wise), the more the model can increase the quantization ratio. We believe these observed phenomena offer valuable insights for future AI hardware design and the development of advanced Efficient AI algorithms.

Large language models (LLMs) have achieved impressive performance across various domains. However, the substantial hardware resources required for their training present a significant barrier to efficiency and scalability. To mitigate this challenge, low-precision training techniques have been widely adopted, leading to notable advancements in training efficiency. Despite these gains, low-precision training involves several componentsx2013such as weights, activations, and gradientsx2013each of which can be represented in different numerical formats. The resulting diversity has created a fragmented landscape in low-precision training research, making it difficult for researchers to gain a unified overview of the field. This survey provides a comprehensive review of existing low-precision training methods. To systematically organize these approaches, we categorize them into three primary groups based on their underlying numerical formats, which is a key factor influencing hardware compatibility, computational efficiency, and ease of reference for readers. The categories are: (1) fixed-point and integer-based methods, (2) floating-point-based methods, and (3) customized format-based methods. Additionally, we discuss quantization-aware training approaches, which share key similarities with low-precision training during forward propagation. Finally, we highlight several promising research directions to advance this field. A collection of papers discussed in this survey is provided in https://github.com/Hao840/Awesome-Low-Precision-Training.

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33\% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3\times speedup over 16-bit baseline. Code is available at https://github.com/utkarsh-dmx/project-resq.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point quantization and thus cannot well fit the LLM losses in this scenario. In contrast, while floating-point quantization training is more commonly implemented in production, the research on it has been relatively superficial. In this paper, we thoroughly explore the effects of floating-point quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in floating-point quantization training performance of LLM models. While presenting an accurate floating-point quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal floating-point quantization precision is directly proportional to the computational power, but within a wide computational power range, we estimate that the best cost-performance precision lies between 4-8 bits.

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

Transformer-based large language models (LLMs) have achieved remarkable success as model sizes continue to grow, yet their deployment remains challenging due to significant computational and memory demands. Quantization has emerged as a promising solution, and state-of-the-art quantization algorithms for LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), where lower-precision weights are multiplied with higher-precision activations. Despite its benefits, current hardware accelerators such as GPUs and TPUs lack native support for efficient mpGEMM, leading to inefficient dequantization operations in the main sequential loop. To address this limitation, we introduce MixPE, a specialized mixed-precision processing element designed for efficient low-bit quantization in LLM inference. MixPE leverages two key innovations to minimize dequantization overhead and unlock the full potential of low-bit quantization. First, recognizing that scale and zero point are shared within each quantization group, we propose performing dequantization after per-group mpGEMM, significantly reducing dequantization overhead. Second, instead of relying on conventional multipliers, MixPE utilizes efficient shift\&add operations for multiplication, optimizing both computation and energy efficiency. Our experimental results demonstrate that MixPE surpasses the state-of-the-art quantization accelerators by 2.6times speedup and 1.4times energy reduction.

Large language models (LLMs) with enormous pre-training tokens and parameter amounts emerge abilities, including math reasoning, code generation, and instruction following. These abilities are further enhanced by supervised fine-tuning (SFT). The open-source community has studied on ad-hoc SFT for each ability, while proprietary LLMs are versatile for all abilities. It is important to investigate how to unlock them with multiple abilities via SFT. In this study, we specifically focus on the data composition between mathematical reasoning, code generation, and general human-aligning abilities during SFT. From a scaling perspective, we investigate the relationship between model abilities and various factors including data amounts, data composition ratio, model parameters, and SFT strategies. Our experiments reveal that different abilities exhibit different scaling patterns, and larger models generally show superior performance with the same amount of data. Mathematical reasoning and code generation improve as data amounts increase consistently, while the general ability is enhanced with about a thousand samples and improves slowly. We find data composition results in various abilities improvements with low data amounts, while conflicts of abilities with high data amounts. Our experiments further show that composition data amount impacts performance, while the influence of composition ratio is insignificant. Regarding the SFT strategies, we evaluate sequential learning multiple abilities are prone to catastrophic forgetting. Our proposed Dual-stage Mixed Fine-tuning (DMT) strategy learns specialized abilities first and then learns general abilities with a small amount of specialized data to prevent forgetting, offering a promising solution to learn multiple abilities with different scaling patterns.

Fine-tuning is a crucial process for adapting large language models (LLMs) to diverse applications. In certain scenarios, such as multi-tenant serving, deploying multiple LLMs becomes necessary to meet complex demands. Recent studies suggest decomposing a fine-tuned LLM into a base model and corresponding delta weights, which are then compressed using low-rank or low-bit approaches to reduce costs. In this work, we observe that existing low-rank and low-bit compression methods can significantly harm the model performance for task-specific fine-tuned LLMs (e.g., WizardMath for math problems). Motivated by the long-tail distribution of singular values in the delta weights, we propose a delta quantization approach using mixed-precision. This method employs higher-bit representation for singular vectors corresponding to larger singular values. We evaluate our approach on various fine-tuned LLMs, including math LLMs, code LLMs, chat LLMs, and even VLMs. Experimental results demonstrate that our approach performs comparably to full fine-tuned LLMs, surpassing both low-rank and low-bit baselines by a considerable margin. Additionally, we show that our method is compatible with various backbone LLMs, such as Llama-2, Llama-3, and Mistral, highlighting its generalizability.

Current large-language models (LLMs) typically adopt a fixed reasoning strategy, either simple or complex, for all questions, regardless of their difficulty. This neglect of variation in task and reasoning process complexity leads to an imbalance between performance and efficiency. Existing methods attempt to implement training-free fast-slow thinking system switching to handle problems of varying difficulty, but are limited by coarse-grained solution-level strategy adjustments. To address this issue, we propose a novel reasoning paradigm: Process-Level Adaptive Thinking Mode Switching (PATS), which enables LLMs to dynamically adjust their reasoning strategy based on the difficulty of each step, optimizing the balance between accuracy and computational efficiency. Our approach integrates Process Reward Models (PRMs) with Beam Search, incorporating progressive mode switching and bad-step penalty mechanisms. Experiments on diverse mathematical benchmarks demonstrate that our methodology achieves high accuracy while maintaining moderate token usage. This study emphasizes the significance of process-level, difficulty-aware reasoning strategy adaptation, offering valuable insights into efficient inference for LLMs.

The massive computational costs associated with large language model (LLM) pretraining have spurred great interest in reduced-precision floating-point representations to accelerate the process. As a result, the BrainFloat16 (BF16) precision has become the de facto standard for LLM training, with hardware support included in recent accelerators. This trend has gone even further in the latest processors, where FP8 has recently been introduced. However, prior experience with FP16, which was found to be less stable than BF16, raises concerns as to whether FP8, with even fewer bits than FP16, can be a cost-effective option for LLM training. We argue that reduced-precision training schemes must have similar training stability and hyperparameter sensitivities to their higher-precision counterparts in order to be cost-effective. However, we find that currently available methods for FP8 training are not robust enough to allow their use as economical replacements. This prompts us to investigate the stability of reduced-precision LLM training in terms of robustness across random seeds and learning rates. To this end, we propose new evaluation techniques and a new metric for quantifying loss landscape sharpness in autoregressive language models. By simulating incremental bit reductions in floating-point representations, we analyze the relationship between representational power and training stability with the intent of aiding future research into the field.

The rapid advancement of large language models (LLMs) has been paralleled by unprecedented increases in computational demands, with training costs for state-of-the-art models doubling every few months. Training models directly in low-precision arithmetic offers a solution, by improving both computational throughput and energy efficiency. Specifically, NVIDIA's recent Blackwell architecture facilitates extremely low-precision operations, specifically FP4 variants, promising substantial efficiency gains. Yet, current algorithms for training LLMs in FP4 precision face significant accuracy degradation and often rely on mixed-precision fallbacks. In this paper, we systematically investigate hardware-supported FP4 training and introduce Quartet, a new approach enabling accurate, end-to-end FP4 training with all the major computations (in e.g. linear layers) being performed in low precision. Through extensive evaluations on Llama-type models, we reveal a new low-precision scaling law that quantifies performance trade-offs across varying bit-widths and allows us to identify a "near-optimal" low-precision training technique in terms of accuracy-vs-computation, called Quartet. We implement Quartet using optimized CUDA kernels tailored for NVIDIA Blackwell GPUs, and show that it can achieve state-of-the-art accuracy for FP4 precision, successfully training billion-scale models. Our method demonstrates that fully FP4-based training is a competitive alternative to standard-precision and FP8 training. Our code is available at https://github.com/IST-DASLab/Quartet.

Quantization emerges as one of the most promising approaches for deploying advanced deep models on resource-constrained hardware. Mixed-precision quantization leverages multiple bit-width architectures to unleash the accuracy and efficiency potential of quantized models. However, existing mixed-precision quantization suffers exhaustive search space that causes immense computational overhead. The quantization process thus relies on separate high-performance devices rather than locally, which also leads to a significant gap between the considered hardware metrics and the real deployment.In this paper, we propose an On-chip Hardware-aware Quantization (OHQ) framework that performs hardware-aware mixed-precision quantization without accessing online devices. First, we construct the On-chip Quantization Awareness (OQA) pipeline, enabling perceive the actual efficiency metrics of the quantization operator on the hardware.Second, we propose Mask-guided Quantization Estimation (MQE) technique to efficiently estimate the accuracy metrics of operators under the constraints of on-chip-level computing power.By synthesizing network and hardware insights through linear programming, we obtain optimized bit-width configurations. Notably, the quantization process occurs on-chip entirely without any additional computing devices and data access. We demonstrate accelerated inference after quantization for various architectures and compression ratios, achieving 70% and 73% accuracy for ResNet-18 and MobileNetV3, respectively. OHQ improves latency by 15~30% compared to INT8 on deployment.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Deploying transformer-based neural networks on resource-constrained edge devices presents a significant challenge. This challenge is often addressed through various techniques, such as low-rank approximation and mixed-precision quantization. In this work, we introduce Mixed Low-Rank and Quantization (MLoRQ), a novel method that integrates both techniques. MLoRQ employs a two-stage optimization process to determine optimal bit-width and rank assignments for each layer, adhering to predefined memory constraints. This process includes: (i) an intra-layer optimization that identifies potentially optimal compression solutions out of all low-rank and quantization combinations; (ii) an inter-layer optimization that assigns bit-width precision and rank to each layer while ensuring the memory constraint is met. An optional final step applies a sequential optimization process using a modified adaptive rounding technique to mitigate compression-induced errors in joint low-rank approximation and quantization. The method is compatible and can be seamlessly integrated with most existing quantization algorithms. MLoRQ shows state-of-the-art results with up to 15\% performance improvement, evaluated on Vision Transformers for image classification, object detection, and instance segmentation tasks.

In embedding-based retrieval, Approximate Nearest Neighbor (ANN) search enables efficient retrieval of similar items from large-scale datasets. While maximizing recall of relevant items is usually the goal of retrieval systems, a low precision may lead to a poor search experience. Unlike lexical retrieval, which inherently limits the size of the retrieved set through keyword matching, dense retrieval via ANN search has no natural cutoff. Moreover, the cosine similarity scores of embedding vectors are often optimized via contrastive or ranking losses, which make them difficult to interpret. Consequently, relying on top-K or cosine-similarity cutoff is often insufficient to filter out irrelevant results effectively. This issue is prominent in product search, where the number of relevant products is often small. This paper introduces a novel relevance filtering component (called "Cosine Adapter") for embedding-based retrieval to address this challenge. Our approach maps raw cosine similarity scores to interpretable scores using a query-dependent mapping function. We then apply a global threshold on the mapped scores to filter out irrelevant results. We are able to significantly increase the precision of the retrieved set, at the expense of a small loss of recall. The effectiveness of our approach is demonstrated through experiments on both public MS MARCO dataset and internal Walmart product search data. Furthermore, online A/B testing on the Walmart site validates the practical value of our approach in real-world e-commerce settings.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

We compare the (1,lambda)-EA and the (1 + lambda)-EA on the recently introduced benchmark DisOM, which is the OneMax function with randomly planted local optima. Previous work showed that if all local optima have the same relative height, then the plus strategy never loses more than a factor O(nlog n) compared to the comma strategy. Here we show that even small random fluctuations in the heights of the local optima have a devastating effect for the plus strategy and lead to super-polynomial runtimes. On the other hand, due to their ability to escape local optima, comma strategies are unaffected by the height of the local optima and remain efficient. Our results hold for a broad class of possible distortions and show that the plus strategy, but not the comma strategy, is generally deceived by sparse unstructured fluctuations of a smooth landscape.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

Instruction Tuning involves finetuning a language model on a collection of instruction-formatted datasets in order to enhance the generalizability of the model to unseen tasks. Studies have shown the importance of balancing different task proportions during finetuning, but finding the right balance remains challenging. Unfortunately, there's currently no systematic method beyond manual tuning or relying on practitioners' intuition. In this paper, we introduce SMART (Submodular data Mixture strAtegy for instRuction Tuning) - a novel data mixture strategy which makes use of a submodular function to assign importance scores to tasks which are then used to determine the mixture weights. Given a fine-tuning budget, SMART redistributes the budget among tasks and selects non-redundant samples from each task. Experimental results demonstrate that SMART significantly outperforms traditional methods such as examples proportional mixing and equal mixing. Furthermore, SMART facilitates the creation of data mixtures based on a few representative subsets of tasks alone and through task pruning analysis, we reveal that in a limited budget setting, allocating budget among a subset of representative tasks yields superior performance compared to distributing the budget among all tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/SMART.

Key-Value (KV) Caching has become an essential technique for accelerating the inference speed and throughput of generative Large Language Models~(LLMs). However, the memory footprint of the KV cache poses a critical bottleneck in LLM deployment as the cache size grows with batch size and sequence length, often surpassing even the size of the model itself. Although recent methods were proposed to select and evict unimportant KV pairs from the cache to reduce memory consumption, the potential ramifications of eviction on the generative process are yet to be thoroughly examined. In this paper, we examine the detrimental impact of cache eviction and observe that unforeseen risks arise as the information contained in the KV pairs is exhaustively discarded, resulting in safety breaches, hallucinations, and context loss. Surprisingly, we find that preserving even a small amount of information contained in the evicted KV pairs via reduced precision quantization substantially recovers the incurred degradation. On the other hand, we observe that the important KV pairs must be kept at a relatively higher precision to safeguard the generation quality. Motivated by these observations, we propose Mixed-precision KV cache~(MiKV), a reliable cache compression method that simultaneously preserves the context details by retaining the evicted KV pairs in low-precision and ensure generation quality by keeping the important KV pairs in high-precision. Experiments on diverse benchmarks and LLM backbones show that our proposed method offers a state-of-the-art trade-off between compression ratio and performance, compared to other baselines.

This paper reveals the phenomenon of parameter heterogeneity in large language models (LLMs). We find that a small subset of ``cherry'' parameters exhibit a disproportionately large influence on model performance, while the vast majority of parameters have minimal impact. This heterogeneity is found to be prevalent across different model families, scales, and types. Motivated by this observation, we propose CherryQ, a novel quantization method that unifies the optimization of mixed-precision parameters. CherryQ identifies and preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate the effectiveness of CherryQ. CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance. Notably, our 3-bit quantized Vicuna-1.5 exhibits competitive performance compared to their 16-bit counterparts. These findings highlight the potential of CherryQ for enabling efficient deployment of LLMs by taking advantage of parameter heterogeneity.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

The growing computational demands of training large language models (LLMs) necessitate more efficient methods. Quantized training presents a promising solution by enabling low-bit arithmetic operations to reduce these costs. While FP8 precision has demonstrated feasibility, leveraging FP4 remains a challenge due to significant quantization errors and limited representational capacity. This work introduces the first FP4 training framework for LLMs, addressing these challenges with two key innovations: a differentiable quantization estimator for precise weight updates and an outlier clamping and compensation strategy to prevent activation collapse. To ensure stability, the framework integrates a mixed-precision training scheme and vector-wise quantization. Experimental results demonstrate that our FP4 framework achieves accuracy comparable to BF16 and FP8, with minimal degradation, scaling effectively to 13B-parameter LLMs trained on up to 100B tokens. With the emergence of next-generation hardware supporting FP4, our framework sets a foundation for efficient ultra-low precision training.

Large language models (LLMs) with hundreds of billions of parameters require powerful server-grade GPUs for inference, limiting their practical deployment. To address this challenge, we introduce the outlier-aware weight quantization (OWQ) method, which aims to minimize LLM's footprint through low-precision representation. OWQ prioritizes a small subset of structured weights sensitive to quantization, storing them in high-precision, while applying highly tuned quantization to the remaining dense weights. This sensitivity-aware mixed-precision scheme reduces the quantization error notably, and extensive experiments demonstrate that 3.1-bit models using OWQ perform comparably to 4-bit models optimized by OPTQ. Furthermore, OWQ incorporates a parameter-efficient fine-tuning for task-specific adaptation, called weak column tuning (WCT), enabling accurate task-specific LLM adaptation with minimal memory overhead in the optimized format. OWQ represents a notable advancement in the flexibility, efficiency, and practicality of LLM optimization literature. The source code is available at https://github.com/xvyaward/owq

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Efficiently serving neural network models with low latency is becoming more challenging due to increasing model complexity and parameter count. Model quantization offers a solution which simultaneously reduces memory footprint and compute requirements. However, aggressive quantization may lead to an unacceptable loss in model accuracy owing to differences in sensitivity to numerical imperfection across different layers in the model. To address this challenge, we propose a mixed-precision post training quantization (PTQ) approach that assigns different numerical precisions to tensors in a network based on their specific needs, for a reduced memory footprint and improved latency while preserving model accuracy. Previous works rely on layer-wise Hessian information to determine numerical precision, but as we demonstrate, Hessian estimation is typically insufficient in determining an effective ordering of layer sensitivities. We address this by augmenting the estimated Hessian with additional information to capture inter-layer dependencies. We demonstrate that this consistently improves PTQ performance along the accuracy-latency Pareto frontier across multiple models. Our method combines second-order information and inter-layer dependencies to guide a bisection search, finding quantization configurations within a user-configurable model accuracy degradation range. We evaluate the effectiveness of our method on the ResNet50, MobileNetV2, and BERT models. Our experiments demonstrate latency reductions compared to a 16-bit baseline of 25.48%, 21.69%, and 33.28% respectively, while maintaining model accuracy to within 99.99% of the baseline model.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

We introduce Reward-Guided Speculative Decoding (RSD), a novel framework aimed at improving the efficiency of inference in large language models (LLMs). RSD synergistically combines a lightweight draft model with a more powerful target model, incorporating a controlled bias to prioritize high-reward outputs, in contrast to existing speculative decoding methods that enforce strict unbiasedness. RSD employs a process reward model to evaluate intermediate decoding steps and dynamically decide whether to invoke the target model, optimizing the trade-off between computational cost and output quality. We theoretically demonstrate that a threshold-based mixture strategy achieves an optimal balance between resource utilization and performance. Extensive evaluations on challenging reasoning benchmarks, including Olympiad-level tasks, show that RSD delivers significant efficiency gains against decoding with the target model only (up to 4.4x fewer FLOPs), while achieving significant better accuracy than parallel decoding method on average (up to +3.5). These results highlight RSD as a robust and cost-effective approach for deploying LLMs in resource-intensive scenarios.

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or system inefficiency. In this paper, we make a comprehensive analysis of the general quantization principles on their effect to the triangle of accuracy, memory consumption and system efficiency. We propose MixLLM that explores the new optimization space of mixed-precision quantization between output features based on the insight that different output features matter differently in the model. MixLLM identifies the output features with high salience in the global view rather than within each single layer, effectively assigning the larger bit-width to output features that need it most to achieve good accuracy with low memory consumption. We present the sweet spot of quantization configuration of algorithm-system co-design that leads to high accuracy and system efficiency. To address the system challenge, we design the two-step dequantization to make use of the int8 Tensor Core easily and fast data type conversion to reduce dequantization overhead significantly, and present the software pipeline to overlap the memory access, dequantization and the MatMul to the best. Extensive experiments show that with only 10% more bits, the PPL increasement can be reduced from about 0.5 in SOTA to within 0.2 for Llama 3.1 70B, while on average MMLU-Pro improves by 0.93 over the SOTA of three popular models. In addition to its superior accuracy, MixLLM also achieves state-of-the-art system efficiency.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Large language models (LLMs) have demonstrated remarkable capabilities in various natural language processing tasks. However, achieving strong performance in specialized domains like mathematical reasoning and non-English languages often requires extensive training on massive datasets. This paper investigates a contrasting approach: strategic fine-tuning on a small, high-quality, bilingual (English-French) dataset to enhance both the reasoning capabilities and French language proficiency of a large language model. Rather than relying on scale, we explore the hypothesis that targeted data curation and optimized training can achieve competitive, or even superior, performance. We demonstrate, through targeted supervised fine-tuning (SFT) on only 2,000 carefully selected samples, significant improvements in mathematical reasoning. Specifically, Pensez 7B exhibits an increase in accuracy of the base model up to 20% on the AIME25 and a 12% increase on a French MATH level 5 benchmark. These results challenge the prevailing assumption that massive datasets are aprerequisite for strong reasoning performance in LLMs, highlighting the potential of strategic data curation and optimized fine-tuning for enhancing both specialized skills and multilingual capabilities. Our findings have implications for the efficient development of high-performing, multilingual LLMs, especially in resource-constrained scenarios.

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

Existing research has demonstrated that refining large language models (LLMs) through the utilization of machine-generated instruction-following data empowers these models to exhibit impressive zero-shot capabilities for novel tasks, without requiring human-authored instructions. In this paper, we systematically investigate, preprocess, and integrate three Chinese instruction-following datasets with the aim of enhancing the Chinese conversational capabilities of Mixtral-8x7B sparse Mixture-of-Experts model. Through instruction fine-tuning on this carefully processed dataset, we successfully construct the Mixtral-8x7B sparse Mixture-of-Experts model named "Aurora." To assess the performance of Aurora, we utilize three widely recognized benchmark tests: C-Eval, MMLU, and CMMLU. Empirical studies validate the effectiveness of instruction fine-tuning applied to Mixtral-8x7B sparse Mixture-of-Experts model. This work is pioneering in the execution of instruction fine-tuning on a sparse expert-mixed model, marking a significant breakthrough in enhancing the capabilities of this model architecture. Our code, data and model are publicly available at https://github.com/WangRongsheng/Aurora

The Mixture-of-Experts (MoE) paradigm has emerged as a powerful approach for scaling transformers with improved resource utilization. However, efficiently fine-tuning MoE models remains largely underexplored. Inspired by recent works on Parameter-Efficient Fine-Tuning (PEFT), we present a unified framework for integrating PEFT modules directly into the MoE mechanism. Aligning with the core principles and architecture of MoE, our framework encompasses a set of design dimensions including various functional and composition strategies. By combining design choices within our framework, we introduce Parameter-Efficient Routed Fine-Tuning (PERFT) as a flexible and scalable family of PEFT strategies tailored for MoE models. Extensive experiments on adapting OLMoE-1B-7B and Mixtral-8times7B for commonsense and arithmetic reasoning tasks demonstrate the effectiveness, scalability, and intriguing dynamics of PERFT. Additionally, we provide empirical findings for each specific design choice to facilitate better application of MoE and PEFT.

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration such as evaluation batch size, GPU count, and GPU version can introduce significant difference in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size. We trace the root cause of this variability to the non-associative nature of floating-point arithmetic under limited numerical precision. This work presents the first systematic investigation into how numerical precision affects reproducibility in LLM inference. Through carefully controlled experiments across various hardware, software, and precision settings, we quantify when and how model outputs diverge. Our analysis reveals that floating-point precision -- while critical for reproducibility -- is often neglected in evaluation practices. Inspired by this, we develop a lightweight inference pipeline, dubbed LayerCast, that stores weights in 16-bit precision but performs all computations in FP32, balancing memory efficiency with numerical stability. Code is available at https://github.com/nanomaoli/llm_reproducibility.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Recently, considerable efforts have been directed towards compressing Large Language Models (LLMs), which showcase groundbreaking capabilities across diverse applications but entail significant deployment costs due to their large sizes. Meanwhile, much less attention has been given to mitigating the costs associated with deploying multiple LLMs of varying sizes despite its practical significance. Thus, this paper introduces any-precision LLM, extending the concept of any-precision DNN to LLMs. Addressing challenges in any-precision LLM, we propose a lightweight method for any-precision quantization of LLMs, leveraging a post-training quantization framework, and develop a specialized software engine for its efficient serving. As a result, our solution significantly reduces the high costs of deploying multiple, different-sized LLMs by overlaying LLMs quantized to varying bit-widths, such as 3, 4, ..., n bits, into a memory footprint comparable to a single n-bit LLM. All the supported LLMs with varying bit-widths demonstrate state-of-the-art model quality and inference throughput, proving itself to be a compelling option for deployment of multiple, different-sized LLMs. The source code will be publicly available soon.

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

Mixture-of-Experts (MoE) has emerged as a prominent architecture for scaling model size while maintaining computational efficiency. In MoE, each token in the input sequence activates a different subset of experts determined by a routing mechanism. However, the unchosen experts in MoE models do not contribute to the output, potentially leading to underutilization of the model's capacity. In this work, we first conduct exploratory studies to demonstrate that increasing the number of activated experts does not necessarily improve and can even degrade the output quality. Then, we show that output distributions from an MoE model using different routing strategies substantially differ, indicating that different experts do not always act synergistically. Motivated by these findings, we propose Self-Contrast Mixture-of-Experts (SCMoE), a training-free strategy that utilizes unchosen experts in a self-contrast manner during inference. In SCMoE, the next-token probabilities are determined by contrasting the outputs from strong and weak activation using the same MoE model. Our method is conceptually simple and computationally lightweight, as it incurs minimal latency compared to greedy decoding. Experiments on several benchmarks (GSM8K, StrategyQA, MBPP and HumanEval) demonstrate that SCMoE can consistently enhance Mixtral 8x7B's reasoning capability across various domains. For example, it improves the accuracy on GSM8K from 61.79 to 66.94. Moreover, combining SCMoE with self-consistency yields additional gains, increasing major@20 accuracy from 75.59 to 78.31.

The optimal training configurations of large language models (LLMs) with respect to model sizes and compute budgets have been extensively studied. But how to optimally configure LLMs during inference has not been explored in sufficient depth. We study compute-optimal inference: designing models and inference strategies that optimally trade off additional inference-time compute for improved performance. As a first step towards understanding and designing compute-optimal inference methods, we assessed the effectiveness and computational efficiency of multiple inference strategies such as Greedy Search, Majority Voting, Best-of-N, Weighted Voting, and their variants on two different Tree Search algorithms, involving different model sizes and computational budgets. We found that a smaller language model with a novel tree search algorithm typically achieves a Pareto-optimal trade-off. These results highlight the potential benefits of deploying smaller models equipped with more sophisticated decoding algorithms in budget-constrained scenarios, e.g., on end-devices, to enhance problem-solving accuracy. For instance, we show that the Llemma-7B model can achieve competitive accuracy to a Llemma-34B model on MATH500 while using 2times less FLOPs. Our findings could potentially apply to any generation task with a well-defined measure of success.

With the widespread adoption of Large Language Models (LLMs), many deep learning practitioners are looking for strategies of running these models more efficiently. One such strategy is to use sparse Mixture-of-Experts (MoE) - a type of model architectures where only a fraction of model layers are active for any given input. This property allows MoE-based language models to generate tokens faster than their dense counterparts, but it also increases model size due to having multiple experts. Unfortunately, this makes state-of-the-art MoE language models difficult to run without high-end GPUs. In this work, we study the problem of running large MoE language models on consumer hardware with limited accelerator memory. We build upon parameter offloading algorithms and propose a novel strategy that accelerates offloading by taking advantage of innate properties of MoE LLMs. Using this strategy, we build can run Mixtral-8x7B with mixed quantization on desktop hardware and free-tier Google Colab instances.

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ (Attention-aware Post-Training Mixed-Precision Quantization) for LLMs, which considers not only the second-order information of each layer's weights, but also, for the first time, the nonlinear effect of attention outputs on the entire model. We leverage the Hessian trace as a sensitivity metric for mixed-precision quantization, ensuring an informed precision reduction that retains model performance. Experiments show APTQ surpasses previous quantization methods, achieving an average of 4 bit width a 5.22 perplexity nearly equivalent to full precision in the C4 dataset. In addition, APTQ attains state-of-the-art zero-shot accuracy of 68.24\% and 70.48\% at an average bitwidth of 3.8 in LLaMa-7B and LLaMa-13B, respectively, demonstrating its effectiveness to produce high-quality quantized LLMs.

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

Large multimodal Mixture-of-Experts (MoEs) effectively scale the model size to boost performance while maintaining fixed active parameters. However, previous works primarily utilized full-precision experts during sparse up-cycling. Despite they show superior performance on end tasks, the large amount of experts introduces higher memory footprint, which poses significant challenges for the deployment on edge devices. In this work, we propose MoTE, a scalable and memory-efficient approach to train Mixture-of-Ternary-Experts models from dense checkpoint. Instead of training fewer high-precision experts, we propose to train more low-precision experts during up-cycling. Specifically, we use the pre-trained FFN as a shared expert and train ternary routed experts with parameters in {-1, 0, 1}. Extensive experiments show that our approach has promising scaling trend along model size. MoTE achieves comparable performance to full-precision baseline MoE-LLaVA while offering lower memory footprint. Furthermore, our approach is compatible with post-training quantization methods and the advantage further amplifies when memory-constraint goes lower. Given the same amount of expert memory footprint of 3.4GB and combined with post-training quantization, MoTE outperforms MoE-LLaVA by a gain of 4.3% average accuracy on end tasks, demonstrating its effectiveness and potential for memory-constrained devices.

The advent of 1-bit large language models (LLMs), led by BitNet b1.58, has spurred interest in ternary LLMs. Despite this, research and practical applications focusing on efficient edge inference for ternary LLMs remain scarce. To bridge this gap, we introduce Bitnet.cpp, an inference system optimized for BitNet b1.58 and ternary LLMs. Given that mixed-precision matrix multiplication (mpGEMM) constitutes the bulk of inference time in ternary LLMs, Bitnet.cpp incorporates a novel mpGEMM library to facilitate sub-2-bits-per-weight, efficient and lossless inference. The library features two core solutions: Ternary Lookup Table (TL), which addresses spatial inefficiencies of previous bit-wise methods, and Int2 with a Scale (I2_S), which ensures lossless edge inference, both enabling high-speed inference. Our experiments show that Bitnet.cpp achieves up to a 6.25x increase in speed over full-precision baselines and up to 2.32x over low-bit baselines, setting new benchmarks in the field. Additionally, we expand TL to element-wise lookup table (ELUT) for low-bit LLMs in the appendix, presenting both theoretical and empirical evidence of its considerable potential. Bitnet.cpp is publicly available at https://github.com/microsoft/BitNet/tree/paper , offering a sophisticated solution for the efficient and practical deployment of edge LLMs.

We study the design decisions of publicly available instruction tuning methods, and break down the development of Flan 2022 (Chung et al., 2022). Through careful ablation studies on the Flan Collection of tasks and methods, we tease apart the effect of design decisions which enable Flan-T5 to outperform prior work by 3-17%+ across evaluation settings. We find task balancing and enrichment techniques are overlooked but critical to effective instruction tuning, and in particular, training with mixed prompt settings (zero-shot, few-shot, and chain-of-thought) actually yields stronger (2%+) performance in all settings. In further experiments, we show Flan-T5 requires less finetuning to converge higher and faster than T5 on single downstream tasks, motivating instruction-tuned models as more computationally-efficient starting checkpoints for new tasks. Finally, to accelerate research on instruction tuning, we make the Flan 2022 collection of datasets, templates, and methods publicly available at https://github.com/google-research/FLAN/tree/main/flan/v2.

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on six datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, ModelSwitch requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

Deep neural networks have achieved state-of-the-art results in a wide range of applications, from natural language processing and computer vision to speech recognition. However, as tasks become increasingly complex, model sizes continue to grow, posing challenges in latency and memory efficiency. To meet these constraints, post-training quantization has emerged as a promising solution. In this paper, we propose a novel hardware-efficient quantization and inference scheme that exploits hardware advantages with minimal accuracy degradation. Specifically, we introduce a W4A8 scheme, where weights are quantized and stored using 4-bit integer precision, and inference computations are performed using 8-bit floating-point arithmetic, demonstrating significant speedups and improved memory utilization compared to 16-bit operations, applicable on various modern accelerators. To mitigate accuracy loss, we develop a novel quantization algorithm, dubbed Dual Precision Quantization (DPQ), that leverages the unique structure of our scheme without introducing additional inference overhead. Experimental results demonstrate improved performance (i.e., increased throughput) while maintaining tolerable accuracy degradation relative to the full-precision model.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

Post-training quantization is the leading method for addressing memory-related bottlenecks in LLM inference, but unfortunately, it suffers from significant performance degradation below 4-bit precision. An alternative approach involves training compressed models directly at a low bitwidth (e.g., binary or ternary models). However, the performance, training dynamics, and scaling trends of such models are not yet well understood. To address this issue, we train and openly release the Spectra LLM suite consisting of 54 language models ranging from 99M to 3.9B parameters, trained on 300B tokens. Spectra includes FloatLMs, post-training quantized QuantLMs (3, 4, 6, and 8 bits), and ternary LLMs (TriLMs) - our improved architecture for ternary language modeling, which significantly outperforms previously proposed ternary models of a given size (in bits), matching half-precision models at scale. For example, TriLM 3.9B is (bit-wise) smaller than the half-precision FloatLM 830M, but matches half-precision FloatLM 3.9B in commonsense reasoning and knowledge benchmarks. However, TriLM 3.9B is also as toxic and stereotyping as FloatLM 3.9B, a model six times larger in size. Additionally, TriLM 3.9B lags behind FloatLM in perplexity on validation splits and web-based corpora but performs better on less noisy datasets like Lambada and PennTreeBank. To enhance understanding of low-bitwidth models, we are releasing 500+ intermediate checkpoints of the Spectra suite at https://github.com/NolanoOrg/SpectraSuite{https://github.com/NolanoOrg/SpectraSuite}.

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules

We propose an acceleration scheme for large language models (LLMs) through Speculative Decoding with Semantic Adaptive Tokens (SDSAT). The primary objective of this design is to enhance the LLM model's ability to generate draft tokens more accurately without compromising the model's accuracy. The core strategies involve: 1) Fine-tune the model by incorporating semantic adaptive tokens that possess flexible decoding capabilities without changing its structure, allowing them to generate high-quality draft tokens. 2) By employing a training method that does not affect the standard tokens, the model can acquire parallel decoding abilities atop its original framework with minimal training overhead. 3) We have designed the "two-step-draft-then-verify" generation strategies using both greedy search and nucleus sampling. Experiments conducted on the CodeLlama-13B and 7B models have yielded speed increases of over 3.5X and 3.0X, respectively. Please refer to https://github.com/hasuoshenyun/SDSAT.

Large Language Model (LLM)-based search agents have shown remarkable capabilities in solving complex tasks by dynamically decomposing problems and addressing them through interleaved reasoning and retrieval. However, this interleaved paradigm introduces substantial efficiency bottlenecks. First, we observe that both highly accurate and overly approximate retrieval methods degrade system efficiency: exact search incurs significant retrieval overhead, while coarse retrieval requires additional reasoning steps during generation. Second, we identify inefficiencies in system design, including improper scheduling and frequent retrieval stalls, which lead to cascading latency -- where even minor delays in retrieval amplify end-to-end inference time. To address these challenges, we introduce SearchAgent-X, a high-efficiency inference framework for LLM-based search agents. SearchAgent-X leverages high-recall approximate retrieval and incorporates two key techniques: priority-aware scheduling and non-stall retrieval. Extensive experiments demonstrate that SearchAgent-X consistently outperforms state-of-the-art systems such as vLLM and HNSW-based retrieval across diverse tasks, achieving up to 3.4times higher throughput and 5times lower latency, without compromising generation quality. SearchAgent-X is available at https://github.com/tiannuo-yang/SearchAgent-X.

Large language models (LLMs) have transformed natural-language processing, yet their scale makes real-world deployment costly. Post-training quantization reduces memory and computation but often degrades accuracy, while quantization-aware training can recover performance at the cost of extra training. Pushing quantization to the ternary (2-bit) regime yields even larger savings but is notoriously unstable. Building on recent work showing that a bias-free, RMS-normalized Transformer with straight-through estimation can reach 1.58-bit precision, we demonstrate that simply inserting RMS normalization before every linear projection and applying a gradual, layer-wise quantization schedule stably fine-tunes full-precision checkpoints into ternary LLMs. Our approach matches or surpasses more elaborate knowledge-distillation pipelines on standard language-modeling benchmarks without adding model complexity. These results indicate that careful normalization alone can close much of the accuracy gap between ternary and full-precision LLMs, making ultra-low-bit inference practical.

The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of research has also happened in the domain of low and mixed-precision Integer training, these works either present results for non-SOTA networks (for instance only AlexNet for ImageNet-1K), or relatively small datasets (like CIFAR-10). In this work, we train state-of-the-art visual understanding neural networks on the ImageNet-1K dataset, with Integer operations on General Purpose (GP) hardware. In particular, we focus on Integer Fused-Multiply-and-Accumulate (FMA) operations which take two pairs of INT16 operands and accumulate results into an INT32 output.We propose a shared exponent representation of tensors and develop a Dynamic Fixed Point (DFP) scheme suitable for common neural network operations. The nuances of developing an efficient integer convolution kernel is examined, including methods to handle overflow of the INT32 accumulator. We implement CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; and these networks achieve or exceed SOTA accuracy within the same number of iterations as their FP32 counterparts without any change in hyper-parameters and with a 1.8X improvement in end-to-end training throughput. To the best of our knowledge these results represent the first INT16 training results on GP hardware for ImageNet-1K dataset using SOTA CNNs and achieve highest reported accuracy using half-precision

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

This paper identifies the misinterpretation of the context can be a significant issue during the reasoning process of large language models, spanning from smaller models like Llama3.2-3B-Instruct to cutting-edge ones like DeepSeek-R1. For example, in the phrase "10 dollars per kilo," LLMs might not recognize that "per" means "for each," leading to calculation errors. We introduce a novel, post-training approach called **Stick to the Facts (SIFT)** to tackle this. SIFT leverages increasing inference-time compute to ground LLM reasoning in contexts. At the core of SIFT lies the *Sticker*, which is generated by the model itself to explicitly emphasize the key information within the context. Given the curated Sticker, SIFT generates two predictions -- one from the original query and one from the query augmented with the Sticker. If they differ, the Sticker is sequentially refined via *forward* optimization (to better align the extracted facts with the query) and *inverse* generation (to conform with the model's inherent tendencies) for more faithful reasoning outcomes. Studies across diverse models (from 3B to 100B+) and benchmarks (e.g., GSM8K, MATH-500) reveal consistent performance improvements. Notably, SIFT improves the pass@1 accuracy of DeepSeek-R1 on AIME2024 from 78.33% to **85.67**%, establishing a new state-of-the-art in the open-source community. The code is available at https://github.com/zhijie-group/SIFT.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

This paper addresses the limitations of traditional keyword-based search in understanding user intent and introduces a novel hybrid search approach that leverages the strengths of non-semantic search engines, Large Language Models (LLMs), and embedding models. The proposed system integrates keyword matching, semantic vector embeddings, and LLM-generated structured queries to deliver highly relevant and contextually appropriate search results. By combining these complementary methods, the hybrid approach effectively captures both explicit and implicit user intent.The paper further explores techniques to optimize query execution for faster response times and demonstrates the effectiveness of this hybrid search model in producing comprehensive and accurate search outcomes.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

There is a consensus that instruction fine-tuning of LLMs requires high-quality data, but what are they? LIMA (NeurIPS 2023) and AlpaGasus (ICLR 2024) are state-of-the-art methods for selecting such high-quality examples, either via manual curation or using GPT-3.5-Turbo as a quality scorer. We show that the extremely simple baseline of selecting the 1,000 instructions with longest responses from standard datasets can consistently outperform these sophisticated methods according to GPT-4 and PaLM-2 as judges, while remaining competitive on the OpenLLM benchmarks that test factual knowledge. We demonstrate this for several state-of-the-art LLMs (Llama-2-7B, Llama-2-13B, and Mistral-7B) and datasets (Alpaca-52k and Evol-Instruct-70k). In addition, a lightweight refinement of such long instructions can further improve the abilities of the fine-tuned LLMs, and allows us to obtain the 2nd highest-ranked Llama-2-7B-based model on AlpacaEval 2.0 while training on only 1,000 examples and no extra preference data. We also conduct a thorough analysis of our models to ensure that their enhanced performance is not simply due to GPT-4's preference for longer responses, thus ruling out any artificial improvement. In conclusion, our findings suggest that fine-tuning on the longest instructions should be the default baseline for any research on instruction fine-tuning.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this job is beam search -- a pruned version of breadth-first search. Quite surprisingly, beam search often returns better results than exact inference due to beneficial search bias for NLP tasks. In this work, we show that the standard implementation of beam search can be made up to 10x faster in practice. Our method assumes that the scoring function is monotonic in the sequence length, which allows us to safely prune hypotheses that cannot be in the final set of hypotheses early on. We devise effective monotonic approximations to popular nonmonontic scoring functions, including length normalization and mutual information decoding. Lastly, we propose a memory-reduced variant of Best-First Beam Search, which has a similar beneficial search bias in terms of downstream performance, but runs in a fraction of the time.

Recent work has shown the immense potential of synthetically generated datasets for training large language models (LLMs), especially for acquiring targeted skills. Current large-scale math instruction tuning datasets such as MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed using outputs from closed-source LLMs with commercially restrictive licenses. A key reason limiting the use of open-source LLMs in these data generation pipelines has been the wide gap between the mathematical skills of the best closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on the recent progress in open-source LLMs, our proposed prompting novelty, and some brute-force scaling, we construct OpenMathInstruct-1, a math instruction tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by synthesizing code-interpreter solutions for GSM8K and MATH, two popular math reasoning benchmarks, using the recently released and permissively licensed Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which is competitive with the best gpt-distilled models. We release our code, models, and the OpenMathInstruct-1 dataset under a commercially permissive license.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Despite their success in many natural language tasks, solving math problems remains a significant challenge for large language models (LLMs). A large gap exists between LLMs' pass-at-one and pass-at-N performance in solving math problems, suggesting LLMs might be close to finding correct solutions, motivating our exploration of fine-tuning methods to unlock LLMs' performance. Using the challenging MATH dataset, we investigate three fine-tuning strategies: (1) solution fine-tuning, where we fine-tune to generate a detailed solution for a given math problem; (2) solution-cluster re-ranking, where the LLM is fine-tuned as a solution verifier/evaluator to choose among generated candidate solution clusters; (3) multi-task sequential fine-tuning, which integrates both solution generation and evaluation tasks together efficiently to enhance the LLM performance. With these methods, we present a thorough empirical study on a series of PaLM 2 models and find: (1) The quality and style of the step-by-step solutions used for fine-tuning can make a significant impact on the model performance; (2) While solution re-ranking and majority voting are both effective for improving the model performance when used separately, they can also be used together for an even greater performance boost; (3) Multi-task fine-tuning that sequentially separates the solution generation and evaluation tasks can offer improved performance compared with the solution fine-tuning baseline. Guided by these insights, we design a fine-tuning recipe that yields approximately 58.8% accuracy on the MATH dataset with fine-tuned PaLM 2-L models, an 11.2% accuracy improvement over the few-shot performance of pre-trained PaLM 2-L model with majority voting.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that {4-bit} precision is almost universally optimal for total model bits and zero-shot accuracy.

DARTS search space (DSS) has become a canonical benchmark for NAS whereas some emerging works pointed out the issue of narrow accuracy range and claimed it would hurt the method ranking. We observe some recent studies already suffer from this issue that overshadows the meaning of scores. In this work, we first propose and orchestrate a suite of improvements to frame a larger and harder DSS, termed LHD, while retaining high efficiency in search. We step forward to renovate a LHD-based new benchmark, taking care of both discernibility and accessibility. Specifically, we re-implement twelve baselines and evaluate them across twelve conditions by combining two underexpolored influential factors: transductive robustness and discretization policy, to reasonably construct a benchmark upon multi-condition evaluation. Considering that the tabular benchmarks are always insufficient to adequately evaluate the methods of neural architecture search (NAS), our work can serve as a crucial basis for the future progress of NAS. https://github.com/chaoji90/LHD

Active Learning (AL) is a well-known standard method for efficiently obtaining annotated data by first labeling the samples that contain the most information based on a query strategy. In the past, a large variety of such query strategies has been proposed, with each generation of new strategies increasing the runtime and adding more complexity. However, to the best of our our knowledge, none of these strategies excels consistently over a large number of datasets from different application domains. Basically, most of the the existing AL strategies are a combination of the two simple heuristics informativeness and representativeness, and the big differences lie in the combination of the often conflicting heuristics. Within this paper, we propose ImitAL, a domain-independent novel query strategy, which encodes AL as a learning-to-rank problem and learns an optimal combination between both heuristics. We train ImitAL on large-scale simulated AL runs on purely synthetic datasets. To show that ImitAL was successfully trained, we perform an extensive evaluation comparing our strategy on 13 different datasets, from a wide range of domains, with 7 other query strategies.

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

Inference-time scaling has emerged as a powerful alternative to parameter scaling for improving language model performance on complex reasoning tasks. While existing methods have shown strong performance gains under fixed compute budgets, there has been little focus on optimally utilizing that budget during inference. In this work, we introduce A*-decoding, a search-based inference-time strategy that builds on the A* search algorithm to optimally utilize a fixed compute budget by prioritizing high-quality reasoning paths during generation. We frame language model decoding as a structured search in a state space of partial solutions, applying the A* transition model to identify promising continuations guided by an external process supervision signal. In our experiments, A*-decoding reaches the performance levels of strong inference scaling baselines like best-of-N and particle filtering while using up to 3x fewer tokens and 30% fewer PRM passes under equivalent compute budgets. On the MATH500 and AIME 2024 benchmarks, A*-decoding enables Llama-3.2-1B-Instruct to match the performance of the 70x larger Llama-3.1-70B-Instruct, and allows Qwen3-1.7B to reach o1-like reasoning accuracy. These results highlight the power of structured search in decoding, offering an alternative to brute-force sampling or scale-driven gains. Our work demonstrates how thoughtful inference-time strategies can enhance reasoning in SLMs, pointing toward future advances in more efficient and scalable language model deployment.

Motivated by reducing the computational and storage costs of LLMs, model compression and KV cache compression have attracted much attention from researchers. However, current methods predominantly emphasize maintaining the performance of compressed LLMs, as measured by perplexity or simple accuracy on tasks of common sense knowledge QA and basic arithmetic reasoning. In this blog, we present a brief review of recent advancements in LLMs related to retrieval-augmented generation, multi-step reasoning, external tools, and computational expressivity, all of which substantially enhance LLM performance. Then, we propose a lottery LLM hypothesis suggesting that for a given LLM and task, there exists a smaller lottery LLM capable of producing the same performance as the original LLM with the assistance of multi-step reasoning and external tools. Based on the review of current progress in LLMs, we discuss and summarize the essential capabilities that the lottery LLM and KV cache compression must possess, which are currently overlooked in existing methods.

The rise of large language models (LLMs) has significantly advanced various natural language processing (NLP) tasks. However, the resource demands of these models pose substantial challenges. Structured pruning is an effective approach to reducing model size, but it often results in significant accuracy degradation, necessitating parameter updates to adapt. Unfortunately, such fine-tuning requires substantial memory, which limits its applicability. To address these challenges, we introduce quantization into the structured pruning framework to reduce memory consumption during both fine-tuning and inference. However, the combined errors from pruning and quantization increase the difficulty of fine-tuning, requiring a more refined quantization scheme. To this end, we propose QPruner, a novel framework that employs structured pruning to reduce model size, followed by a layer-wise mixed-precision quantization scheme. Quantization precisions are assigned to each layer based on their importance to the target task, and Bayesian optimization is employed to refine precision allocation strategies, ensuring a balance between model accuracy and memory efficiency. Extensive experiments on benchmark datasets demonstrate that QPruner significantly outperforms existing methods in memory savings while maintaining or improving model performance.

The recent rise of large language models (LLMs) has resulted in increased efforts towards running LLMs at reduced precision. Running LLMs at lower precision supports resource constraints and furthers their democratization, enabling users to run billion-parameter LLMs on their personal devices. To supplement this ongoing effort, we propose INT-FP-QSim: an open-source simulator that enables flexible evaluation of LLMs and vision transformers at various numerical precisions and formats. INT-FP-QSim leverages existing open-source repositories such as TensorRT, QPytorch and AIMET for a combined simulator that supports various floating point and integer formats. With the help of our simulator, we survey the impact of different numerical formats on the performance of LLMs and vision transformers at 4-bit weights and 4-bit or 8-bit activations. We also compare recently proposed methods like Adaptive Block Floating Point, SmoothQuant, GPTQ and RPTQ on the model performances. We hope INT-FP-QSim will enable researchers to flexibly simulate models at various precisions to support further research in quantization of LLMs and vision transformers.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

We demonstrate, for the first time, fully quantized training (FQT) of large language models (LLMs) using predominantly 4-bit floating-point (FP4) precision for weights, activations, and gradients on datasets up to 200 billion tokens. We extensively investigate key design choices for FP4, including block sizes, scaling formats, and rounding methods. Our analysis shows that the NVFP4 format, where each block of 16 FP4 values (E2M1) shares a scale represented in E4M3, provides optimal results. We use stochastic rounding for backward and update passes and round-to-nearest for the forward pass to enhance stability. Additionally, we identify a theoretical and empirical threshold for effective quantized training: when the gradient norm falls below approximately 3 times the quantization noise, quantized training becomes less effective. Leveraging these insights, we successfully train a 7-billion-parameter model on 256 Intel Gaudi2 accelerators. The resulting FP4-trained model achieves downstream task performance comparable to a standard BF16 baseline, confirming that FP4 training is a practical and highly efficient approach for large-scale LLM training. A reference implementation is supplied in https://github.com/Anonymous1252022/fp4-all-the-way .

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Recent large language models (LLMs) have demonstrated versatile capabilities in long-context scenarios. Although some recent benchmarks have been developed to evaluate the long-context capabilities of LLMs, there is a lack of benchmarks evaluating the mathematical reasoning abilities of LLMs over long contexts, which is crucial for LLMs' application in real-world scenarios. In this paper, we introduce MathHay, an automated benchmark designed to assess the long-context mathematical reasoning capabilities of LLMs. Unlike previous benchmarks like Needle in a Haystack, which focus primarily on information retrieval within long texts, MathHay demands models with both information-seeking and complex mathematical reasoning abilities. We conduct extensive experiments on MathHay to assess the long-context mathematical reasoning abilities of eight top-performing LLMs. Even the best-performing model, Gemini-1.5-Pro-002, still struggles with mathematical reasoning over long contexts, achieving only 51.26% accuracy at 128K tokens. This highlights the significant room for improvement on the MathHay benchmark.

Effective decision-making in Large Language Models (LLMs) is essential for handling intricate tasks. However, existing approaches prioritize performance but often overlook the balance between effectiveness and computational cost. To address this, we first introduce the 3E Criteria to systematically assess the cost-effectiveness of search strategies, revealing that existing methods often trade significant efficiency for marginal performance gains. To improve LLM decision-making while maintaining efficiency, we propose the Speculative Reward Model (SRM), a plug-and-play framework that seamlessly integrates with existing search strategies. Specifically, SRM employs an external reward assigner to predict optimal actions, reducing reliance on LLMs' internal self-evaluation. And a speculative verification mechanism is used to prune suboptimal choices and guide the search toward more promising steps. We evaluate SRM on several complex decision-making tasks including mathematical reasoning, planning and numerical reasoning in specialized domains. Experimental results show that SRM reduces costs to 1/10 of the original search framework on average while maintaining effectiveness.

Text generation with beam search has proven successful in a wide range of applications. The commonly-used implementation of beam decoding follows a first come, first served heuristic: it keeps a set of already completed sequences over time steps and stops when the size of this set reaches the beam size. We introduce a patience factor, a simple modification to this decoding algorithm, that generalizes the stopping criterion and provides flexibility to the depth of search. Extensive empirical results demonstrate that the patience factor improves decoding performance of strong pretrained models on news text summarization and machine translation over diverse language pairs, with a negligible inference slowdown. Our approach only modifies one line of code and can be thus readily incorporated in any implementation.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

Large multi-modal models (LMMs) exhibit remarkable performance across numerous tasks. However, generalist LMMs often suffer from performance degradation when tuned over a large collection of tasks. Recent research suggests that Mixture of Experts (MoE) architectures are useful for instruction tuning, but for LMMs of parameter size around O(50-100B), the prohibitive cost of replicating and storing the expert models severely limits the number of experts we can use. We propose Omni-SMoLA, an architecture that uses the Soft MoE approach to (softly) mix many multimodal low rank experts, and avoids introducing a significant number of new parameters compared to conventional MoE models. The core intuition here is that the large model provides a foundational backbone, while different lightweight experts residually learn specialized knowledge, either per-modality or multimodally. Extensive experiments demonstrate that the SMoLA approach helps improve the generalist performance across a broad range of generative vision-and-language tasks, achieving new SoTA generalist performance that often matches or outperforms single specialized LMM baselines, as well as new SoTA specialist performance.

Dense retrieval has become a prominent method to obtain relevant context or world knowledge in open-domain NLP tasks. When we use a learned dense retriever on a retrieval corpus at inference time, an often-overlooked design choice is the retrieval unit in which the corpus is indexed, e.g. document, passage, or sentence. We discover that the retrieval unit choice significantly impacts the performance of both retrieval and downstream tasks. Distinct from the typical approach of using passages or sentences, we introduce a novel retrieval unit, proposition, for dense retrieval. Propositions are defined as atomic expressions within text, each encapsulating a distinct factoid and presented in a concise, self-contained natural language format. We conduct an empirical comparison of different retrieval granularity. Our results reveal that proposition-based retrieval significantly outperforms traditional passage or sentence-based methods in dense retrieval. Moreover, retrieval by proposition also enhances the performance of downstream QA tasks, since the retrieved texts are more condensed with question-relevant information, reducing the need for lengthy input tokens and minimizing the inclusion of extraneous, irrelevant information.

The emergence of pre-trained AI systems with powerful capabilities across a diverse and ever-increasing set of complex domains has raised a critical challenge for AI safety as tasks can become too complicated for humans to judge directly. Irving et al. [2018] proposed a debate method in this direction with the goal of pitting the power of such AI models against each other until the problem of identifying (mis)-alignment is broken down into a manageable subtask. While the promise of this approach is clear, the original framework was based on the assumption that the honest strategy is able to simulate deterministic AI systems for an exponential number of steps, limiting its applicability. In this paper, we show how to address these challenges by designing a new set of debate protocols where the honest strategy can always succeed using a simulation of a polynomial number of steps, whilst being able to verify the alignment of stochastic AI systems, even when the dishonest strategy is allowed to use exponentially many simulation steps.

Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

In conversational AI research, there's a noticeable trend towards developing models with a larger number of parameters, exemplified by models like ChatGPT. While these expansive models tend to generate increasingly better chat responses, they demand significant computational resources and memory. This study explores a pertinent question: Can a combination of smaller models collaboratively achieve comparable or enhanced performance relative to a singular large model? We introduce an approach termed "blending", a straightforward yet effective method of integrating multiple chat AIs. Our empirical evidence suggests that when specific smaller models are synergistically blended, they can potentially outperform or match the capabilities of much larger counterparts. For instance, integrating just three models of moderate size (6B/13B paramaeters) can rival or even surpass the performance metrics of a substantially larger model like ChatGPT (175B+ paramaters). This hypothesis is rigorously tested using A/B testing methodologies with a large user base on the Chai research platform over a span of thirty days. The findings underscore the potential of the "blending" strategy as a viable approach for enhancing chat AI efficacy without a corresponding surge in computational demands.

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Financial reports offer critical insights into a company's operations, yet their extensive length typically spanning 30 40 pages poses challenges for swift decision making in dynamic markets. To address this, we leveraged finetuned Large Language Models (LLMs) to distill key indicators and operational metrics from these reports basis questions from the user. We devised a method to locate critical data, and leverage the FinQA dataset to fine-tune both Llama-2 7B and T5 models for customized question answering. We achieved results comparable to baseline on the final numerical answer, a competitive accuracy in numerical reasoning and calculation.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

In reasoning tasks, even a minor error can cascade into inaccurate results, leading to suboptimal performance of large language models in such domains. Earlier fine-tuning approaches sought to mitigate this by leveraging more precise supervisory signals from human labeling, larger models, or self-sampling, although at a high cost. Conversely, we develop a method that avoids external resources, relying instead on introducing perturbations to the input. Our training approach randomly masks certain tokens within the chain of thought, a technique we found to be particularly effective for reasoning tasks. When applied to fine-tuning with GSM8K, this method achieved a 5% improvement in accuracy over standard supervised fine-tuning with a few codes modified and no additional labeling effort. Furthermore, it is complementary to existing methods. When integrated with related data augmentation methods, it leads to an average improvement of 3% improvement in GSM8K accuracy and 1% improvement in MATH accuracy across five datasets of various quality and size, as well as two base models. We further investigate the mechanisms behind this improvement through case studies and quantitative analysis, suggesting that our approach may provide superior support for the model in capturing long-distance dependencies, especially those related to questions. This enhancement could deepen understanding of premises in questions and prior steps. Our code is available at Github.

Retrieval-augmented Generation (RAG) has primarily been studied in limited settings, such as factoid question answering; more challenging, reasoning-intensive benchmarks have seen limited success from minimal RAG. In this work, we challenge this prevailing view on established, reasoning-intensive benchmarks: MMLU, MMLU Pro, AGI Eval, GPQA, and MATH. We identify a key missing component in prior work: a usable, web-scale datastore aligned with the breadth of pretraining data. To this end, we introduce CompactDS: a diverse, high-quality, web-scale datastore that achieves high retrieval accuracy and subsecond latency on a single-node. The key insights are (1) most web content can be filtered out without sacrificing coverage, and a compact, high-quality subset is sufficient; and (2) combining in-memory approximate nearest neighbor (ANN) retrieval and on-disk exact search balances speed and recall. Using CompactDS, we show that a minimal RAG pipeline achieves consistent accuracy improvements across all benchmarks and model sizes (8B--70B), with relative gains of 10% on MMLU, 33% on MMLU Pro, 14% on GPQA, and 19% on MATH. No single data source suffices alone, highlighting the importance of diversity of sources (web crawls, curated math, academic papers, textbooks). Finally, we show that our carefully designed in-house datastore matches or outperforms web search engines such as Google Search, as well as recently proposed, complex agent-based RAG systems--all while maintaining simplicity, reproducibility, and self-containment. We release CompactDS and our retrieval pipeline, supporting future research exploring retrieval-based AI systems.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Multi-modal large language models(MLLMs) have achieved remarkable progress and demonstrated powerful knowledge comprehension and reasoning abilities. However, the mastery of domain-specific knowledge, which is essential for evaluating the intelligence of MLLMs, continues to be a challenge. Current multi-modal benchmarks for domain-specific knowledge concentrate on multiple-choice questions and are predominantly available in English, which imposes limitations on the comprehensiveness of the evaluation. To this end, we introduce CMMU, a novel benchmark for multi-modal and multi-type question understanding and reasoning in Chinese. CMMU consists of 3,603 questions in 7 subjects, covering knowledge from primary to high school. The questions can be categorized into 3 types: multiple-choice, multiple-response, and fill-in-the-blank, bringing greater challenges to MLLMs. In addition, we propose a rigorous evaluation strategy called ShiftCheck for assessing multiple-choice questions. The strategy aims to reduce position bias, minimize the influence of randomness on correctness, and perform a quantitative analysis of position bias. We evaluate seven open-source MLLMs along with GPT4-V, Gemini-Pro, and Qwen-VL-Plus. The results demonstrate that CMMU poses a significant challenge to the recent MLLMs.

As instruction-tuned large language models (LLMs) evolve, aligning pretrained foundation models presents increasing challenges. Existing alignment strategies, which typically leverage diverse and high-quality data sources, often overlook the intrinsic uncertainty of tasks, learning all data samples equally. This may lead to suboptimal data efficiency and model performance. In response, we propose uncertainty-aware learning (UAL) to improve the model alignment of different task scenarios, by introducing the sample uncertainty (elicited from more capable LLMs). We implement UAL in a simple fashion -- adaptively setting the label smoothing value of training according to the uncertainty of individual samples. Analysis shows that our UAL indeed facilitates better token clustering in the feature space, validating our hypothesis. Extensive experiments on widely used benchmarks demonstrate that our UAL significantly and consistently outperforms standard supervised fine-tuning. Notably, LLMs aligned in a mixed scenario have achieved an average improvement of 10.62\% on high-entropy tasks (i.e., AlpacaEval leaderboard), and 1.81\% on complex low-entropy tasks (i.e., MetaMath and GSM8K).

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, {MetaMath-70B} achieves an accuracy of 82.3% on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

Low-precision data types are essential in modern neural networks during both training and inference as they enhance throughput and computational capacity by better exploiting available hardware resources. Despite the incorporation of FP8 in commercially available neural network accelerators, a comprehensive exposition of its underlying mechanisms, along with rigorous performance and accuracy evaluations, is still lacking. In this work, we contribute in three significant ways. First, we analyze the implementation details and quantization options associated with FP8 for inference on the Intel Gaudi AI accelerator. Second, we empirically quantify the throughput improvements afforded by the use of FP8 at both the operator level and in end-to-end scenarios. Third, we assess the accuracy impact of various FP8 quantization methods. Our experimental results indicate that the Intel Gaudi 2 accelerator consistently achieves high computational unit utilization, frequently exceeding 90% MFU, while incurring an accuracy degradation of less than 1%.

Ever-growing scale of large language models (LLMs) is pushing for improved efficiency, favoring fully quantized training (FQT) over BF16. While FQT accelerates training, it faces consistency challenges and requires searching over an exponential number of cases, each needing over 200B tokens to ensure stability. Pseudo-quantization training (PQT) addresses the issues of FQT, although it is not well-studied. We explore the practical implications of PQT in detail and propose a noise distribution R that is floating-point (FP)-friendly, with ideal properties including stochastic precision annealing. As a result, the proposed method serves as an effective theoretical foundation for low-precision FP parameters through PQT, utilizing efficient fake quantization via an addition and subsequent FP casting. We demonstrate that Gaussian weight sampling is (1) scalable: supports low-precision FP parameters down to FP6 and high-precision noise up to 9-bit with BF16 operator. The proposed method is (2) efficient: incurring computational overhead as low as 1.40\% on the A100 GPU in terms of Llama2 training tokens per second, and requiring 2 bytes per parameter in GPU memory. We demonstrate that PQT with Gaussian weight sampling is (3) stable: closely following or even surpassing performance of the BF16 baseline while pre-training GPT2 and Llama2 models with up to 1B parameters and 300B tokens.

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 to introduce the study of algorithms which use predictions parsimoniously. We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of 60.74% on MiniF2F and 21.18% on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attractive for Deep Learning training for two reasons: the range of values it can represent is the same as that of IEEE 754 floating-point format (FP32) and conversion to/from FP32 is simple. Maintaining the same range as FP32 is important to ensure that no hyper-parameter tuning is required for convergence; e.g., IEEE 754 compliant half-precision floating point (FP16) requires hyper-parameter tuning. In this paper, we discuss the flow of tensors and various key operations in mixed precision training, and delve into details of operations, such as the rounding modes for converting FP32 tensors to BFLOAT16. We have implemented a method to emulate BFLOAT16 operations in Tensorflow, Caffe2, IntelCaffe, and Neon for our experiments. Our results show that deep learning training using BFLOAT16 tensors achieves the same state-of-the-art (SOTA) results across domains as FP32 tensors in the same number of iterations and with no changes to hyper-parameters.

As Large Language Models (LLMs) have made significant advancements across various tasks, such as question answering, translation, text summarization, and dialogue systems, the need for accuracy in information becomes crucial, especially for serious financial products serving billions of users like Alipay. To address this, Alipay has developed a Retrieval-Augmented Generation (RAG) system that grounds LLMs on the most accurate and up-to-date information. However, for a real-world product serving millions of users, the inference speed of LLMs becomes a critical factor compared to a mere experimental model. Hence, this paper presents a generic framework for accelerating the inference process, resulting in a substantial increase in speed and cost reduction for our RAG system, with lossless generation accuracy. In the traditional inference process, each token is generated sequentially by the LLM, leading to a time consumption proportional to the number of generated tokens. To enhance this process, our framework, named lookahead, introduces a multi-branch strategy. Instead of generating a single token at a time, we propose a Trie-based Retrieval (TR) process that enables the generation of multiple branches simultaneously, each of which is a sequence of tokens. Subsequently, for each branch, a Verification and Accept (VA) process is performed to identify the longest correct sub-sequence as the final output. Our strategy offers two distinct advantages: (1) it guarantees absolute correctness of the output, avoiding any approximation algorithms, and (2) the worst-case performance of our approach is equivalent to the conventional process. We conduct extensive experiments to demonstrate the significant improvements achieved by applying our inference acceleration framework. Code is avaliable: https://github.com/alipay/PainlessInferenceAcceleration.

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

Quite surprisingly, exact maximum a posteriori (MAP) decoding of neural language generators frequently leads to low-quality results. Rather, most state-of-the-art results on language generation tasks are attained using beam search despite its overwhelmingly high search error rate. This implies that the MAP objective alone does not express the properties we desire in text, which merits the question: if beam search is the answer, what was the question? We frame beam search as the exact solution to a different decoding objective in order to gain insights into why high probability under a model alone may not indicate adequacy. We find that beam search enforces uniform information density in text, a property motivated by cognitive science. We suggest a set of decoding objectives that explicitly enforce this property and find that exact decoding with these objectives alleviates the problems encountered when decoding poorly calibrated language generation models. Additionally, we analyze the text produced using various decoding strategies and see that, in our neural machine translation experiments, the extent to which this property is adhered to strongly correlates with BLEU.

In this paper, we introduce AceMath, a suite of frontier math models that excel in solving complex math problems, along with highly effective reward models capable of evaluating generated solutions and reliably identifying the correct ones. To develop the instruction-tuned math models, we propose a supervised fine-tuning (SFT) process that first achieves competitive performance across general domains, followed by targeted fine-tuning for the math domain using a carefully curated set of prompts and synthetically generated responses. The resulting model, AceMath-72B-Instruct greatly outperforms Qwen2.5-Math-72B-Instruct, GPT-4o and Claude-3.5 Sonnet. To develop math-specialized reward model, we first construct AceMath-RewardBench, a comprehensive and robust benchmark for evaluating math reward models across diverse problems and difficulty levels. After that, we present a systematic approach to build our math reward models. The resulting model, AceMath-72B-RM, consistently outperforms state-of-the-art reward models. Furthermore, when combining AceMath-72B-Instruct with AceMath-72B-RM, we achieve the highest average rm@8 score across the math reasoning benchmarks. We will release model weights, training data, and evaluation benchmarks at: https://research.nvidia.com/labs/adlr/acemath

Serving Large Language Models (LLMs) is critical for AI-powered applications but demands substantial computational resources, particularly in memory bandwidth and computational throughput. Low-precision computation has emerged as a key technique to improve efficiency while reducing resource consumption. Existing approaches for generating low-precision kernels are limited to weight bit widths that are powers of two and suffer from suboptimal performance due to high-level GPU programming abstractions. These abstractions restrict critical optimizations, such as fine-grained register management and optimized memory access patterns, which are essential for efficient low-precision computations. In this paper, we introduce a virtual machine (VM) designed for General-Purpose GPU (GPGPU) computing, enabling support for low-precision data types with arbitrary bit widths while maintaining GPU programmability. The proposed VM features a thread-block-level programming model, a hierarchical memory space, a novel algebraic layout system, and extensive support for diverse low-precision data types. VM programs are compiled into highly efficient GPU programs with automatic vectorization and instruction selection. Extensive experiments demonstrate that our VM efficiently supports a full spectrum of low-precision data types, and outperforms state-of-the-art low-precision kernels on their supported types. Compared to existing compilers like Triton and Ladder, as well as hand-optimized kernels such as QuantLLM and Marlin, our VM achieves performance improvements of 1.75x, 2.61x, 1.29x and 1.03x, respectively.

Large Language Models (LLMs) have proven their exceptional capabilities in performing language-related tasks. However, their deployment poses significant challenges due to their considerable memory and storage requirements. In response to this issue, weight-only quantization, particularly 3 and 4-bit weight-only quantization, has emerged as one of the most viable solutions. As the number of bits decreases, the quantization grid broadens, thus emphasizing the importance of up and down rounding. While previous studies have demonstrated that fine-tuning up and down rounding with the addition of perturbations can enhance accuracy in some scenarios, our study is driven by the precise and limited boundary of these perturbations, where only the threshold for altering the rounding value is of significance. Consequently, we propose a concise and highly effective approach for optimizing the weight rounding task. Our method, named SignRound, involves lightweight block-wise tuning using signed gradient descent, enabling us to achieve outstanding results within 400 steps. SignRound outperforms the established baseline of rounding-to-nearest (RTN) and competes impressively against recent methods, without introducing additional inference overhead. The source code will be publicly available at https://github.com/intel/neural-compressor soon.

The growing demand for Large Language Models (LLMs) in applications such as content generation, intelligent chatbots, and sentiment analysis poses considerable challenges for LLM service providers. To efficiently use GPU resources and boost throughput, batching multiple requests has emerged as a popular paradigm; to further speed up batching, LLM quantization techniques reduce memory consumption and increase computing capacity. However, prevalent quantization schemes (e.g., 8-bit weight-activation quantization) cannot fully leverage the capabilities of modern GPUs, such as 4-bit integer operators, resulting in sub-optimal performance. To maximize LLMs' serving throughput, we introduce Atom, a low-bit quantization method that achieves high throughput improvements with negligible accuracy loss. Atom significantly boosts serving throughput by using low-bit operators and considerably reduces memory consumption via low-bit quantization. It attains high accuracy by applying a novel mixed-precision and fine-grained quantization process. We evaluate Atom on 4-bit weight-activation quantization setups in the serving context. Atom improves end-to-end throughput by up to 7.73times compared to the FP16 and by 2.53times compared to INT8 quantization, while maintaining the same latency target.

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i.e., Quantization-Aware Training (QAT), is still open: for example, a recent study (arXiv:2411.04330v2) put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, which is Pareto-competitive with FP16, i.e., it provides better accuracy at lower model size, while training models with weights and activations in 4-bits or less. Moreover, QuEST allows stable training with 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https://github.com/IST-DASLab/QuEST.

To bridge the ever increasing gap between deep neural networks' complexity and hardware capability, network quantization has attracted more and more research attention. The latest trend of mixed precision quantization takes advantage of hardware's multiple bit-width arithmetic operations to unleash the full potential of network quantization. However, this also results in a difficult integer programming formulation, and forces most existing approaches to use an extremely time-consuming search process even with various relaxations. Instead of solving a problem of the original integer programming, we propose to optimize a proxy metric, the concept of network orthogonality, which is highly correlated with the loss of the integer programming but also easy to optimize with linear programming. This approach reduces the search time and required data amount by orders of magnitude, with little compromise on quantization accuracy. Specifically, we achieve 72.08% Top-1 accuracy on ResNet-18 with 6.7Mb, which does not require any searching iterations. Given the high efficiency and low data dependency of our algorithm, we used it for the post-training quantization, which achieve 71.27% Top-1 accuracy on MobileNetV2 with only 1.5Mb. Our code is available at https://github.com/MAC-AutoML/OMPQ.

Sampling is a basic operation in many inference-time algorithms of large language models (LLMs). To scale up inference efficiently with a limited compute, it is crucial to find an optimal allocation for sample compute budgets: Which sampling configurations (model, temperature, language, etc.) do we use? How many samples do we generate in each configuration? We formulate these choices as a learning problem and propose OSCA, an algorithm that Optimizes Sample Compute Allocation by finding an optimal mix of different inference configurations. Our experiments show that with our learned mixed allocation, we can achieve accuracy better than the best single configuration with 128x less compute on code generation and 25x less compute on 4 reasoning tasks. OSCA is also shown to be effective in agentic workflows beyond single-turn tasks, achieving a better accuracy on SWE-Bench with 3x less compute than the default configuration. Our code and generations are released at https://github.com/LeiLiLab/OSCA.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Instruction fine-tuning (IFT) can increase the informativeness of large language models (LLMs), but may reduce their truthfulness. This trade-off arises because IFT steers LLMs to generate responses containing long-tail knowledge that was not well covered during pre-training. As a result, models become more informative but less accurate when generalizing to unseen tasks. In this paper, we empirically demonstrate how unfamiliar knowledge in IFT datasets can negatively affect the truthfulness of LLMs, and we introduce two new IFT paradigms, UNIT_{cut} and UNIT_{ref}, to address this issue. UNIT_{cut} identifies and removes unfamiliar knowledge from IFT datasets to mitigate its impact on model truthfulness, whereas UNIT_{ref} trains LLMs to recognize their uncertainty and explicitly indicate it at the end of their responses. Our experiments show that UNIT_{cut} substantially improves LLM truthfulness, while UNIT_{ref} maintains high informativeness and reduces hallucinations by distinguishing between confident and uncertain statements.

LLM-based web agents have recently made significant progress, but much of it has occurred in closed-source systems, widening the gap with open-source alternatives. Progress has been held back by two key challenges: first, a narrow focus on single-step tasks that overlooks the complexity of multi-step web interactions; and second, the high compute costs required to post-train LLM-based web agents. To address this, we present the first statistically grounded study on compute allocation for LLM web-agent post-training. Our approach uses a two-stage pipeline, training a Llama 3.1 8B student to imitate a Llama 3.3 70B teacher via supervised fine-tuning (SFT), followed by on-policy reinforcement learning. We find this process highly sensitive to hyperparameter choices, making exhaustive sweeps impractical. To spare others from expensive trial-and-error, we sample 1,370 configurations and use bootstrapping to estimate effective hyperparameters. Our results show that combining SFT with on-policy RL consistently outperforms either approach alone on both WorkArena and MiniWob++. Further, this strategy requires only 55% of the compute to match the peak performance of pure SFT on MiniWob++, effectively pushing the compute-performance Pareto frontier, and is the only strategy that can close the gap with closed-source models.

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, we argue that effective SMoE training remains challenging because of the suboptimal routing process where experts that perform computation do not directly contribute to the routing process. In this work, we propose competition, a novel mechanism to route tokens to experts with the highest neural response. Theoretically, we show that the competition mechanism enjoys a better sample efficiency than the traditional softmax routing. Furthermore, we develop CompeteSMoE, a simple yet effective algorithm to train large language models by deploying a router to learn the competition policy, thus enjoying strong performances at a low training overhead. Our extensive empirical evaluations on both the visual instruction tuning and language pre-training tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies. We have made the implementation available at: https://github.com/Fsoft-AIC/CompeteSMoE. This work is an improved version of the previous study at arXiv:2402.02526

LLM test-time compute (or LLM inference) via search has emerged as a promising research area with rapid developments. However, current frameworks often adopt distinct perspectives on three key aspects (task definition, LLM profiling, and search procedures), making direct comparisons challenging. Moreover, the search algorithms employed often diverge from standard implementations, and their specific characteristics are not thoroughly specified. In this survey, we provide a comprehensive technical review that unifies task definitions and provides modular definitions of LLM profiling and search procedures. The definitions enable precise comparisons of various LLM inference frameworks while highlighting their departures from conventional search algorithms. We also discuss the applicability, performance, and efficiency of these methods. For further details and ongoing updates, please refer to our GitHub repository: https://github.com/xinzhel/LLM-Agent-Survey/blob/main/search.md

Query expansion (QE) enhances retrieval by incorporating relevant terms, with large language models (LLMs) offering an effective alternative to traditional rule-based and statistical methods. However, LLM-based QE suffers from a fundamental limitation: it often fails to generate relevant knowledge, degrading search performance. Prior studies have focused on hallucination, yet its underlying cause--LLM knowledge deficiencies--remains underexplored. This paper systematically examines two failure cases in LLM-based QE: (1) when the LLM lacks query knowledge, leading to incorrect expansions, and (2) when the query is ambiguous, causing biased refinements that narrow search coverage. We conduct controlled experiments across multiple datasets, evaluating the effects of knowledge and query ambiguity on retrieval performance using sparse and dense retrieval models. Our results reveal that LLM-based QE can significantly degrade the retrieval effectiveness when knowledge in the LLM is insufficient or query ambiguity is high. We introduce a framework for evaluating QE under these conditions, providing insights into the limitations of LLM-based retrieval augmentation.

Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current models are constrained by limitations in handling long texts and reinforcement learning (RL) training efficiency. To address these issues, we propose a simple yet effective test-time scaling approach Multi-round Thinking. This method iteratively refines model reasoning by leveraging previous answers as prompts for subsequent rounds. Extensive experiments across multiple models, including QwQ-32B and DeepSeek-R1, consistently show performance improvements on various benchmarks such as AIME 2024, MATH-500, GPQA-diamond, and LiveCodeBench. For instance, the accuracy of QwQ-32B improved from 80.3% (Round 1) to 82.1% (Round 2) on the AIME 2024 dataset, while DeepSeek-R1 showed a similar increase from 79.7% to 82.0%. These results confirm that Multi-round Thinking is a broadly applicable, straightforward approach to achieving stable enhancements in model performance, underscoring its potential for future developments in test-time scaling techniques. The key prompt: {Original question prompt} The assistant's previous answer is: <answer> {last round answer} </answer>, and please re-answer.

Recent advancements in large language models (LLMs) have shifted focus toward scaling inference-time compute, improving performance without retraining the model. A common approach is to sample multiple outputs in parallel, and select one of these as the final output. However, work to date has focused on English and a handful of domains such as math and code. In contrast, we are most interested in techniques that generalize across open-ended tasks, formally verifiable tasks, and across languages. In this work, we study how to robustly scale inference-time compute for open-ended generative tasks in a multilingual, multi-task setting. Our findings show that both sampling strategy based on temperature variation and selection strategy must be adapted to account for diverse domains and varied language settings. We evaluate existing selection methods, revealing that strategies effective in English often fail to generalize across languages. We propose novel sampling and selection strategies specifically adapted for multilingual and multi-task inference scenarios, and show they yield notable gains across languages and tasks. In particular, our combined sampling and selection methods lead to an average +6.8 jump in win-rates for our 8B models on m-ArenaHard-v2.0 prompts, against proprietary models such as Gemini. At larger scale, Command-A (111B model) equipped with our methods, shows +9.0 improvement in win-rates on the same benchmark with just five samples against single-sample decoding, a substantial increase at minimal cost. Our results underscore the need for language- and task-aware approaches to inference-time compute, aiming to democratize performance improvements in underrepresented languages.

We introduce BM25S, an efficient Python-based implementation of BM25 that only depends on Numpy and Scipy. BM25S achieves up to a 500x speedup compared to the most popular Python-based framework by eagerly computing BM25 scores during indexing and storing them into sparse matrices. It also achieves considerable speedups compared to highly optimized Java-based implementations, which are used by popular commercial products. Finally, BM25S reproduces the exact implementation of five BM25 variants based on Kamphuis et al. (2020) by extending eager scoring to non-sparse variants using a novel score shifting method. The code can be found at https://github.com/xhluca/bm25s

In the era of large language models, Mixture-of-Experts (MoE) is a promising architecture for managing computational costs when scaling up model parameters. However, conventional MoE architectures like GShard, which activate the top-K out of N experts, face challenges in ensuring expert specialization, i.e. each expert acquires non-overlapping and focused knowledge. In response, we propose the DeepSeekMoE architecture towards ultimate expert specialization. It involves two principal strategies: (1) finely segmenting the experts into mN ones and activating mK from them, allowing for a more flexible combination of activated experts; (2) isolating K_s experts as shared ones, aiming at capturing common knowledge and mitigating redundancy in routed experts. Starting from a modest scale with 2B parameters, we demonstrate that DeepSeekMoE 2B achieves comparable performance with GShard 2.9B, which has 1.5 times the expert parameters and computation. In addition, DeepSeekMoE 2B nearly approaches the performance of its dense counterpart with the same number of total parameters, which set the upper bound of MoE models. Subsequently, we scale up DeepSeekMoE to 16B parameters and show that it achieves comparable performance with LLaMA2 7B, with only about 40% of computations. Further, our preliminary efforts to scale up DeepSeekMoE to 145B parameters consistently validate its substantial advantages over the GShard architecture, and show its performance comparable with DeepSeek 67B, using only 28.5% (maybe even 18.2%) of computations.

Test-Time Scaling (TTS) improves the reasoning performance of Large Language Models (LLMs) by allocating additional compute during inference. We conduct a structured survey of TTS methods and categorize them into sampling-based, search-based, and trajectory optimization strategies. We observe that reasoning-optimized models often produce less diverse outputs, which limits TTS effectiveness. To address this, we propose ADAPT (A Diversity Aware Prefix fine-Tuning), a lightweight method that applies prefix tuning with a diversity-focused data strategy. Experiments on mathematical reasoning tasks show that ADAPT reaches 80% accuracy using eight times less compute than strong baselines. Our findings highlight the essential role of generative diversity in maximizing TTS effectiveness.

Large Language Models (LLMs) have emerged as powerful tools for addressing modern challenges and enabling practical applications. However, their computational expense remains a significant barrier to widespread adoption. Quantization has emerged as a promising technique to democratize access and enable low resource device deployment. Despite these advancements, the safety and trustworthiness of quantized models remain underexplored, as prior studies often overlook contemporary architectures and rely on overly simplistic benchmarks and evaluations. To address this gap, we introduce OpenSafetyMini, a novel open-ended safety dataset designed to better distinguish between models. We evaluate 4 state-of-the-art quantization techniques across LLaMA and Mistral models using 4 benchmarks, including human evaluations. Our findings reveal that the optimal quantization method varies for 4-bit precision, while vector quantization techniques deliver the best safety and trustworthiness performance at 2-bit precision, providing foundation for future research.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

The hallucinations of large language models (LLMs) are increasingly mitigated by allowing LLMs to search for information and to ground their answers in real sources. Unfortunately, LLMs often struggle with posing the right search queries, especially when dealing with complex or otherwise indirect topics. Observing that LLMs can learn to search for relevant facts by trying different queries and learning to up-weight queries that successfully produce relevant results, we introduce Learning to Retrieve by Trying (LeReT), a reinforcement learning framework that explores search queries and uses preference-based optimization to improve their quality. LeReT can improve the absolute retrieval accuracy by up to 29% and the downstream generator evaluations by 17%. The simplicity and flexibility of LeReT allows it to be applied to arbitrary off-the-shelf retrievers and makes it a promising technique for improving general LLM pipelines. Project website: http://sherylhsu.com/LeReT/.

Machine learning models have recently found tremendous success in data-driven control systems. However, standard learning models often suffer from an accuracy-robustness trade-off, which is a limitation that must be overcome in the control of safety-critical systems that require both high performance and rigorous robustness guarantees. In this work, we build upon the recent "locally biased smoothing" method to develop classifiers that simultaneously inherit high accuracy from standard models and high robustness from robust models. Specifically, we extend locally biased smoothing to the multi-class setting, and then overcome its performance bottleneck by generalizing the formulation to "mix" the outputs of a standard neural network and a robust neural network. We prove that when the robustness of the robust base model is certifiable, within a closed-form ell_p radius, no alteration or attack on an input can result in misclassification of the mixed classifier; the proposed model inherits the certified robustness. Moreover, we use numerical experiments on the CIFAR-10 benchmark dataset to verify that the mixed model noticeably improves the accuracy-robustness trade-off.

We present BabyLlama-2, a 345 million parameter model distillation-pretrained from two teachers on a 10 million word corpus for the BabyLM competition. On BLiMP and SuperGLUE benchmarks, BabyLlama-2 outperforms baselines trained on both 10 and 100 million word datasets with the same data mix, as well as its teacher models. Through an extensive hyperparameter sweep, we demonstrate that the advantages of distillation cannot be attributed to suboptimal hyperparameter selection of the teachers. Our findings underscore the need for further investigation into distillation techniques, particularly in data-limited settings.

We investigate continued pretraining of LLMs for language adaptation on a tight academic budget: a setting in which only a few GPUs can be used in parallel, for a heavily constrained duration. We focus on adapting Mistral-7B to German or Arabic and evaluate several techniques to improve efficiency and effectiveness in this setting. Our German models adapted on this tight compute budget underperform compared to the base Mistral-7B, while our Arabic models outperform several baselines, showing that for sufficiently well-represented languages, continued pretraining for specialization is not always helpful. Our main findings focus on training precision and tokenizer swapping. Our results show that pure bfloat16 training is a viable alternative to mixed-precision training, while being much faster when only using a few GPUs. Swapping the tokenizer for a specialized one yields more efficient tokenization and is competitive with the original tokenizer, which already contains some German tokens, but did not significantly increase performance for German. Code and model weights are available at on GitHub.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

We study both stream-based and pool-based active learning with neural network approximations. A recent line of works proposed bandit-based approaches that transformed active learning into a bandit problem, achieving both theoretical and empirical success. However, the performance and computational costs of these methods may be susceptible to the number of classes, denoted as K, due to this transformation. Therefore, this paper seeks to answer the question: "How can we mitigate the adverse impacts of K while retaining the advantages of principled exploration and provable performance guarantees in active learning?" To tackle this challenge, we propose two algorithms based on the newly designed exploitation and exploration neural networks for stream-based and pool-based active learning. Subsequently, we provide theoretical performance guarantees for both algorithms in a non-parametric setting, demonstrating a slower error-growth rate concerning K for the proposed approaches. We use extensive experiments to evaluate the proposed algorithms, which consistently outperform state-of-the-art baselines.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

Post-training Quantization (PTQ) technique has been extensively adopted for large language models (LLMs) compression owing to its efficiency and low resource requirement. However, current research lacks a in-depth analysis of the superior and applicable scenarios of each PTQ strategy. In addition, existing algorithms focus primarily on performance, overlooking the trade-off among model size, performance, and quantization bitwidth. To mitigate these confusions, we provide a novel benchmark for LLMs PTQ in this paper. Firstly, in order to support our benchmark, we propose a comprehensive taxonomy for existing mainstream methods by scrutinizing their computational strategies (e.g., optimization-based, compensation-based, etc.). Then, we conduct extensive experiments with the baseline within each class, covering models with various sizes (7B-70B), bitwidths, training levels (LLaMA1/2/3/3.1), architectures (Mixtral, DeepSeekMoE and Mamba) and modality (LLaVA1.5 and VILA1.5) on a wide range of evaluation metrics.Through comparative analysis on the results, we summarize the superior of each PTQ strategy and modelsize-bitwidth trade-off considering the performance. For example, our benchmark reveals that compensation-based technique demonstrates outstanding cross-architecture robustness and extremely low-bit PTQ for ultra large models should be reexamined. Finally, we further accordingly claim that a practical combination of compensation and other PTQ strategy can achieve SOTA various robustness. We believe that our benchmark will provide valuable recommendations for the deployment of LLMs and future research on PTQ approaches.

We present SmolTulu-1.7b-Instruct, referenced in this report as SmolTulu-DPO-1130, an instruction-tuned language model that adapts AllenAI's Tulu 3 post-training pipeline to enhance Huggingface's SmolLM2-1.7B base model. Through comprehensive empirical analysis using a 135M parameter model, we demonstrate that the relationship between learning rate and batch size significantly impacts model performance in a task-dependent manner. Our findings reveal a clear split: reasoning tasks like ARC and GSM8K benefit from higher learning rate to batch size ratios, while pattern recognition tasks such as HellaSwag and IFEval show optimal performance with lower ratios. These insights informed the development of SmolTulu, which achieves state-of-the-art performance among sub-2B parameter models on instruction following, scoring 67.7% on IFEval (Delta11%), and mathematical reasoning with 51.6% on GSM8K (Delta3.4%), with an alternate version achieving scoring 57.1% on ARC (Delta5.4%). We release our model, training recipes, and ablation studies to facilitate further research in efficient model alignment, demonstrating that careful adaptation of optimization dynamics can help bridge the capability gap between small and large language models.

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods only compare model outputs to ground-truth answers, obscuring insights into reasoning processes. To address these limitations, we introduce GSM-Ranges, a dataset generator derived from GSM8K that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales. Additionally, we propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy. Our experiments with various models reveal a significant increase in logical error rates-up to 14 percentage points-as numerical complexity rises, demonstrating a general weakness in reasoning with out-of-distribution numerical values. Moreover, while models demonstrate high accuracy on standalone arithmetic tasks, their performance deteriorates substantially when computations are embedded within word problems. These findings provide a comprehensive evaluation of LLMs' mathematical reasoning capabilities and inform future research directions for improving numerical generalization in language models.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Solving Mixed-Integer Programming (MIP) problems often requires substantial computational resources due to their combinatorial nature. Parallelization has emerged as a critical strategy to accelerate solution times and enhance scalability to tackle large, complex instances. This paper investigates the parallelization capabilities of Balans, a recently proposed multi-armed bandits-based adaptive large neighborhood search for MIPs. While Balans's modular architecture inherently supports parallel exploration of diverse parameter configurations, this potential has not been thoroughly examined. To address this gap, we introduce ParBalans, an extension that leverages both solver-level and algorithmic-level parallelism to improve performance on challenging MIP instances. Our experimental results demonstrate that ParBalans exhibits competitive performance compared to the state-of-the-art commercial solver Gurobi, particularly on hard optimization benchmarks.

Large language models (LLMs) excel in natural language generation but often confidently produce incorrect responses, especially in tasks like mathematical reasoning. Chain-of-thought prompting, self-verification, and multi-agent debate are among the strategies proposed to improve the reasoning and factual accuracy of LLMs. Building on Du et al.'s multi-agent debate framework, we find that multi-agent debate helps at any model scale, and that diversity of thought elicits stronger reasoning in debating LLMs. Across various model sizes, performance on mathematical reasoning tasks benefits most when diverse trained models are used. Remarkably, after 4 rounds of debate, a diverse set of medium-capacity models (Gemini-Pro, Mixtral 7BX8, and PaLM 2-M) outperforms GPT-4 on the GSM-8K benchmark, scoring 91% accuracy. By comparison, when 3 instances of Gemini-Pro are used, performance only reaches 82%. Finally, this diverse set of medium-capacity models sets a new state-of-the-art performance on the ASDiv benchmark (94%). These results underscore the idea that the future of AI is agentic, with diverse cooperating agents yielding emergent capabilities beyond even the most powerful individual models.

We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of widetilde O(|S||A|t_{mix}^2 epsilon^{-2}) and a lower bound of Omega(|S||A|t_{mix} epsilon^{-2}). In these expressions, |S| and |A| denote the cardinalities of the state and action spaces respectively, t_{mix} serves as a uniform upper limit for the total variation mixing times, and epsilon signifies the error tolerance. Therefore, a notable gap of t_{mix} still remains to be bridged. Our primary contribution is the development of an estimator for the optimal policy of average reward MDPs with a sample complexity of widetilde O(|S||A|t_{mix}epsilon^{-2}). This marks the first algorithm and analysis to reach the literature's lower bound. Our new algorithm draws inspiration from ideas in Li et al. (2020), Jin and Sidford (2021), and Wang et al. (2023). Additionally, we conduct numerical experiments to validate our theoretical findings.

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

In this report, we present the third technical report on the development of slow-thinking models as part of the STILL project. As the technical pathway becomes clearer, scaling RL training has become a central technique for implementing such reasoning models. We systematically experiment with and document the effects of various factors influencing RL training, conducting experiments on both base models and fine-tuned models. Specifically, we demonstrate that our RL training approach consistently improves the Qwen2.5-32B base models, enhancing both response length and test accuracy. Furthermore, we show that even when a model like DeepSeek-R1-Distill-Qwen-1.5B has already achieved a high performance level, it can be further refined through RL training, reaching an accuracy of 39.33% on AIME 2024. Beyond RL training, we also explore the use of tool manipulation, finding that it significantly boosts the reasoning performance of large reasoning models. This approach achieves a remarkable accuracy of 86.67% with greedy search on AIME 2024, underscoring its effectiveness in enhancing model capabilities. We release our resources at the STILL project website: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose (1+epsilon)-th moment is bounded for some epsilonin (0,1]. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of O(dT^{1{1+epsilon}}), where d is the dimension of contextual information and T is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only O(log T) rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when epsilon=1. Numerical experimental results confirm the merits of our algorithms.

Despite the rapid progress in the capabilities of Large Language Models (LLMs), they continue to have difficulty following relatively simple, unambiguous instructions, especially when compositions are involved. In this paper, we take inspiration from recent work that suggests that models may follow instructions better when they are expressed in pseudo-code. However, writing pseudo-code programs can be tedious and using few-shot demonstrations to craft code representations for use in inference can be unnatural for non-expert users of LLMs. To overcome these limitations, we propose fine-tuning LLMs with instruction-tuning data that additionally includes instructions re-expressed in pseudo-code along with the final response. We evaluate models trained using our method on 11 publicly available benchmarks comprising of tasks related to instruction-following, mathematics, and common-sense reasoning. We conduct rigorous experiments with 5 different models and find that not only do models follow instructions better when trained with pseudo-code, they also retain their capabilities on the other tasks related to mathematical and common sense reasoning. Specifically, we observe a relative gain of 3--19% on instruction-following benchmark, and an average gain of upto 14% across all tasks.

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of density ratio modeling, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show -- perhaps surprisingly -- that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as coverability (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2022) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various down-stream tasks. Traditional fine-tuning methods such as stochastic gradient descent and Adam optimization require backpropagation, which are error-prone in the low-precision settings. To overcome these limitations, we propose the Quantized Zeroth-Order (QuZO) framework, specifically designed for fine-tuning LLMs through low-precision (e.g., 4- or 8-bit) forward passes. Our method can avoid the error-prone low-precision straight-through estimator, and utilizes optimized stochastic rounding to mitigate the increased bias. QuZO simplifies the training process, while achieving results comparable to first-order methods in {rm FP}8 and superior accuracy in {rm INT}8 and {rm INT}4 training. Experiments demonstrate that low-bit training QuZO achieves performance comparable to MeZO optimization on GLUE, Multi-Choice, and Generation tasks, while reducing memory cost by 2.94 times in LLaMA2-7B fine-tuning compared to quantized first-order methods.

Despite their remarkable capabilities, Large Language Models (LLMs) are found to be surprisingly sensitive to minor variations in prompts, often generating significantly divergent outputs in response to minor variations in the prompts, such as spelling errors, alteration of wording or the prompt template. However, while assessing the quality of an LLM, the focus often tends to be solely on its performance on downstream tasks, while very little to no attention is paid to prompt sensitivity. To fill this gap, we propose POSIX - a novel PrOmpt Sensitivity IndeX as a reliable measure of prompt sensitivity, thereby offering a more comprehensive evaluation of LLM performance. The key idea behind POSIX is to capture the relative change in loglikelihood of a given response upon replacing the corresponding prompt with a different intent-preserving prompt. We provide thorough empirical evidence demonstrating the efficacy of POSIX in capturing prompt sensitivity and subsequently use it to measure and thereby compare prompt sensitivity of various open-source LLMs. We find that merely increasing the parameter count or instruction tuning does not necessarily reduce prompt sensitivity whereas adding some few-shot exemplars, even just one, almost always leads to significant decrease in prompt sensitivity. We also find that alterations to prompt template lead to the highest sensitivity in the case of MCQ type tasks, whereas paraphrasing results in the highest sensitivity in open-ended generation tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/POSIX.

Since the release of T\"ULU [Wang et al., 2023b], open resources for instruction tuning have developed quickly, from better base models to new finetuning techniques. We test and incorporate a number of these advances into T\"ULU, resulting in T\"ULU 2, a suite of improved T\"ULU models for advancing the understanding and best practices of adapting pretrained language models to downstream tasks and user preferences. Concretely, we release: (1) T\"ULU-V2-mix, an improved collection of high-quality instruction datasets; (2) T\"ULU 2, LLAMA-2 models finetuned on the V2 mixture; (3) T\"ULU 2+DPO, T\"ULU 2 models trained with direct preference optimization (DPO), including the largest DPO-trained model to date (T\"ULU 2+DPO 70B); (4) CODE T\"ULU 2, CODE LLAMA models finetuned on our V2 mix that outperform CODE LLAMA and its instruction-tuned variant, CODE LLAMA-Instruct. Our evaluation from multiple perspectives shows that the T\"ULU 2 suite achieves state-of-the-art performance among open models and matches or exceeds the performance of GPT-3.5-turbo-0301 on several benchmarks. We release all the checkpoints, data, training and evaluation code to facilitate future open efforts on adapting large language models.

A practical approach to activate long chain-of-thoughts reasoning ability in pre-trained large language models is to perform supervised fine-tuning on instruction datasets synthesized by strong Large Reasoning Models such as DeepSeek-R1, offering a cost-effective alternative to reinforcement learning. However, large-scale instruction sets with more than 100k samples incur significant training overhead, while effective strategies for automatic long-CoT instruction selection still remain unexplored. In this work, we propose Select2Reason, a novel and efficient instruction-tuning data selection framework for long-CoT reasoning. From the perspective of emergence of rethinking behaviors like self-correction and backtracking, we investigate common metrics that may determine the quality of long-CoT reasoning instructions. Select2Reason leverages a quantifier to estimate difficulty of question and jointly incorporates a reasoning trace length-based heuristic through a weighted scheme for ranking to prioritize high-utility examples. Empirical results on OpenR1-Math-220k demonstrate that fine-tuning LLM on only 10% of the data selected by Select2Reason achieves performance competitive with or superior to full-data tuning and open-source baseline OpenR1-Qwen-7B across three competition-level and six comprehensive mathematical benchmarks. Further experiments highlight the scalability in varying data size, efficiency during inference, and its adaptability to other instruction pools with minimal cost.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. With an inference budget of 64 generations, VGS with DeepSeek-R1-Distill-1.5B achieves an average accuracy of 45.7% across four competition math benchmarks (AIME 2024 & 2025, HMMT Feb 2024 & 2025), reaching parity with o3-mini-medium. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced.

Summarization models often generate text that is poorly calibrated to quality metrics because they are trained to maximize the likelihood of a single reference (MLE). To address this, recent work has added a calibration step, which exposes a model to its own ranked outputs to improve relevance or, in a separate line of work, contrasts positive and negative sets to improve faithfulness. While effective, much of this work has focused on how to generate and optimize these sets. Less is known about why one setup is more effective than another. In this work, we uncover the underlying characteristics of effective sets. For each training instance, we form a large, diverse pool of candidates and systematically vary the subsets used for calibration fine-tuning. Each selection strategy targets distinct aspects of the sets, such as lexical diversity or the size of the gap between positive and negatives. On three diverse scientific long-form summarization datasets (spanning biomedical, clinical, and chemical domains), we find, among others, that faithfulness calibration is optimal when the negative sets are extractive and more likely to be generated, whereas for relevance calibration, the metric margin between candidates should be maximized and surprise--the disagreement between model and metric defined candidate rankings--minimized. Code to create, select, and optimize calibration sets is available at https://github.com/griff4692/calibrating-summaries

Large language models are usually fine-tuned to align with human preferences. However, fine-tuning a large language model can be challenging. In this work, we introduce weak-to-strong search, framing the alignment of a large language model as a test-time greedy search to maximize the log-likelihood difference between small tuned and untuned models while sampling from the frozen large model. This method serves both as (i) a compute-efficient model up-scaling strategy that avoids directly tuning the large model and as (ii) an instance of weak-to-strong generalization that enhances a strong model with weak test-time guidance. Empirically, we demonstrate the flexibility of weak-to-strong search across different tasks. In controlled-sentiment generation and summarization, we use tuned and untuned gpt2s to effectively improve the alignment of large models without additional training. Crucially, in a more difficult instruction-following benchmark, AlpacaEval 2.0, we show that reusing off-the-shelf small model pairs (e.g., zephyr-7b-beta and its untuned version) can significantly improve the length-controlled win rates of both white-box and black-box large models against gpt-4-turbo (e.g., 34.4 rightarrow 37.9 for Llama-3-70B-Instruct and 16.0 rightarrow 20.1 for gpt-3.5-turbo-instruct), despite the small models' low win rates approx 10.0.

Aligned Large Language Models (LLMs) showcase remarkable versatility, capable of handling diverse real-world tasks. Meanwhile, aligned LLMs are also expected to exhibit speciality, excelling in specific applications. However, fine-tuning with extra data, a common practice to gain speciality, often leads to catastrophic forgetting (CF) of previously acquired versatility, hindering the model's performance across diverse tasks. In response to this challenge, we propose CoFiTune, a coarse to fine framework in an attempt to strike the balance between speciality and versatility. At the coarse-grained level, an empirical tree-search algorithm is utilized to pinpoint and update specific modules that are crucial for speciality, while keeping other parameters frozen; at the fine-grained level, a soft-masking mechanism regulates the update to the LLMs, mitigating the CF issue without harming speciality. In an overall evaluation of both speciality and versatility, CoFiTune consistently outperforms baseline methods across diverse tasks and model scales. Compared to the full-parameter SFT, CoFiTune leads to about 14% versatility improvement and marginal speciality loss on a 13B model. Lastly, based on further analysis, we provide a speculative insight into the information forwarding process in LLMs, which helps explain the effectiveness of the proposed method. The code is available at https://github.com/rattlesnakey/CoFiTune.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Large language models (LLMs) demand substantial computational and memory resources, creating deployment challenges. Quantization-aware training (QAT) addresses these challenges by reducing model precision while maintaining performance. However, the scaling behavior of QAT, especially at 4-bit precision (W4A4), is not well understood. Existing QAT scaling laws often ignore key factors such as the number of training tokens and quantization granularity, which limits their applicability. This paper proposes a unified scaling law for QAT that models quantization error as a function of model size, training data volume, and quantization group size. Through 268 QAT experiments, we show that quantization error decreases as model size increases, but rises with more training tokens and coarser quantization granularity. To identify the sources of W4A4 quantization error, we decompose it into weight and activation components. Both components follow the overall trend of W4A4 quantization error, but with different sensitivities. Specifically, weight quantization error increases more rapidly with more training tokens. Further analysis shows that the activation quantization error in the FC2 layer, caused by outliers, is the primary bottleneck of W4A4 QAT quantization error. By applying mixed-precision quantization to address this bottleneck, we demonstrate that weight and activation quantization errors can converge to similar levels. Additionally, with more training data, weight quantization error eventually exceeds activation quantization error, suggesting that reducing weight quantization error is also important in such scenarios. These findings offer key insights for improving QAT research and development.

Learned sparse retrieval systems aim to combine the effectiveness of contextualized language models with the scalability of conventional data structures such as inverted indexes. Nevertheless, the indexes generated by these systems exhibit significant deviations from the ones that use traditional retrieval models, leading to a discrepancy in the performance of existing query optimizations that were specifically developed for traditional structures. These disparities arise from structural variations in query and document statistics, including sub-word tokenization, leading to longer queries, smaller vocabularies, and different score distributions within posting lists. This paper introduces Block-Max Pruning (BMP), an innovative dynamic pruning strategy tailored for indexes arising in learned sparse retrieval environments. BMP employs a block filtering mechanism to divide the document space into small, consecutive document ranges, which are then aggregated and sorted on the fly, and fully processed only as necessary, guided by a defined safe early termination criterion or based on approximate retrieval requirements. Through rigorous experimentation, we show that BMP substantially outperforms existing dynamic pruning strategies, offering unparalleled efficiency in safe retrieval contexts and improved tradeoffs between precision and efficiency in approximate retrieval tasks.

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.

With LLMs shifting their role from statistical modeling of language to serving as general-purpose AI agents, how should LLM evaluations change? Arguably, a key ability of an AI agent is to flexibly combine, as needed, the basic skills it has learned. The capability to combine skills plays an important role in (human) pedagogy and also in a paper on emergence phenomena (Arora & Goyal, 2023). This work introduces Skill-Mix, a new evaluation to measure ability to combine skills. Using a list of N skills the evaluator repeatedly picks random subsets of k skills and asks the LLM to produce text combining that subset of skills. Since the number of subsets grows like N^k, for even modest k this evaluation will, with high probability, require the LLM to produce text significantly different from any text in the training set. The paper develops a methodology for (a) designing and administering such an evaluation, and (b) automatic grading (plus spot-checking by humans) of the results using GPT-4 as well as the open LLaMA-2 70B model. Administering a version of to popular chatbots gave results that, while generally in line with prior expectations, contained surprises. Sizeable differences exist among model capabilities that are not captured by their ranking on popular LLM leaderboards ("cramming for the leaderboard"). Furthermore, simple probability calculations indicate that GPT-4's reasonable performance on k=5 is suggestive of going beyond "stochastic parrot" behavior (Bender et al., 2021), i.e., it combines skills in ways that it had not seen during training. We sketch how the methodology can lead to a Skill-Mix based eco-system of open evaluations for AI capabilities of future models.

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

This study introduces Query Attribute Modeling (QAM), a hybrid framework that enhances search precision and relevance by decomposing open text queries into structured metadata tags and semantic elements. QAM addresses traditional search limitations by automatically extracting metadata filters from free-form text queries, reducing noise and enabling focused retrieval of relevant items. Experimental evaluation using the Amazon Toys Reviews dataset (10,000 unique items with 40,000+ reviews and detailed product attributes) demonstrated QAM's superior performance, achieving a mean average precision at 5 (mAP@5) of 52.99\%. This represents significant improvement over conventional methods, including BM25 keyword search, encoder-based semantic similarity search, cross-encoder re-ranking, and hybrid search combining BM25 and semantic results via Reciprocal Rank Fusion (RRF). The results establish QAM as a robust solution for Enterprise Search applications, particularly in e-commerce systems.

Current mathematical reasoning benchmarks for large language models (LLMs) are approaching saturation, with some achieving > 90% accuracy, and are increasingly compromised by training-set contamination. We introduce Putnam-AXIOM, a benchmark of 522 university-level competition problems drawn from the prestigious William Lowell Putnam Mathematical Competition, and Putnam-AXIOM Variation, an unseen companion set of 100 functional variants generated by programmatically perturbing variables and constants. The variation protocol produces an unlimited stream of equally difficult, unseen instances -- yielding a contamination-resilient test bed. On the Original set, OpenAI's o1-preview -- the strongest evaluated model -- scores 41.9%, but its accuracy drops by 19.6% (46.8% relative decrease) on the paired Variations. The remaining eighteen models show the same downward trend, ten of them with non-overlapping 95% confidence intervals. These gaps suggest memorization and highlight the necessity of dynamic benchmarks. We complement "boxed" accuracy with Teacher-Forced Accuracy (TFA), a lightweight metric that directly scores reasoning traces and automates natural language proof evaluations. Putnam-AXIOM therefore provides a rigorous, contamination-resilient evaluation framework for assessing advanced mathematical reasoning of LLMs. Data and evaluation code are publicly available at https://github.com/brando90/putnam-axiom.

As inference on Large Language Models (LLMs) emerges as an important workload in machine learning applications, weight quantization has become a standard technique for efficient GPU deployment. Quantization not only reduces model size, but has also been shown to yield substantial speedups for single-user inference, due to reduced memory movement, with low accuracy impact. Yet, it remains open whether speedups are achievable also in batched settings with multiple parallel clients, which are highly relevant for practical serving. It is unclear whether GPU kernels can be designed to remain practically memory-bound, while supporting the substantially increased compute requirements of batched workloads. This paper resolves this question positively by describing the design of Mixed-precision Auto-Regressive LINear kernels, called MARLIN. Concretely, given a model whose weights are compressed via quantization to, e.g., 4 bits per element, MARLIN shows that batchsizes up to 16-32 can be supported with close to maximum (4times) quantization speedup, and larger batchsizes up to 64-128 with gradually decreasing, but still significant, acceleration. MARLIN accomplishes this via a combination of techniques, such as asynchronous memory access, complex task scheduling and pipelining, and bespoke quantization support. Our experiments show that MARLIN's near-optimal performance on individual LLM layers across different scenarios can also lead to end-to-end LLM inference speedups (of up to 2.8times) when integrated with the popular vLLM serving engine. Finally, MARLIN is extensible to further compression techniques, like NVIDIA 2:4 sparsity, leading to additional speedups.

Retrieval-augmented language models (RALMs) improve performance by accessing long-tail and up-to-date knowledge from external data stores, but are challenging to build. Existing approaches require either expensive retrieval-specific modifications to LM pre-training or use post-hoc integration of the data store that leads to suboptimal performance. We introduce Retrieval-Augmented Dual Instruction Tuning (RA-DIT), a lightweight fine-tuning methodology that provides a third option by retrofitting any LLM with retrieval capabilities. Our approach operates in two distinct fine-tuning steps: (1) one updates a pre-trained LM to better use retrieved information, while (2) the other updates the retriever to return more relevant results, as preferred by the LM. By fine-tuning over tasks that require both knowledge utilization and contextual awareness, we demonstrate that each stage yields significant performance improvements, and using both leads to additional gains. Our best model, RA-DIT 65B, achieves state-of-the-art performance across a range of knowledge-intensive zero- and few-shot learning benchmarks, significantly outperforming existing in-context RALM approaches by up to +8.9% in 0-shot setting and +1.4% in 5-shot setting on average.

We introduce SealQA, a new challenge benchmark for evaluating SEarch-Augmented Language models on fact-seeking questions where web search yields conflicting, noisy, or unhelpful results. SealQA comes in three flavors: (1) Seal-0 (main) and (2) Seal-Hard, which assess factual accuracy and reasoning capabilities, with Seal-0 focusing on the most challenging questions where chat models (e.g., GPT-4.1) typically achieve near-zero accuracy; and (3) LongSeal, which extends SealQA to test long-context, multi-document reasoning in "needle-in-a-haystack" settings. Our evaluation reveals critical limitations in current models: Even frontier LLMs perform poorly across all SealQA flavors. On Seal-0, frontier agentic models equipped with tools like o3 and o4-mini achieve only 17.1% and 6.3% accuracy, respectively, at their best reasoning efforts. We find that advanced reasoning models such as DeepSeek-R1-671B and o3-mini are highly vulnerable to noisy search results. Notably, increasing test-time compute does not yield reliable gains across o3-mini, o4-mini, and o3, with performance often plateauing or even declining early. Additionally, while recent models are less affected by the "lost-in-the-middle" issue, they still fail to reliably identify relevant documents in LongSeal when faced with numerous distractors. To facilitate future work, we release SealQA at huggingface.co/datasets/vtllms/sealqa.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

When provided with sufficient explanatory context, smaller Language Models have been shown to exhibit strong reasoning ability on challenging short-answer question-answering tasks where the questions are unseen in training. We evaluate two methods for further improvement in this setting. Both methods focus on combining rationales generated by a larger Language Model with longer contexts created from a multi-hop dense retrieval system. The first method (RR) involves training a Rationale Ranking model to score both generated rationales and retrieved contexts with respect to relevance and truthfulness. We then use the scores to derive combined contexts from both knowledge sources using a number of combinatory strategies. For the second method (RATD) we utilise retrieval-augmented training datasets developed by Hartill et al. 2023 to train a smaller Reasoning model such that it becomes proficient at utilising relevant information from longer text sequences that may be only partially evidential and frequently contain many irrelevant sentences. We find that both methods significantly improve results. Our single best Reasoning model materially improves upon strong comparable prior baselines for unseen evaluation datasets (StrategyQA 58.9 rightarrow 61.7 acc., CommonsenseQA 63.6 rightarrow 72.7 acc., ARC-DA 31.6 rightarrow 52.1 F1, IIRC 25.5 rightarrow 27.3 F1) and a version utilising our prior knowledge of each type of question in selecting a context combination strategy does even better. Our proposed models also generally outperform direct prompts against much larger models (BLOOM 175B and StableVicuna 13B) in both few-shot chain-of-thought and standard few-shot settings.

Production-grade LLM systems require robust adherence to dozens or even hundreds of instructions simultaneously. However, the instruction-following capabilities of LLMs at high instruction densities have not yet been characterized, as existing benchmarks only evaluate models on tasks with a single or few instructions. We introduce IFScale, a simple benchmark of 500 keyword-inclusion instructions for a business report writing task to measure how instruction-following performance degrades as instruction density increases. We evaluate 20 state-of-the-art models across seven major providers and find that even the best frontier models only achieve 68% accuracy at the max density of 500 instructions. Our analysis reveals model size and reasoning capability to correlate with 3 distinct performance degradation patterns, bias towards earlier instructions, and distinct categories of instruction-following errors. Our insights can help inform design of instruction-dense prompts in real-world applications and highlight important performance-latency tradeoffs. We open-source the benchmark and all results for further analysis at https://distylai.github.io/IFScale.

We present NUPunkt and CharBoundary, two sentence boundary detection libraries optimized for high-precision, high-throughput processing of legal text in large-scale applications such as due diligence, e-discovery, and legal research. These libraries address the critical challenges posed by legal documents containing specialized citations, abbreviations, and complex sentence structures that confound general-purpose sentence boundary detectors. Our experimental evaluation on five diverse legal datasets comprising over 25,000 documents and 197,000 annotated sentence boundaries demonstrates that NUPunkt achieves 91.1% precision while processing 10 million characters per second with modest memory requirements (432 MB). CharBoundary models offer balanced and adjustable precision-recall tradeoffs, with the large model achieving the highest F1 score (0.782) among all tested methods. Notably, NUPunkt provides a 29-32% precision improvement over general-purpose tools while maintaining exceptional throughput, processing multi-million document collections in minutes rather than hours. Both libraries run efficiently on standard CPU hardware without requiring specialized accelerators. NUPunkt is implemented in pure Python with zero external dependencies, while CharBoundary relies only on scikit-learn and optional ONNX runtime integration for optimized performance. Both libraries are available under the MIT license, can be installed via PyPI, and can be interactively tested at https://sentences.aleainstitute.ai/. These libraries address critical precision issues in retrieval-augmented generation systems by preserving coherent legal concepts across sentences, where each percentage improvement in precision yields exponentially greater reductions in context fragmentation, creating cascading benefits throughout retrieval pipelines and significantly enhancing downstream reasoning quality.

Retrieval systems are central to many NLP pipelines, but often rely on surface-level cues such as keyword overlap and lexical semantic similarity. To evaluate retrieval beyond these shallow signals, recent benchmarks introduce reasoning-heavy queries; however, they primarily shift the burden to query-side processing techniques -- like prompting or multi-hop retrieval -- that can help resolve complexity. In contrast, we present ImpliRet, a benchmark that shifts the reasoning challenge to document-side processing: The queries are simple, but relevance depends on facts stated implicitly in documents through temporal (e.g., resolving "two days ago"), arithmetic, and world knowledge relationships. We evaluate a range of sparse and dense retrievers, all of which struggle in this setting: the best nDCG@10 is only 15.07%. We also test whether long-context models can overcome this limitation. But even with a short context of only ten documents, including the positive document, GPT-4.1 scores only 35.06%, showing that document-side reasoning remains a challenge. Our codes are available at github.com/ZeinabTaghavi/IMPLIRET.Contribution.

We study the depth of grade-school math (GSM) problem-solving capabilities of LLMs. To this end, we evaluate their performance on pairs of existing math word problems together so that the answer to the second problem depends on correctly answering the first problem. Our findings reveal a significant reasoning gap in most LLMs, that is performance difference between solving the compositional pairs and solving each question independently. This gap is more pronounced in smaller, more cost-efficient, and math-specialized models. Moreover, instruction-tuning recipes and code generation have varying effects across LLM sizes, while finetuning on GSM can lead to task overfitting. Our analysis indicates that large reasoning gaps are not because of test-set leakage, but due to distraction from additional context and poor second-hop reasoning. Overall, LLMs exhibit systematic differences in their reasoning abilities, despite what their performance on standard benchmarks indicates.

This paper investigates an under-explored challenge in large language models (LLMs): the impact of KV cache compression methods on LLMs' fundamental capabilities. While existing methods achieve impressive compression ratios on long-context benchmarks, their effects on core model capabilities remain understudied. We present a comprehensive empirical study evaluating prominent KV cache compression methods across diverse tasks, spanning world knowledge, commonsense reasoning, arithmetic reasoning, code generation, safety, and long-context understanding and generation.Our analysis reveals that KV cache compression methods exhibit task-specific performance degradation. Arithmetic reasoning tasks prove particularly sensitive to aggressive compression, with different methods showing performance drops of 17.4%-43.3%. Notably, the DeepSeek R1 Distill model exhibits more robust compression tolerance compared to instruction-tuned models, showing only 9.67%-25.53% performance degradation. Based on our analysis of attention patterns and cross-task compression performance, we propose ShotKV, a novel compression approach that distinctly handles prefill and decoding phases while maintaining shot-level semantic coherence. Empirical results show that ShotKV achieves 9%-18% performance improvements on long-context generation tasks under aggressive compression ratios.

Large Language Models (LLMs) exhibit strong potential in mathematical reasoning, yet their effectiveness is often limited by a shortage of high-quality queries. This limitation necessitates scaling up computational responses through self-generated data, yet current methods struggle due to spurious correlated data caused by ineffective exploration across all reasoning stages. To address such challenge, we introduce MARGE: Improving Math Reasoning with Guided Exploration, a novel method to address this issue and enhance mathematical reasoning through hit-guided exploration. MARGE systematically explores intermediate reasoning states derived from self-generated solutions, enabling adequate exploration and improved credit assignment throughout the reasoning process. Through extensive experiments across multiple backbone models and benchmarks, we demonstrate that MARGE significantly improves reasoning capabilities without requiring external annotations or training additional value models. Notably, MARGE improves both single-shot accuracy and exploration diversity, mitigating a common trade-off in alignment methods. These results demonstrate MARGE's effectiveness in enhancing mathematical reasoning capabilities and unlocking the potential of scaling self-generated training data. Our code and models are available at https://github.com/georgao35/MARGE{this link}.

Commercial large language models (LLMs), like OpenAI's GPT-4 powering ChatGPT and Anthropic's Claude 3 Opus, have dominated natural language processing (NLP) benchmarks across different domains. New competing Open-Source alternatives like Mixtral 8x7B or Llama 3 have emerged and seem to be closing the gap while often offering higher throughput and being less costly to use. Open-Source LLMs can also be self-hosted, which makes them interesting for enterprise and clinical use cases where sensitive data should not be processed by third parties. We participated in the 12th BioASQ challenge, which is a retrieval augmented generation (RAG) setting, and explored the performance of current GPT models Claude 3 Opus, GPT-3.5-turbo and Mixtral 8x7b with in-context learning (zero-shot, few-shot) and QLoRa fine-tuning. We also explored how additional relevant knowledge from Wikipedia added to the context-window of the LLM might improve their performance. Mixtral 8x7b was competitive in the 10-shot setting, both with and without fine-tuning, but failed to produce usable results in the zero-shot setting. QLoRa fine-tuning and Wikipedia context did not lead to measurable performance gains. Our results indicate that the performance gap between commercial and open-source models in RAG setups exists mainly in the zero-shot setting and can be closed by simply collecting few-shot examples for domain-specific use cases. The code needed to rerun these experiments is available through GitHub.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

In the machine learning ecosystem, hardware selection is often regarded as a mere utility, overshadowed by the spotlight on algorithms and data. This oversight is particularly problematic in contexts like ML-as-a-service platforms, where users often lack control over the hardware used for model deployment. How does the choice of hardware impact generalization properties? This paper investigates the influence of hardware on the delicate balance between model performance and fairness. We demonstrate that hardware choices can exacerbate existing disparities, attributing these discrepancies to variations in gradient flows and loss surfaces across different demographic groups. Through both theoretical and empirical analysis, the paper not only identifies the underlying factors but also proposes an effective strategy for mitigating hardware-induced performance imbalances.

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer architecture in which a particular embedding vector's dimension scales with its query frequency. Through theoretical analysis and systematic experiments, we demonstrate that using mixed dimensions can drastically reduce the memory usage, while maintaining and even improving the ML performance. Empirically, we show that the proposed mixed dimension layers improve accuracy by 0.1% using half as many parameters or maintain it using 16X fewer parameters for click-through rate prediction task on the Criteo Kaggle dataset.

What makes a good Large Language Model (LLM)? That it performs well on the relevant benchmarks -- which hopefully measure, with some validity, the presence of capabilities that are also challenged in real application. But what makes the model perform well? What gives a model its abilities? We take a recently introduced type of benchmark that is meant to challenge capabilities in a goal-directed, agentive context through self-play of conversational games, and analyse how performance develops as a function of model characteristics like number of parameters, or type of training. We find that while there is a clear relationship between number of parameters and performance, there is still a wide spread of performance points within a given size bracket, which is to be accounted for by training parameters such as fine-tuning data quality and method. From a more practical angle, we also find a certain degree of unpredictability about performance across access methods, possible due to unexposed sampling parameters, and a, very welcome, performance stability against at least moderate weight quantisation during inference.

This paper revisits the implementation of Load-balancing Loss (LBL) when training Mixture-of-Experts (MoEs) models. Specifically, LBL for MoEs is defined as N_E sum_{i=1}^{N_E} f_i p_i, where N_E is the total number of experts, f_i represents the frequency of expert i being selected, and p_i denotes the average gating score of the expert i. Existing MoE training frameworks usually employ the parallel training strategy so that f_i and the LBL are calculated within a micro-batch and then averaged across parallel groups. In essence, a micro-batch for training billion-scale LLMs normally contains very few sequences. So, the micro-batch LBL is almost at the sequence level, and the router is pushed to distribute the token evenly within each sequence. Under this strict constraint, even tokens from a domain-specific sequence (e.g., code) are uniformly routed to all experts, thereby inhibiting expert specialization. In this work, we propose calculating LBL using a global-batch to loose this constraint. Because a global-batch contains much more diverse sequences than a micro-batch, which will encourage load balance at the corpus level. Specifically, we introduce an extra communication step to synchronize f_i across micro-batches and then use it to calculate the LBL. Through experiments on training MoEs-based LLMs (up to 42.8B total parameters and 400B tokens), we surprisingly find that the global-batch LBL strategy yields excellent performance gains in both pre-training perplexity and downstream tasks. Our analysis reveals that the global-batch LBL also greatly improves the domain specialization of MoE experts.

Ranking has always been one of the top concerns in information retrieval researches. For decades, the lexical matching signal has dominated the ad-hoc retrieval process, but solely using this signal in retrieval may cause the vocabulary mismatch problem. In recent years, with the development of representation learning techniques, many researchers turn to Dense Retrieval (DR) models for better ranking performance. Although several existing DR models have already obtained promising results, their performance improvement heavily relies on the sampling of training examples. Many effective sampling strategies are not efficient enough for practical usage, and for most of them, there still lacks theoretical analysis in how and why performance improvement happens. To shed light on these research questions, we theoretically investigate different training strategies for DR models and try to explain why hard negative sampling performs better than random sampling. Through the analysis, we also find that there are many potential risks in static hard negative sampling, which is employed by many existing training methods. Therefore, we propose two training strategies named a Stable Training Algorithm for dense Retrieval (STAR) and a query-side training Algorithm for Directly Optimizing Ranking pErformance (ADORE), respectively. STAR improves the stability of DR training process by introducing random negatives. ADORE replaces the widely-adopted static hard negative sampling method with a dynamic one to directly optimize the ranking performance. Experimental results on two publicly available retrieval benchmark datasets show that either strategy gains significant improvements over existing competitive baselines and a combination of them leads to the best performance.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but are not easy to parallelize. Alternatively, methods such as temperature sampling and its modifications (top-k sampling, nucleus sampling, typical decoding, and others), are embarrassingly parallel, but have no guarantees about duplicate samples. We present a framework for sampling according to an arithmetic code book implicitly defined by a large language model, compatible with common sampling variations, with provable beam diversity under certain conditions, as well as being embarrassingly parallel and providing unbiased and consistent expectations from the original model. We demonstrate the effectiveness of our approach on WMT machine translation, more than halving the standard deviation when estimating expected BLEU score reward, and closing the BLEU score gap between independent sampling and beam search by up to 63%.

Despite high benchmark scores, Large Language Models (LLMs) often fail simple problem, raising a critical question: Do LLMs learn mathematical principles or merely memorize patterns? Rather than designing increasingly complex benchmarks like recent works, we investigate this using elementary two-integer addition (0 to 2^{64}), probing two core properties: commutativity (A+B=B+A) and compositional generalization (via isomorphic symbolic mappings, e.g., 7 rightarrow y). While state-of-the-art LLMs achieve 73.8-99.8\% accuracy on numerical addition, performance collapses to leq7.5\% under symbolic mapping, indicating failure to generalize learned rules. Non-monotonic performance scaling with digit count and frequent commutativity violations (over 1,700 cases of A+B neq B+A) further support this. Explicitly providing addition rules degrades performance by 81.2\% on average, while self-explanation maintains baseline accuracy, suggesting LLM arithmetic processing is misaligned with human-defined principles. Our findings indicate current LLMs rely on memory pattern over genuine rule learning, highlighting architectural limitations and the need for new approaches to achieve true mathematical reasoning.

This study examines 4-bit quantization methods like GPTQ in large language models (LLMs), highlighting GPTQ's overfitting and limited enhancement in Zero-Shot tasks. While prior works merely focusing on zero-shot measurement, we extend task scope to more generative categories such as code generation and abstractive summarization, in which we found that INT4 quantization can significantly underperform. However, simply shifting to higher precision formats like FP6 has been particularly challenging, thus overlooked, due to poor performance caused by the lack of sophisticated integration and system acceleration strategies on current AI hardware. Our results show that FP6, even with a coarse-grain quantization scheme, performs robustly across various algorithms and tasks, demonstrating its superiority in accuracy and versatility. Notably, with the FP6 quantization, \codestar-15B model performs comparably to its FP16 counterpart in code generation, and for smaller models like the 406M it closely matches their baselines in summarization. Neither can be achieved by INT4. To better accommodate various AI hardware and achieve the best system performance, we propose a novel 4+2 design for FP6 to achieve similar latency to the state-of-the-art INT4 fine-grain quantization. With our design, FP6 can become a promising solution to the current 4-bit quantization methods used in LLMs.

Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama 2 family models at 2 bits per parameter.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.

Despite the critical need to align search targets with users' intention, retrievers often only prioritize query information without delving into the users' intended search context. Enhancing the capability of retrievers to understand intentions and preferences of users, akin to language model instructions, has the potential to yield more aligned search targets. Prior studies restrict the application of instructions in information retrieval to a task description format, neglecting the broader context of diverse and evolving search scenarios. Furthermore, the prevailing benchmarks utilized for evaluation lack explicit tailoring to assess instruction-following ability, thereby hindering progress in this field. In response to these limitations, we propose a novel benchmark,INSTRUCTIR, specifically designed to evaluate instruction-following ability in information retrieval tasks. Our approach focuses on user-aligned instructions tailored to each query instance, reflecting the diverse characteristics inherent in real-world search scenarios. Through experimental analysis, we observe that retrievers fine-tuned to follow task-style instructions, such as INSTRUCTOR, can underperform compared to their non-instruction-tuned counterparts. This underscores potential overfitting issues inherent in constructing retrievers trained on existing instruction-aware retrieval datasets.

Active learning is a paradigm that significantly enhances the performance of machine learning models when acquiring labeled data is expensive. While several benchmarks exist for evaluating active learning strategies, their findings exhibit some misalignment. This discrepancy motivates us to develop a transparent and reproducible benchmark for the community. Our efforts result in an open-sourced implementation (https://github.com/ariapoy/active-learning-benchmark) that is reliable and extensible for future research. By conducting thorough re-benchmarking experiments, we have not only rectified misconfigurations in existing benchmark but also shed light on the under-explored issue of model compatibility, which directly causes the observed discrepancy. Resolving the discrepancy reassures that the uncertainty sampling strategy of active learning remains an effective and preferred choice for most datasets. Our experience highlights the importance of dedicating research efforts towards re-benchmarking existing benchmarks to produce more credible results and gain deeper insights.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE), where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, enhancing computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves lower loss with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

Large language models (LLMs) excel in most NLP tasks but also require expensive cloud servers for deployment due to their size, while smaller models that can be deployed on lower cost (e.g., edge) devices, tend to lag behind in terms of response quality. Therefore in this work we propose a hybrid inference approach which combines their respective strengths to save cost and maintain quality. Our approach uses a router that assigns queries to the small or large model based on the predicted query difficulty and the desired quality level. The desired quality level can be tuned dynamically at test time to seamlessly trade quality for cost as per the scenario requirements. In experiments our approach allows us to make up to 40% fewer calls to the large model, with no drop in response quality.

Premise selection is a crucial yet challenging step in mathematical formalization, especially for users with limited experience. Due to the lack of available formalization projects, existing approaches that leverage language models often suffer from data scarcity. In this work, we introduce an innovative method for training a premise retriever to support the formalization of mathematics. Our approach employs a BERT model to embed proof states and premises into a shared latent space. The retrieval model is trained within a contrastive learning framework and incorporates a domain-specific tokenizer along with a fine-grained similarity computation method. Experimental results show that our model is highly competitive compared to existing baselines, achieving strong performance while requiring fewer computational resources. Performance is further enhanced through the integration of a re-ranking module. To streamline the formalization process, we will release a search engine that enables users to query Mathlib theorems directly using proof states, significantly improving accessibility and efficiency. Codes are available at https://github.com/ruc-ai4math/Premise-Retrieval.

We consider an extension to the classic position auctions in which sponsored creatives can be added within AI generated content rather than shown in predefined slots. New challenges arise from the natural requirement that sponsored creatives should smoothly fit into the context. With the help of advanced LLM technologies, it becomes viable to accurately estimate the benefits of adding each individual sponsored creatives into each potential positions within the AI generated content by properly taking the context into account. Therefore, we assume one click-through rate estimation for each position-creative pair, rather than one uniform estimation for each sponsored creative across all positions in classic settings. As a result, the underlying optimization becomes a general matching problem, thus the substitution effects should be treated more carefully compared to standard position auction settings, where the slots are independent with each other. In this work, we formalize a concrete mathematical model of the extended position auction problem and study the welfare-maximization and revenue-maximization mechanism design problem. Formally, we consider two different user behavior models and solve the mechanism design problems therein respectively. For the Multinomial Logit (MNL) model, which is order-insensitive, we can efficiently implement the optimal mechanisms. For the cascade model, which is order-sensitive, we provide approximately optimal solutions.

Recent studies have shown that, relative position encoding performs well in selective state space model scanning algorithms, and the architecture that balances SSM and Attention enhances the efficiency and effectiveness of the algorithm, while the sparse activation of the mixture of experts reduces the training cost. I studied the effectiveness of using different position encodings in structured state space dual algorithms, and the more effective SSD-Attn internal and external function mixing method, and designed a more efficient cross domain mixture of experts. I found that the same matrix is very wonderful in different algorithms, which allows us to establish a new hybrid sparse architecture: Cheems. Compared with other hybrid architectures, it is more efficient and more effective in language modeling tasks.

Prior research works have evaluated quantized LLMs using limited metrics such as perplexity or a few basic knowledge tasks and old datasets. Additionally, recent large-scale models such as Llama 3.1 with up to 405B have not been thoroughly examined. This paper evaluates the performance of instruction-tuned LLMs across various quantization methods (GPTQ, AWQ, SmoothQuant, and FP8) on models ranging from 7B to 405B. Using 13 benchmarks, we assess performance across six task types: commonsense Q\&A, knowledge and language understanding, instruction following, hallucination detection, mathematics, and dialogue. Our key findings reveal that (1) quantizing a larger LLM to a similar size as a smaller FP16 LLM generally performs better across most benchmarks, except for hallucination detection and instruction following; (2) performance varies significantly with different quantization methods, model size, and bit-width, with weight-only methods often yielding better results in larger models; (3) task difficulty does not significantly impact accuracy degradation due to quantization; and (4) the MT-Bench evaluation method has limited discriminatory power among recent high-performing LLMs.

This work introduces systematic approach for enhancing large language models (LLMs) to address Bangla AI mathematical challenges. Through the assessment of diverse LLM configurations, fine-tuning with specific datasets, and the implementation of Retrieval-Augmented Generation (RAG), we enhanced the model's reasoning precision in a multilingual setting. Crucial discoveries indicate that customized prompting, dataset augmentation, and iterative reasoning improve the model's efficiency regarding Olympiad-level mathematical challenges.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

We combine beam search with the probabilistic pruning technique of nucleus sampling to create two deterministic nucleus search algorithms for natural language generation. The first algorithm, p-exact search, locally prunes the next-token distribution and performs an exact search over the remaining space. The second algorithm, dynamic beam search, shrinks and expands the beam size according to the entropy of the candidate's probability distribution. Despite the probabilistic intuition behind nucleus search, experiments on machine translation and summarization benchmarks show that both algorithms reach the same performance levels as standard beam search.

Large Language Models (LLMs) have shown an impressive capability in code generation and, specifically, to automatically implement requirements described in natural language. The LLM effectiveness generally increases with its size: The higher the number of LLM's trainable parameters the better its ability to implement code. However, when it comes to deploying LLM-based code generators, larger LLMs pose significant challenges related to their memory (and, consequently, carbon) footprint. A previous work by Wei et al. proposed to leverage quantization techniques to reduce the memory footprint of LLM-based code generators without substantially degrading their effectiveness. In short, they studied LLMs featuring up to 16B parameters, quantizing their precision from floating point 32 bits down to int 8 bits and showing their limited impact on code generation performance. Given the fast pace at which LLM capabilities and quantization techniques are evolving, in this work we present a differentiated replication of the work by Wei et al. in which we consider (i) on the one side, more recent and larger code-related LLMs, of up to 34B parameters; (ii) the latest advancements in model quantization techniques, which allow pushing the compression to the extreme quantization level of 2 bits per model parameter and; (iii) different types of calibration datasets to guide the quantization process, including code-specific ones. Our empirical evaluation reveals that the new frontier for LLM quantization is 4-bit precision, resulting in an average memory footprint reduction of 70% compared to the original model without observing any significant decrease in performance. Additionally, when the quantization becomes even more extreme (3 and 2 bits), a code-specific calibration dataset helps to limit the loss of performance.

The use of synthetic data has played a critical role in recent state-of-art breakthroughs. However, overly relying on a single oracle teacher model to generate data has been shown to lead to model collapse and invite propagation of biases. These limitations are particularly evident in multilingual settings, where the absence of a universally effective teacher model that excels across all languages presents significant challenges. In this work, we address these extreme difference by introducing "multilingual arbitrage", which capitalizes on performance variations between multiple models for a given language. To do so, we strategically route samples through a diverse pool of models, each with unique strengths in different languages. Across exhaustive experiments on state-of-art models, our work suggests that arbitrage techniques allow for spectacular gains in performance that far outperform relying on a single teacher. In particular, compared to the best single teacher, we observe gains of up to 56.5% improvement in win rates averaged across all languages when switching to multilingual arbitrage. We observe the most significant gains for the least resourced languages in our pool.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Advancement in Large Language Models (LLMs) reasoning capabilities enables them to solve scientific problems with enhanced efficacy. Thereby, a high-quality benchmark for comprehensive and appropriate assessment holds significance, while existing ones either confront the risk of data contamination or lack involved disciplines. To be specific, due to the data source overlap of LLMs training and static benchmark, the keys or number pattern of answers inadvertently memorized (i.e. data contamination), leading to systematic overestimation of their reasoning capabilities, especially numerical reasoning. We propose SciDA, a multidisciplinary benchmark that consists exclusively of over 1k Olympic-level numerical computation problems, allowing randomized numerical initializations for each inference round to avoid reliance on fixed numerical patterns. We conduct a series of experiments with both closed-source and open-source top-performing LLMs, and it is observed that the performance of LLMs drop significantly under random numerical initialization. Thus, we provide truthful and unbiased assessments of the numerical reasoning capabilities of LLMs. The data is available at https://huggingface.co/datasets/m-a-p/SciDA

Retrieval-Augmented Generation (RAG) systems face significant performance gaps when applied to technical domains requiring precise information extraction from complex documents. Current evaluation methodologies relying on document-level metrics inadequately capture token-resolution retrieval accuracy that is critical for domain-related documents. We propose a framework combining granular evaluation metrics with synthetic data generation to optimize domain-specific RAG performance. First, we introduce token-aware metrics Precision Omega and Intersection-over-Union (IoU) that quantify context preservation versus information density trade-offs inherent in technical texts. Second, we develop a reasoning model-driven pipeline using instruction-tuned LLMs (DeepSeek-R1, DeepSeek-R1 distilled variants, and Phi-4) to generate context-anchored QA pairs with discontinuous reference spans across three specialized corpora: SEC 10-K filings (finance), biomedical abstracts (PubMed), and APT threat reports (cybersecurity). Our empirical analysis reveals critical insights: smaller chunks (less than 10 tokens) improve precision by 31-42% (IoU = 0.071 vs. baseline 0.053) at recall costs (-18%), while domain-specific embedding strategies yield 22% variance in optimal chunk sizing (5-20 tokens). The DeepSeek-R1-Distill-Qwen-32B model demonstrates superior concept alignment (+14% mean IoU over alternatives), though no configuration universally dominates. Financial texts favor larger chunks for risk factor coverage (Recall = 0.81 at size = 20), whereas cybersecurity content benefits from atomic segmentation, Precision Omega = 0.28 at size = 5. Our code is available on https://github.com/aryan-jadon/Synthetic-Data-Generation-and-Evaluation-using-Reasoning-Model

We present a generic framework for creating differentially private versions of any hypothesis test in a black-box way. We analyze the resulting tests analytically and experimentally. Most crucially, we show good practical performance for small data sets, showing that at epsilon = 1 we only need 5-6 times as much data as in the fully public setting. We compare our work to the one existing framework of this type, as well as to several individually-designed private hypothesis tests. Our framework is higher power than other generic solutions and at least competitive with (and often better than) individually-designed tests.

Large Mixture of Experts (MoE) models could achieve state-of-the-art quality on various language tasks, including machine translation task, thanks to the efficient model scaling capability with expert parallelism. However, it has brought a fundamental issue of larger memory consumption and increased memory bandwidth bottleneck at deployment time. In this paper, we propose Mixture of Quantized Experts (MoQE) which is a simple weight-only quantization method applying ultra low-bit down to 2-bit quantizations only to expert weights for mitigating the increased memory and latency issues of MoE models. We show that low-bit quantization together with the MoE architecture delivers a reliable model performance while reducing the memory size significantly even without any additional training in most cases. In particular, expert layers in MoE models are much more robust to the quantization than conventional feedforward networks (FFN) layers. In our comprehensive analysis, we show that MoE models with 2-bit expert weights can deliver better model performance than the dense model trained on the same dataset. As a result of low-bit quantization, we show the model size can be reduced by 79.6% of the original half precision floating point (fp16) MoE model. Combined with an optimized GPU runtime implementation, it also achieves 1.24X speed-up on A100 GPUs.

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.

Dense retrieval has made significant advancements in information retrieval (IR) by achieving high levels of effectiveness while maintaining online efficiency during a single-pass retrieval process. However, the application of pseudo relevance feedback (PRF) to further enhance retrieval effectiveness results in a doubling of online latency. To address this challenge, this paper presents a single-pass dense retrieval framework that shifts the PRF process offline through the utilization of pre-generated pseudo-queries. As a result, online retrieval is reduced to a single matching with the pseudo-queries, hence providing faster online retrieval. The effectiveness of the proposed approach is evaluated on the standard TREC DL and HARD datasets, and the results demonstrate its promise. Our code is openly available at https://github.com/Rosenberg37/OPRF.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

We investigate the effectiveness of reinforcement learning methods for finetuning large language models when transitioning from offline to semi-online to fully online regimes for both verifiable and non-verifiable tasks. Our experiments cover training on verifiable math as well as non-verifiable instruction following with a set of benchmark evaluations for both. Across these settings, we extensively compare online and semi-online Direct Preference Optimization and Group Reward Policy Optimization objectives, and surprisingly find similar performance and convergence between these variants, which all strongly outperform offline methods. We provide a detailed analysis of the training dynamics and hyperparameter selection strategies to achieve optimal results. Finally, we show that multi-tasking with verifiable and non-verifiable rewards jointly yields improved performance across both task types.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Post-Training Quantization (PTQ) is a powerful technique for model compression, reducing the precision of neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point quantization (FP8) in the context of PTQ for model inference. However, the exploration of floating-point formats smaller than 8 bits and their comparison with integer quantization remains relatively limited. In this work, we present minifloats, which are reduced-precision floating-point formats capable of further reducing the memory footprint, latency, and energy cost of a model while approaching full-precision model accuracy. Our work presents a novel PTQ design-space exploration, comparing minifloat and integer quantization schemes across a range of 3 to 8 bits for both weights and activations. We examine the applicability of various PTQ techniques to minifloats, including weight equalization, bias correction, SmoothQuant, gradient-based learned rounding, and the GPTQ method. Our experiments validate the effectiveness of low-precision minifloats when compared to their integer counterparts across a spectrum of accuracy-precision trade-offs on a set of reference deep learning vision workloads. Finally, we evaluate our results against an FPGA-based hardware cost model, showing that integer quantization often remains the Pareto-optimal option, given its relatively smaller hardware resource footprint.

Self-improvement methods enable large language models (LLMs) to generate solutions themselves and iteratively train on filtered, high-quality rationales. This process proves effective and reduces the reliance on human supervision in LLMs' reasoning, but the performance soon plateaus. We delve into the process and find that models tend to over-sample on easy queries and under-sample on queries they have yet to master. As iterations proceed, this imbalance in sampling is exacerbated, leading to a long-tail distribution where solutions to difficult queries almost diminish. This phenomenon limits the performance gain of self-improving models. A straightforward solution is brute-force sampling to balance the distribution, which significantly raises computational costs. In this paper, we introduce Guided Self-Improvement (GSI), a strategy aimed at improving the efficiency of sampling challenging heavy-tailed data. It leverages Socratic-style guidance signals to help LLM reasoning with complex queries, reducing the exploration effort and minimizing computational overhead. Experiments on four models across diverse mathematical tasks show that GSI strikes a balance between performance and efficiency, while also being effective on held-out tasks.

Decomposition-based multi-hop retrieval methods rely on many autoregressive steps to break down complex queries, which breaks end-to-end differentiability and is computationally expensive. Decomposition-free methods tackle this, but current decomposition-free approaches struggle with longer multi-hop problems and generalization to out-of-distribution data. To address these challenges, we introduce GRITHopper-7B, a novel multi-hop dense retrieval model that achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks. GRITHopper combines generative and representational instruction tuning by integrating causal language modeling with dense retrieval training. Through controlled studies, we find that incorporating additional context after the retrieval process, referred to as post-retrieval language modeling, enhances dense retrieval performance. By including elements such as final answers during training, the model learns to better contextualize and retrieve relevant information. GRITHopper-7B offers a robust, scalable, and generalizable solution for multi-hop dense retrieval, and we release it to the community for future research and applications requiring multi-hop reasoning and retrieval capabilities.

When deploying large language models (LLMs), it is important to ensure that these models are not only capable, but also reliable. Many benchmarks have been created to track LLMs' growing capabilities, however there has been no similar focus on measuring their reliability. To understand the potential ramifications of this gap, we investigate how well current benchmarks quantify model reliability. We find that pervasive label errors can compromise these evaluations, obscuring lingering model failures and hiding unreliable behavior. Motivated by this gap in the evaluation of reliability, we then propose the concept of so-called platinum benchmarks, i.e., benchmarks carefully curated to minimize label errors and ambiguity. As a first attempt at constructing such benchmarks, we revise examples from fifteen existing popular benchmarks. We evaluate a wide range of models on these platinum benchmarks and find that, indeed, frontier LLMs still exhibit failures on simple tasks such as elementary-level math word problems. Analyzing these failures further reveals previously unidentified patterns of problems on which frontier models consistently struggle. We provide code at https://github.com/MadryLab/platinum-benchmarks

Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training that then guides important design decisions during the search. However, a significant drawback of these methods is their heavy reliance on offline training, which requires collecting training datasets and computationally costly training epochs yet offering only limited generalization to unseen (larger) instances. In this paper, we propose Balans, an adaptive meta-solver for MIPs with online learning capability that does not require any supervision or apriori training. At its core, Balans is based on adaptive large-neighborhood search, operating on top of an MIP solver by successive applications of destroy and repair neighborhood operators. During the search, the selection among different neighborhood definitions is guided on the fly for the instance at hand via multi-armed bandit algorithms. Our extensive experiments on hard optimization instances show that Balans offers significant performance gains over the default MIP solver, is better than committing to any single best neighborhood, and improves over the state-of-the-art large-neighborhood search for MIPs. Finally, we release Balans as a highly configurable, MIP solver agnostic, open-source software.

When selecting data for training large-scale models, standard practice is to filter for examples that match human notions of data quality. Such filtering yields qualitatively clean datapoints that intuitively should improve model behavior. However, in practice the opposite can often happen: we find that selecting according to similarity with "high quality" data sources may not increase (and can even hurt) performance compared to randomly selecting data. To develop better methods for selecting data, we start by framing dataset selection as an optimization problem that we can directly solve for: given target tasks, a learning algorithm, and candidate data, select the subset that maximizes model performance. This framework thus avoids handpicked notions of data quality, and instead models explicitly how the learning process uses train datapoints to predict on the target tasks. Our resulting method greatly improves language model (LM) performance on both pre-specified tasks and previously unseen tasks. Specifically, choosing target tasks representative of standard LM problems and evaluating on diverse held-out benchmarks, our selected datasets provide a 2x compute multiplier over baseline methods.