Daily Papers

Visual Grounding (VG) tasks, such as referring expression detection and segmentation tasks are important for linking visual entities to context, especially in complex reasoning tasks that require detailed query interpretation. This paper explores VG beyond basic perception, highlighting challenges for methods that require reasoning like human cognition. Recent advances in large language methods (LLMs) and Vision-Language methods (VLMs) have improved abilities for visual comprehension, contextual understanding, and reasoning. These methods are mainly split into end-to-end and compositional methods, with the latter offering more flexibility. Compositional approaches that integrate LLMs and foundation models show promising performance but still struggle with complex reasoning with language-based logical representations. To address these limitations, we propose NAVER, a compositional visual grounding method that integrates explicit probabilistic logic reasoning within a finite-state automaton, equipped with a self-correcting mechanism. This design improves robustness and interpretability in inference through explicit logic reasoning. Our results show that NAVER achieves SoTA performance comparing to recent end-to-end and compositional baselines. The code is available at https://github.com/ControlNet/NAVER .

Large Language Models (LLMs) have achieved significant progress in language understanding and reasoning. Evaluating and analyzing their logical reasoning abilities has therefore become essential. However, existing datasets and benchmarks are often limited to overly simplistic, unnatural, or contextually constrained examples. In response to the growing demand, we introduce SmartyPat-Bench, a challenging, naturally expressed, and systematically labeled benchmark derived from real-world high-quality Reddit posts containing subtle logical fallacies. Unlike existing datasets and benchmarks, it provides more detailed annotations of logical fallacies and features more diverse data. To further scale up the study and address the limitations of manual data collection and labeling - such as fallacy-type imbalance and labor-intensive annotation - we introduce SmartyPat, an automated framework powered by logic programming-based oracles. SmartyPat utilizes Prolog rules to systematically generate logically fallacious statements, which are then refined into fluent natural-language sentences by LLMs, ensuring precise fallacy representation. Extensive evaluation demonstrates that SmartyPat produces fallacies comparable in subtlety and quality to human-generated content and significantly outperforms baseline methods. Finally, experiments reveal nuanced insights into LLM capabilities, highlighting that while excessive reasoning steps hinder fallacy detection accuracy, structured reasoning enhances fallacy categorization performance.

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at multiple levels and conducts symbolic reasoning with such structured abstraction. To fill these fundamental gaps, we devise LOGICSEG, a holistic visual semantic parser that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. In particular, the semantic concepts of interest are structured as a hierarchy, from which a set of constraints are derived for describing the symbolic relations and formalized as first-order logic rules. After fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. During inference, logical constraints are packaged into an iterative process and injected into the network in a form of several matrix multiplications, so as to achieve hierarchy-coherent prediction with logic reasoning. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models. Extensive experiments over four datasets with various segmentation models and backbones verify the effectiveness and generality of LOGICSEG. We believe this study opens a new avenue for visual semantic parsing.

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

We have witnessed that strong LLMs like Qwen-Math, MiMo, and Phi-4 possess immense reasoning potential inherited from the pre-training stage. With reinforcement learning (RL), these models can improve dramatically on reasoning tasks. Recent studies have shown that even RL on a single problem can unleash these models' reasoning capabilities. However, RL is not only expensive but also unstable. Even one-shot RL requires hundreds of GPU hours. This raises a critical question: Is there a more efficient way to unleash the reasoning potential of these powerful base LLMs? In this work, we demonstrate that Critique Fine-Tuning (CFT) on only one problem can effectively unleash the reasoning potential of LLMs. Our method constructs critique data by collecting diverse model-generated solutions to a single problem and using teacher LLMs to provide detailed critiques. We fine-tune Qwen and Llama family models, ranging from 1.5B to 14B parameters, on the CFT data and observe significant performance gains across diverse reasoning tasks. For example, with just 5 GPU hours of training, Qwen-Math-7B-CFT show an average improvement of 15% on six math benchmarks and 16% on three logic reasoning benchmarks. These results are comparable to or even surpass the results from RL with 20x less compute. Ablation studies reveal the robustness of one-shot CFT across different prompt problems. These results highlight one-shot CFT as a simple, general, and compute-efficient approach to unleashing the reasoning capabilities of modern LLMs.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.

Pretrained Vision-Language Models (VLMs) have achieved remarkable performance in image retrieval from text. However, their performance drops drastically when confronted with linguistically complex texts that they struggle to comprehend. Inspired by the Divide-and-Conquer algorithm and dual-process theory, in this paper, we regard linguistically complex texts as compound proposition texts composed of multiple simple proposition sentences and propose an end-to-end Neural Divide-and-Conquer Reasoning framework, dubbed NDCR. It contains three main components: 1) Divide: a proposition generator divides the compound proposition text into simple proposition sentences and produces their corresponding representations, 2) Conquer: a pretrained VLMs-based visual-linguistic interactor achieves the interaction between decomposed proposition sentences and images, 3) Combine: a neural-symbolic reasoner combines the above reasoning states to obtain the final solution via a neural logic reasoning approach. According to the dual-process theory, the visual-linguistic interactor and neural-symbolic reasoner could be regarded as analogical reasoning System 1 and logical reasoning System 2. We conduct extensive experiments on a challenging image retrieval from contextual descriptions data set. Experimental results and analyses indicate NDCR significantly improves performance in the complex image-text reasoning problem. Code link: https://github.com/YunxinLi/NDCR.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations during the inference can violate the exchangeability assumption, challenge the coverage guarantees, and result in a subsequent decline in empirical coverage. In this work, we propose a certifiably robust learning-reasoning conformal prediction framework (COLEP) via probabilistic circuits, which comprise a data-driven learning component that trains statistical models to learn different semantic concepts, and a reasoning component that encodes knowledge and characterizes the relationships among the trained models for logic reasoning. To achieve exact and efficient reasoning, we employ probabilistic circuits (PCs) within the reasoning component. Theoretically, we provide end-to-end certification of prediction coverage for COLEP in the presence of bounded adversarial perturbations. We also provide certified coverage considering the finite size of the calibration set. Furthermore, we prove that COLEP achieves higher prediction coverage and accuracy over a single model as long as the utilities of knowledge models are non-trivial. Empirically, we show the validity and tightness of our certified coverage, demonstrating the robust conformal prediction of COLEP on various datasets, including GTSRB, CIFAR10, and AwA2. We show that COLEP achieves up to 12% improvement in certified coverage on GTSRB, 9% on CIFAR-10, and 14% on AwA2.

In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

Recent advancements in large multimodal models (LMMs) have showcased impressive code generation capabilities, primarily evaluated through image-to-code benchmarks. However, these benchmarks are limited to specific visual programming scenarios where the logic reasoning and the multimodal understanding capacities are split apart. To fill this gap, we propose ScratchEval, a novel benchmark designed to evaluate the visual programming reasoning ability of LMMs. ScratchEval is based on Scratch, a block-based visual programming language widely used in children's programming education. By integrating visual elements and embedded programming logic, ScratchEval requires the model to process both visual information and code structure, thereby comprehensively evaluating its programming intent understanding ability. Our evaluation approach goes beyond the traditional image-to-code mapping and focuses on unified logical thinking and problem-solving abilities, providing a more comprehensive and challenging framework for evaluating the visual programming ability of LMMs. ScratchEval not only fills the gap in existing evaluation methods, but also provides new insights for the future development of LMMs in the field of visual programming. Our benchmark can be accessed at https://github.com/HKBUNLP/ScratchEval .

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Given a natural language statement, how to verify its veracity against a large-scale textual knowledge source like Wikipedia? Most existing neural models make predictions without giving clues about which part of a false claim goes wrong. In this paper, we propose LOREN, an approach for interpretable fact verification. We decompose the verification of the whole claim at phrase-level, where the veracity of the phrases serves as explanations and can be aggregated into the final verdict according to logical rules. The key insight of LOREN is to represent claim phrase veracity as three-valued latent variables, which are regularized by aggregation logical rules. The final claim verification is based on all latent variables. Thus, LOREN enjoys the additional benefit of interpretability -- it is easy to explain how it reaches certain results with claim phrase veracity. Experiments on a public fact verification benchmark show that LOREN is competitive against previous approaches while enjoying the merit of faithful and accurate interpretability. The resources of LOREN are available at: https://github.com/jiangjiechen/LOREN.

Modern Question Answering (QA) and Reasoning approaches based on Large Language Models (LLMs) commonly use prompting techniques, such as Chain-of-Thought (CoT), assuming the resulting generation will have a more granular exploration and reasoning over the question space and scope. However, such methods struggle with generating outputs that are faithful to the intermediate chain of reasoning produced by the model. On the other end of the spectrum, neuro-symbolic methods such as Faithful CoT (F-CoT) propose to combine LLMs with external symbolic solvers. While such approaches boast a high degree of faithfulness, they usually require a model trained for code generation and struggle with tasks that are ambiguous or hard to formalise strictly. We introduce Faithful Logic-Aided Reasoning and Exploration (\ours), a novel interpretable approach for traversing the problem space using task decompositions. We use the LLM to plan a solution, soft-formalise the query into facts and predicates using a logic programming code and simulate that code execution using an exhaustive multi-hop search over the defined space. Our method allows us to compute the faithfulness of the reasoning process w.r.t. the generated code and analyse the steps of the multi-hop search without relying on external solvers. Our methods achieve SOTA results on 7 out of 9 diverse reasoning benchmarks. We also show that model faithfulness positively correlates with overall performance and further demonstrate that {\ours} allows pinpointing the decisive factors sufficient for and leading to the correct answer with optimal reasoning during the multi-hop search.

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.

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Human processes video reasoning in a sequential spatio-temporal reasoning logic, we first identify the relevant frames ("when") and then analyse the spatial relationships ("where") between key objects, and finally leverage these relationships to draw inferences ("what"). However, can Video Large Language Models (Video-LLMs) also "reason through a sequential spatio-temporal logic" in videos? Existing Video-LLM benchmarks primarily focus on assessing object presence, neglecting relational reasoning. Consequently, it is difficult to measure whether a model truly comprehends object interactions (actions/events) in videos or merely relies on pre-trained "memory" of co-occurrences as biases in generating answers. In this work, we introduce a Video Spatio-Temporal Reasoning (V-STaR) benchmark to address these shortcomings. The key idea is to decompose video understanding into a Reverse Spatio-Temporal Reasoning (RSTR) task that simultaneously evaluates what objects are present, when events occur, and where they are located while capturing the underlying Chain-of-thought (CoT) logic. To support this evaluation, we construct a dataset to elicit the spatial-temporal reasoning process of Video-LLMs. It contains coarse-to-fine CoT questions generated by a semi-automated GPT-4-powered pipeline, embedding explicit reasoning chains to mimic human cognition. Experiments from 14 Video-LLMs on our V-STaR reveal significant gaps between current Video-LLMs and the needs for robust and consistent spatio-temporal reasoning.

Large language models (LLMs) have shown exceptional performance as general-purpose assistants, excelling across a variety of reasoning tasks. This achievement represents a significant step toward achieving artificial general intelligence (AGI). Despite these advancements, the effectiveness of LLMs often hinges on the specific prompting strategies employed, and there remains a lack of a robust framework to facilitate learning and generalization across diverse reasoning tasks. To address these challenges, we introduce a novel learning framework, THOUGHT-LIKE-PRO In this framework, we utilize imitation learning to imitate the Chain-of-Thought (CoT) process which is verified and translated from reasoning trajectories generated by a symbolic Prolog logic engine. This framework proceeds in a self-driven manner, that enables LLMs to formulate rules and statements from given instructions and leverage the symbolic Prolog engine to derive results. Subsequently, LLMs convert Prolog-derived successive reasoning trajectories into natural language CoT for imitation learning. Our empirical findings indicate that our proposed approach substantially enhances the reasoning abilities of LLMs and demonstrates robust generalization across out-of-distribution reasoning tasks.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Applying Reinforcement Learning (RL) to Video Large Language Models (Video-LLMs) shows significant promise for complex video reasoning. However, popular Reinforcement Fine-Tuning (RFT) methods, such as outcome-based Group Relative Policy Optimization (GRPO), are limited by data preparation bottlenecks (e.g., noise or high cost) and exhibit unstable improvements in the quality of long chain-of-thoughts (CoTs) and downstream performance.To address these limitations, we propose VerIPO, a Verifier-guided Iterative Policy Optimization method designed to gradually improve video LLMs' capacity for generating deep, long-term reasoning chains. The core component is Rollout-Aware Verifier, positioned between the GRPO and Direct Preference Optimization (DPO) training phases to form the GRPO-Verifier-DPO training loop. This verifier leverages small LLMs as a judge to assess the reasoning logic of rollouts, enabling the construction of high-quality contrastive data, including reflective and contextually consistent CoTs. These curated preference samples drive the efficient DPO stage (7x faster than GRPO), leading to marked improvements in reasoning chain quality, especially in terms of length and contextual consistency. This training loop benefits from GRPO's expansive search and DPO's targeted optimization. Experimental results demonstrate: 1) Significantly faster and more effective optimization compared to standard GRPO variants, yielding superior performance; 2) Our trained models exceed the direct inference of large-scale instruction-tuned Video-LLMs, producing long and contextually consistent CoTs on diverse video reasoning tasks; and 3) Our model with one iteration outperforms powerful LMMs (e.g., Kimi-VL) and long reasoning models (e.g., Video-R1), highlighting its effectiveness and stability.

Multimodal large language models (MLLMs) demonstrate significant potential in the field of medical diagnosis. However, they face critical challenges in specialized domains such as ophthalmology, particularly the fragmentation of annotation granularity and inconsistencies in clinical reasoning logic, which hinder precise cross-modal understanding. This paper introduces FundusExpert, an ophthalmology-specific MLLM with integrated positioning-diagnosis reasoning capabilities, along with FundusGen, a dataset constructed through the intelligent Fundus-Engine system. Fundus-Engine automates localization and leverages MLLM-based semantic expansion to integrate global disease classification, local object detection, and fine-grained feature analysis within a single fundus image. Additionally, by constructing a clinically aligned cognitive chain, it guides the model to generate interpretable reasoning paths. FundusExpert, fine-tuned with instruction data from FundusGen, achieves the best performance in ophthalmic question-answering tasks, surpassing the average accuracy of the 40B MedRegA by 26.6%. It also excels in zero-shot report generation tasks, achieving a clinical consistency of 77.0%, significantly outperforming GPT-4o's 47.6%. Furthermore, we reveal a scaling law between data quality and model capability (L propto N^{0.068}), demonstrating that the cognitive alignment annotations in FundusGen enhance data utilization efficiency. By integrating region-level localization with diagnostic reasoning chains, our work develops a scalable, clinically-aligned MLLM and explores a pathway toward bridging the visual-language gap in specific MLLMs. Our project can be found at https://github.com/MeteorElf/FundusExpert.

Large language models have been extended to the speech domain, leading to the development of speech large language models (SLLMs). While existing SLLMs demonstrate strong performance in speech instruction-following for core languages (e.g., English), they often struggle with non-core languages due to the scarcity of paired speech-text data and limited multilingual semantic reasoning capabilities. To address this, we propose the semi-implicit Cross-lingual Speech Chain-of-Thought (XS-CoT) framework, which integrates speech-to-text translation into the reasoning process of SLLMs. The XS-CoT generates four types of tokens: instruction and response tokens in both core and non-core languages, enabling cross-lingual transfer of reasoning capabilities. To mitigate inference latency in generating target non-core response tokens, we incorporate a semi-implicit CoT scheme into XS-CoT, which progressively compresses the first three types of intermediate reasoning tokens while retaining global reasoning logic during training. By leveraging the robust reasoning capabilities of the core language, XS-CoT improves responses for non-core languages by up to 45\% in GPT-4 score when compared to direct supervised fine-tuning on two representative SLLMs, Qwen2-Audio and SALMONN. Moreover, the semi-implicit XS-CoT reduces token delay by more than 50\% with a slight drop in GPT-4 scores. Importantly, XS-CoT requires only a small amount of high-quality training data for non-core languages by leveraging the reasoning capabilities of core languages. To support training, we also develop a data pipeline and open-source speech instruction-following datasets in Japanese, German, and French.

Large Language Models (LLMs) have demonstrated great potential in various language processing tasks, and recent studies have explored their application in compiler optimizations. However, all these studies focus on the conventional open-source LLMs, such as Llama2, which lack enhanced reasoning mechanisms. In this study, we investigate the errors produced by the fine-tuned 7B-parameter Llama2 model as it attempts to learn and apply a simple peephole optimization for the AArch64 assembly code. We provide an analysis of the errors produced by the LLM and compare it with state-of-the-art OpenAI models which implement advanced reasoning logic, including GPT-4o and GPT-o1 (preview). We demonstrate that OpenAI GPT-o1, despite not being fine-tuned, outperforms the fine-tuned Llama2 and GPT-4o. Our findings indicate that this advantage is largely due to the chain-of-thought reasoning implemented in GPT-o1. We hope our work will inspire further research on using LLMs with enhanced reasoning mechanisms and chain-of-thought for code generation and optimization.

The notable success of large language models (LLMs) has sparked an upsurge in building language agents to complete various complex tasks. We present AMOR, an agent framework based on open-source LLMs, which reasons with external knowledge bases and adapts to specific domains through human supervision to the reasoning process. AMOR builds reasoning logic over a finite state machine (FSM) that solves problems through autonomous executions and transitions over disentangled modules. This allows humans to provide direct feedback to the individual modules, and thus naturally forms process supervision. Based on this reasoning and feedback framework, we develop AMOR through two-stage fine-tuning: warm-up and adaptation. The former fine-tunes the LLM with examples automatically constructed from various public datasets, enabling AMOR to generalize across different knowledge environments, while the latter tailors AMOR to specific domains using process feedback. Extensive experiments across multiple domains demonstrate the advantage of AMOR to strong baselines, thanks to its FSM-based reasoning and process feedback mechanism. The code and data are publicly available at https://github.com/JianGuanTHU/AMOR.

As opposed to evaluating computation and logic-based reasoning, current benchmarks for evaluating large language models (LLMs) in medicine are primarily focused on question-answering involving domain knowledge and descriptive reasoning. While such qualitative capabilities are vital to medical diagnosis, in real-world scenarios, doctors frequently use clinical calculators that follow quantitative equations and rule-based reasoning paradigms for evidence-based decision support. To this end, we propose MedCalc-Bench, a first-of-its-kind dataset focused on evaluating the medical calculation capability of LLMs. MedCalc-Bench contains an evaluation set of over 1000 manually reviewed instances from 55 different medical calculation tasks. Each instance in MedCalc-Bench consists of a patient note, a question requesting to compute a specific medical value, a ground truth answer, and a step-by-step explanation showing how the answer is obtained. While our evaluation results show the potential of LLMs in this area, none of them are effective enough for clinical settings. Common issues include extracting the incorrect entities, not using the correct equation or rules for a calculation task, or incorrectly performing the arithmetic for the computation. We hope our study highlights the quantitative knowledge and reasoning gaps in LLMs within medical settings, encouraging future improvements of LLMs for various clinical calculation tasks.

Large Language Models (LLMs) have exhibited impressive capabilities across numerous domains, yet they often struggle with complex reasoning and decision-making tasks. Decision-making games, which inherently require multifaceted reasoning logic, serve as ideal sandboxes for evaluating and enhancing the reasoning abilities of LLMs. In this work, we first explore whether LLMs can master complex decision-making games through targeted post-training. To this end, we design data synthesis strategies and curate extensive offline datasets from two classic games, Doudizhu and Go. We further develop a suite of techniques to effectively incorporate this data into LLM training, resulting in two novel agents: Mastermind-Dou and Mastermind-Go. Our experimental results demonstrate that these Mastermind LLMs achieve competitive performance in their respective games. Additionally, we explore whether integrating decision-making data can enhance the general reasoning abilities of LLMs. Our findings suggest that such post-training improves certain aspects of reasoning, providing valuable insights for optimizing LLM data collection and synthesis strategies.

Large language models (LLMs) have demonstrated excellent capabilities in the field of biomedical question answering, but their application in real-world clinical consultations still faces core challenges. Existing systems rely on a one-way information transmission mode where patients must fully describe their symptoms in a single round, leading to nonspecific diagnostic recommendations when complaints are vague. Traditional multi-turn dialogue methods based on supervised learning are constrained by static data-driven paradigms, lacking generalizability and struggling to intelligently extract key clinical information. To address these limitations, we propose DoctorAgent-RL, a reinforcement learning (RL)-based multi-agent collaborative framework that models medical consultations as a dynamic decision-making process under uncertainty. The doctor agent continuously optimizes its questioning strategy within the RL framework through multi-turn interactions with the patient agent, dynamically adjusting its information-gathering path based on comprehensive rewards from the Consultation Evaluator. This RL fine-tuning mechanism enables LLMs to autonomously develop interaction strategies aligned with clinical reasoning logic, rather than superficially imitating patterns in existing dialogue data. Notably, we constructed MTMedDialog, the first English multi-turn medical consultation dataset capable of simulating patient interactions. Experiments demonstrate that DoctorAgent-RL outperforms existing models in both multi-turn reasoning capability and final diagnostic performance, demonstrating practical value in assisting clinical consultations. https://github.com/JarvisUSTC/DoctorAgent-RL

Large Vision-Language Models (VLMs) have achieved remarkable performance across a wide range of tasks. However, their deployment in safety-critical domains poses significant challenges. Existing safety fine-tuning methods, which focus on textual or multimodal content, fall short in addressing challenging cases or disrupt the balance between helpfulness and harmlessness. Our evaluation highlights a safety reasoning gap: these methods lack safety visual reasoning ability, leading to such bottlenecks. To address this limitation and enhance both visual perception and reasoning in safety-critical contexts, we propose a novel dataset that integrates multi-image inputs with safety Chain-of-Thought (CoT) labels as fine-grained reasoning logic to improve model performance. Specifically, we introduce the Multi-Image Safety (MIS) dataset, an instruction-following dataset tailored for multi-image safety scenarios, consisting of training and test splits. Our experiments demonstrate that fine-tuning InternVL2.5-8B with MIS significantly outperforms both powerful open-source models and API-based models in challenging multi-image tasks requiring safety-related visual reasoning. This approach not only delivers exceptional safety performance but also preserves general capabilities without any trade-offs. Specifically, fine-tuning with MIS increases average accuracy by 0.83% across five general benchmarks and reduces the Attack Success Rate (ASR) on multiple safety benchmarks by a large margin. Data and Models are released under: https://dripnowhy.github.io/MIS/{https://dripnowhy.github.io/MIS/}

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness. In this study, we identify a critical yet underexplored issue in RL training: low-probability tokens disproportionately influence model updates due to their large gradient magnitudes. This dominance hinders the effective learning of high-probability tokens, whose gradients are essential for LLMs' performance but are substantially suppressed. To mitigate this interference, we propose two novel methods: Advantage Reweighting and Low-Probability Token Isolation (Lopti), both of which effectively attenuate gradients from low-probability tokens while emphasizing parameter updates driven by high-probability tokens. Our approaches promote balanced updates across tokens with varying probabilities, thereby enhancing the efficiency of RL training. Experimental results demonstrate that they substantially improve the performance of GRPO-trained LLMs, achieving up to a 46.2% improvement in K&K Logic Puzzle reasoning tasks. Our implementation is available at https://github.com/zhyang2226/AR-Lopti.

Recent advances in semi-supervised semantic segmentation have been heavily reliant on pseudo labeling to compensate for limited labeled data, disregarding the valuable relational knowledge among semantic concepts. To bridge this gap, we devise LogicDiag, a brand new neural-logic semi-supervised learning framework. Our key insight is that conflicts within pseudo labels, identified through symbolic knowledge, can serve as strong yet commonly ignored learning signals. LogicDiag resolves such conflicts via reasoning with logic-induced diagnoses, enabling the recovery of (potentially) erroneous pseudo labels, ultimately alleviating the notorious error accumulation problem. We showcase the practical application of LogicDiag in the data-hungry segmentation scenario, where we formalize the structured abstraction of semantic concepts as a set of logic rules. Extensive experiments on three standard semi-supervised semantic segmentation benchmarks demonstrate the effectiveness and generality of LogicDiag. Moreover, LogicDiag highlights the promising opportunities arising from the systematic integration of symbolic reasoning into the prevalent statistical, neural learning approaches.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Chain-of-Thought(CoT) prompting and its variants explore equipping large language models (LLMs) with high-level reasoning abilities by emulating human-like linear cognition and logic. However, the human mind is complicated and mixed with both linear and nonlinear thinking. In this work, we propose Inferential Exclusion Prompting (IEP), a novel prompting that combines the principles of elimination and inference in order to guide LLMs to think non-linearly. IEP guides LLMs to plan and then utilize Natural Language Inference (NLI) to deduce each possible solution's entailment relation with context, commonsense, or facts, therefore yielding a broader perspective by thinking back for inferring. This forward planning and backward eliminating process allows IEP to better simulate the complex human thinking processes compared to other CoT-based methods, which only reflect linear cognitive processes. We conducted a series of empirical studies and have corroborated that IEP consistently outperforms CoT across various tasks. Additionally, we observe that integrating IEP and CoT further improves the LLMs' performance on certain tasks, highlighting the necessity of equipping LLMs with mixed logic processes. Moreover, to better evaluate comprehensive features inherent in human logic, we introduce Mental-Ability Reasoning Benchmark (MARB). The benchmark comprises six novel subtasks with a total of 9,115 questions, among which 1,685 are developed with hand-crafted rationale references. We believe both IEP and MARB can serve as a promising direction for unveiling LLMs' logic and verbal reasoning abilities and drive further advancements. MARB will be available at ~anonymity link soon.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Large language models have recently evolved from fluent text generation to advanced reasoning across diverse domains, giving rise to reasoning language models. Among these domains, mathematical reasoning serves as a representative benchmark as it requires precise multi-step logic and abstract reasoning, which can be generalized to other tasks. While closed-source RLMs such as GPT-o3 demonstrate impressive reasoning capabilities, their proprietary nature limits transparency and reproducibility. Although many open-source projects aim to close this gap, most of them lack sufficient openness by omitting critical resources such as datasets and detailed training configurations, which hinders reproducibility. To contribute toward greater transparency in RLM development, we introduce the MiroMind-M1 series, a set of fully open-source RLMs built on the Qwen-2.5 backbone that match or exceed the performance of existing open-source RLMs. Specifically, our models are trained in two stages: SFT on a carefully curated corpus of 719K math-reasoning problems with verified CoT trajectories, followed by RLVR on 62K challenging and verifiable problems. To enhance the robustness and efficiency of the RLVR process, we introduce Context-Aware Multi-Stage Policy Optimization, an algorithm that integrates length-progressive training with an adaptive repetition penalty to encourage context-aware RL training. Our model achieves state-of-the-art or competitive performance and superior token efficiency among Qwen-2.5-based open-source 7B and 32B models on the AIME24, AIME25, and MATH benchmarks. To facilitate reproducibility, we release the complete stack: models (MiroMind-M1-SFT-7B, MiroMind-M1-RL-7B, MiroMind-M1-RL-32B); datasets (MiroMind-M1-SFT-719K, MiroMind-M1-RL-62K); and all training and evaluation configurations. We hope these resources will support further research and foster community advancement.

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments through game-theoretic tasks, e.g., board and card games that require pure logic and strategic reasoning to compete with opponents. We first propose GTBench, a language-driven environment composing 10 widely-recognized tasks, across a comprehensive game taxonomy: complete versus incomplete information, dynamic versus static, and probabilistic versus deterministic scenarios. Then, we investigate two key problems: (1) Characterizing game-theoretic reasoning of LLMs; (2) LLM-vs-LLM competitions as reasoning evaluation. We observe that (1) LLMs have distinct behaviors regarding various gaming scenarios; for example, LLMs fail in complete and deterministic games yet they are competitive in probabilistic gaming scenarios; (2) Open-source LLMs, e.g., CodeLlama-34b-Instruct, are less competitive than commercial LLMs, e.g., GPT-4, in complex games. In addition, code-pretraining greatly benefits strategic reasoning, while advanced reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) do not always help. Detailed error profiles are also provided for a better understanding of LLMs' behavior.

We present LogiGAN, an unsupervised adversarial pre-training framework for improving logical reasoning abilities of language models. Upon automatic identifying logical reasoning phenomena in massive text corpus via detection heuristics, we train language models to predict the masked-out logical statements. Inspired by the facilitation effect of reflective thinking in human learning, we analogically simulate the learning-thinking process with an adversarial Generator-Verifier architecture to assist logic learning. LogiGAN implements a novel sequential GAN approach that (a) circumvents the non-differentiable challenge of the sequential GAN by leveraging the Generator as a sentence-level generative likelihood scorer with a learning objective of reaching scoring consensus with the Verifier; (b) is computationally feasible for large-scale pre-training with arbitrary target length. Both base and large size language models pre-trained with LogiGAN demonstrate obvious performance improvement on 12 datasets requiring general reasoning abilities, revealing the fundamental role of logic in broad reasoning, as well as the effectiveness of LogiGAN. Ablation studies on LogiGAN components reveal the relative orthogonality between linguistic and logic abilities and suggest that reflective thinking's facilitation effect might also generalize to machine learning.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

A growing variety of prompt engineering techniques has been proposed for Large Language Models (LLMs), yet systematic evaluation of each technique on individual software engineering (SE) tasks remains underexplored. In this study, we present a systematic evaluation of 14 established prompt techniques across 10 SE tasks using four LLM models. As identified in the prior literature, the selected prompting techniques span six core dimensions (Zero-Shot, Few-Shot, Thought Generation, Ensembling, Self-Criticism, and Decomposition). They are evaluated on tasks such as code generation, bug fixing, and code-oriented question answering, to name a few. Our results show which prompting techniques are most effective for SE tasks requiring complex logic and intensive reasoning versus those that rely more on contextual understanding and example-driven scenarios. We also analyze correlations between the linguistic characteristics of prompts and the factors that contribute to the effectiveness of prompting techniques in enhancing performance on SE tasks. Additionally, we report the time and token consumption for each prompting technique when applied to a specific task and model, offering guidance for practitioners in selecting the optimal prompting technique for their use cases.

Vision-language models (VLMs) have made significant progress in recent visual-question-answering (VQA) benchmarks that evaluate complex visio-linguistic reasoning. However, are these models truly effective? In this work, we show that VLMs still struggle with natural images and questions that humans can easily answer, which we term natural adversarial samples. We also find it surprisingly easy to generate these VQA samples from natural image-text corpora using off-the-shelf models like CLIP and ChatGPT. We propose a semi-automated approach to collect a new benchmark, NaturalBench, for reliably evaluating VLMs with 10,000 human-verified VQA samples. Crucially, we adopt a vision-centric design by pairing each question with two images that yield different answers, preventing blind solutions from answering without using the images. This makes NaturalBench more challenging than previous benchmarks that can be solved with commonsense priors. We evaluate 53 state-of-the-art VLMs on NaturalBench, showing that models like LLaVA-OneVision, Cambrian-1, Llama3.2-Vision, Molmo, Qwen2-VL, and even GPT-4o lag 50%-70% behind human performance (over 90%). We analyze why NaturalBench is hard from two angles: (1) Compositionality: Solving NaturalBench requires diverse visio-linguistic skills, including understanding attribute bindings, object relationships, and advanced reasoning like logic and counting. To this end, unlike prior work that uses a single tag per sample, we tag each NaturalBench sample with 1 to 8 skill tags for fine-grained evaluation. (2) Biases: NaturalBench exposes severe biases in VLMs, as models often choose the same answer regardless of the image. Lastly, we apply our benchmark curation method to diverse data sources, including long captions (over 100 words) and non-English languages like Chinese and Hindi, highlighting its potential for dynamic evaluations of VLMs.

Scalable oversight protocols aim to enable humans to accurately supervise superhuman AI. In this paper we study debate, where two AI's compete to convince a judge; consultancy, where a single AI tries to convince a judge that asks questions; and compare to a baseline of direct question-answering, where the judge just answers outright without the AI. We use large language models (LLMs) as both AI agents and as stand-ins for human judges, taking the judge models to be weaker than agent models. We benchmark on a diverse range of asymmetries between judges and agents, extending previous work on a single extractive QA task with information asymmetry, to also include mathematics, coding, logic and multimodal reasoning asymmetries. We find that debate outperforms consultancy across all tasks when the consultant is randomly assigned to argue for the correct/incorrect answer. Comparing debate to direct question answering, the results depend on the type of task: in extractive QA tasks with information asymmetry debate outperforms direct question answering, but in other tasks without information asymmetry the results are mixed. Previous work assigned debaters/consultants an answer to argue for. When we allow them to instead choose which answer to argue for, we find judges are less frequently convinced by the wrong answer in debate than in consultancy. Further, we find that stronger debater models increase judge accuracy, though more modestly than in previous studies.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

Most recent works focus on answering first order logical queries to explore the knowledge graph reasoning via multi-hop logic predictions. However, existing reasoning models are limited by the circumscribed logical paradigms of training samples, which leads to a weak generalization of unseen logic. To address these issues, we propose a plug-in module called Logic Diffusion (LoD) to discover unseen queries from surroundings and achieves dynamical equilibrium between different kinds of patterns. The basic idea of LoD is relation diffusion and sampling sub-logic by random walking as well as a special training mechanism called gradient adaption. Besides, LoD is accompanied by a novel loss function to further achieve the robust logical diffusion when facing noisy data in training or testing sets. Extensive experiments on four public datasets demonstrate the superiority of mainstream knowledge graph reasoning models with LoD over state-of-the-art. Moreover, our ablation study proves the general effectiveness of LoD on the noise-rich knowledge graph.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.

Due to their similarity-based learning objectives, pretrained sentence encoders often internalize stereotypical assumptions that reflect the social biases that exist within their training corpora. In this paper, we describe several kinds of stereotypes concerning different communities that are present in popular sentence representation models, including pretrained next sentence prediction and contrastive sentence representation models. We compare such models to textual entailment models that learn language logic for a variety of downstream language understanding tasks. By comparing strong pretrained models based on text similarity with textual entailment learning, we conclude that the explicit logic learning with textual entailment can significantly reduce bias and improve the recognition of social communities, without an explicit de-biasing process

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.

Neural-symbolic learning, an intersection of neural networks and symbolic reasoning, aims to blend neural networks' learning capabilities with symbolic AI's interpretability and reasoning. This paper introduces an approach designed to improve the performance of neural models in learning reasoning tasks. It achieves this by integrating Answer Set Programming (ASP) solvers and domain-specific expertise, which is an approach that diverges from traditional complex neural-symbolic models. In this paper, a shallow artificial neural network (ANN) is specifically trained to solve Sudoku puzzles with minimal training data. The model has a unique loss function that integrates losses calculated using the ASP solver outputs, effectively enhancing its training efficiency. Most notably, the model shows a significant improvement in solving Sudoku puzzles using only 12 puzzles for training and testing without hyperparameter tuning. This advancement indicates that the model's enhanced reasoning capabilities have practical applications, extending well beyond Sudoku puzzles to potentially include a variety of other domains. The code can be found on GitHub: https://github.com/Fadi2200/ASPEN.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

Large Language Models (LLMs) are primarily trained on high-resource natural languages, limiting their effectiveness in low-resource settings and in tasks requiring deep logical reasoning. This research introduces Rosetta-PL, a benchmark designed to evaluate LLMs' logical reasoning and generalization capabilities in a controlled environment. We construct Rosetta-PL by translating a dataset of logical propositions from Lean into a custom logical language, which is then used to fine-tune an LLM (e.g., GPT-4o). Our experiments analyze the impact of the size of the dataset and the translation methodology on the performance of the model. Our results indicate that preserving logical relationships in the translation process significantly boosts precision, with accuracy plateauing beyond roughly 20,000 training samples. These insights provide valuable guidelines for optimizing LLM training in formal reasoning tasks and improving performance in various low-resource language applications.

Pre-trained large language model (LLM) is under exploration to perform NLP tasks that may require logical reasoning. Logic-driven data augmentation for representation learning has been shown to improve the performance of tasks requiring logical reasoning, but most of these data rely on designed templates and therefore lack generalization. In this regard, we propose an AMR-based logical equivalence-driven data augmentation method (AMR-LE) for generating logically equivalent data. Specifically, we first parse a text into the form of an AMR graph, next apply four logical equivalence laws (contraposition, double negation, commutative and implication laws) on the AMR graph to construct a logically equivalent/inequivalent AMR graph, and then convert it into a logically equivalent/inequivalent sentence. To help the model to better learn these logical equivalence laws, we propose a logical equivalence-driven contrastive learning training paradigm, which aims to distinguish the difference between logical equivalence and inequivalence. Our AMR-LE (Ensemble) achieves #2 on the ReClor leaderboard https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347 . Our model shows better performance on seven downstream tasks, including ReClor, LogiQA, MNLI, MRPC, RTE, QNLI, and QQP. The source code and dataset are public at https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning .

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

We present FOLIO, a human-annotated, open-domain, and logically complex and diverse dataset for reasoning in natural language (NL), equipped with first order logic (FOL) annotations. FOLIO consists of 1,435 examples (unique conclusions), each paired with one of 487 sets of premises which serve as rules to be used to deductively reason for the validity of each conclusion. The logical correctness of premises and conclusions is ensured by their parallel FOL annotations, which are automatically verified by our FOL inference engine. In addition to the main NL reasoning task, NL-FOL pairs in FOLIO automatically constitute a new NL-FOL translation dataset using FOL as the logical form. Our experiments on FOLIO systematically evaluate the FOL reasoning ability of supervised fine-tuning on medium-sized language models (BERT, RoBERTa) and few-shot prompting on large language models (GPT-NeoX, OPT, GPT-3, Codex). For NL-FOL translation, we experiment with GPT-3 and Codex. Our results show that one of the most capable Large Language Model (LLM) publicly available, GPT-3 davinci, achieves only slightly better than random results with few-shot prompting on a subset of FOLIO, and the model is especially bad at predicting the correct truth values for False and Unknown conclusions. Our dataset and code are available at https://github.com/Yale-LILY/FOLIO.

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning task and thus is a valuable source of data for evaluating how modern, increasingly capable LLMs can handle hard logical reasoning tasks. I construct a dataset of LSAT logic games and their associated metadata, and extensively evaluate LLMs' performance in a Chain-of-Thought prompting setting. Given the weak performance in this setting, I explore other prompting frameworks on a smaller subset of the dataset, adapting ideas from Reflexion to this task. This results in a substantially improved accuracy of 70 percent for GPT-4 and 46 percent for GPT-3.5 on this data subset, highlighting the capacity of LLMs to revise their logical errors, despite initially weak performance. Finally, I analyze the types of logic games that models perform better or worse on, as well as the types of logical errors I observe from human annotation, providing detailed insights on the logical reasoning capabilities of LLMs.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves 94.21% of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves 92.04 % of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Theory-of-Mind (ToM) tasks pose a unique challenge for small language models (SLMs) with limited scale, which often lack the capacity to perform deep social reasoning. In this work, we propose DEL-ToM, a framework that improves ToM reasoning through inference-time scaling rather than architectural changes. Our approach decomposes ToM tasks into a sequence of belief updates grounded in Dynamic Epistemic Logic (DEL), enabling structured and transparent reasoning. We train a verifier, called the Process Belief Model (PBM), to score each belief update step using labels generated automatically via a DEL simulator. During inference, candidate belief traces generated by a language model are evaluated by the PBM, and the highest-scoring trace is selected. This allows SLMs to emulate more deliberate reasoning by allocating additional compute at test time. Experiments across multiple model scales and benchmarks show that DEL-ToM consistently improves performance, demonstrating that verifiable belief supervision can significantly enhance ToM abilities of SLMs without retraining.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Large language models, despite extensive alignment with human values and ethical principles, remain vulnerable to sophisticated jailbreak attacks that exploit their reasoning abilities. Existing safety measures often detect overt malicious intent but fail to address subtle, reasoning-driven vulnerabilities. In this work, we introduce POATE (Polar Opposite query generation, Adversarial Template construction, and Elaboration), a novel jailbreak technique that harnesses contrastive reasoning to provoke unethical responses. POATE crafts semantically opposing intents and integrates them with adversarial templates, steering models toward harmful outputs with remarkable subtlety. We conduct extensive evaluation across six diverse language model families of varying parameter sizes to demonstrate the robustness of the attack, achieving significantly higher attack success rates (~44%) compared to existing methods. To counter this, we propose Intent-Aware CoT and Reverse Thinking CoT, which decompose queries to detect malicious intent and reason in reverse to evaluate and reject harmful responses. These methods enhance reasoning robustness and strengthen the model's defense against adversarial exploits.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Vision language models (VLMs) are expected to perform effective multimodal reasoning and make logically coherent decisions, which is critical to tasks such as diagram understanding and spatial problem solving. However, current VLM reasoning lacks large-scale and well-structured training datasets. To bridge this gap, we propose VisualSphinx, a first-of-its-kind large-scale synthetic visual logical reasoning training data. To tackle the challenge of image synthesis with grounding answers, we propose a rule-to-image synthesis pipeline, which extracts and expands puzzle rules from seed questions and generates the code of grounding synthesis image synthesis for puzzle sample assembly. Experiments demonstrate that VLM trained using GRPO on VisualSphinx benefit from logical coherence and readability of our dataset and exhibit improved performance on logical reasoning tasks. The enhanced reasoning capabilities developed from VisualSphinx also benefit other reasoning tasks such as algebraic reasoning, arithmetic reasoning and geometry reasoning.

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR enables scalable, automated synthesis of inductive reasoning tasks with precisely controlled difficulty. For each task, SLR synthesizes (i) a latent ground-truth rule, (ii) an executable validation program used by a symbolic judge to deterministically verify model outputs, and (iii) an instruction prompt for the reasoning task. Using SLR, we create SLR-Bench, a benchmark comprising over 19k prompts spanning 20 curriculum levels that progressively increase in relational, arithmetic, and recursive complexity. Large-scale evaluation reveals that contemporary LLMs readily produce syntactically valid rules, yet often fail at correct logical inference. Recent reasoning LLMs do somewhat better, but incur substantial increases in test-time compute, sometimes exceeding 15k completion tokens. Finally, logic-tuning via SLR doubles Llama-3-8B accuracy on SLR-Bench, achieving parity with Gemini-Flash-Thinking at a fraction of computational cost. SLR is fully automated, requires no human annotation, ensures dataset novelty, and offers a scalable environment for probing and advancing LLMs' reasoning capabilities.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic expression that characterizes its semantics? How do the semantics of two losses relate to each other? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning about group polarization using logical systems. In this work we consider the modal logic PNL that captures the notion of agents agreeing or disagreeing on a given topic. Our contribution involves enhancing PNL with advanced formal reasoning techniques, instead of relying on axiomatic systems for analyzing group polarization. To achieve this, we introduce a semantic game tailored for (hybrid) extensions of PNL. This game fosters dynamic reasoning about concrete network models, aligning with our goal of strengthening PNL's effectiveness in studying group polarization. We show how this semantic game leads to a provability game by systemically exploring the truth in all models. This leads to the first cut-free sequent systems for some variants of PNL. Using polarization of formulas, the proposed calculi can be modularly adapted to consider different frame properties of the underlying model.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Large language models (LLMs), while promising, face criticisms for biases, hallucinations, and a lack of reasoning capability. This paper introduces SocraSynth, a multi-LLM agent reasoning platform developed to mitigate these issues. SocraSynth utilizes conditional statistics and systematic context enhancement through continuous arguments, alongside adjustable debate contentiousness levels. The platform typically involves a human moderator and two LLM agents representing opposing viewpoints on a given subject. SocraSynth operates in two main phases: knowledge generation and reasoning evaluation. In the knowledge generation phase, the moderator defines the debate topic and contentiousness level, prompting the agents to formulate supporting arguments for their respective stances. The reasoning evaluation phase then employs Socratic reasoning and formal logic principles to appraise the quality of the arguments presented. The dialogue concludes with the moderator adjusting the contentiousness from confrontational to collaborative, gathering final, conciliatory remarks to aid in human reasoning and decision-making. Through case studies in three distinct application domains, this paper showcases SocraSynth's effectiveness in fostering rigorous research, dynamic reasoning, comprehensive assessment, and enhanced collaboration. This underscores the value of multi-agent interactions in leveraging LLMs for advanced knowledge extraction and decision-making support.

Generalized quantifiers (e.g., few, most) are used to indicate the proportions predicates are satisfied (for example, some apples are red). One way to interpret quantifier semantics is to explicitly bind these satisfactions with percentage scopes (e.g., 30%-40% of apples are red). This approach can be helpful for tasks like logic formalization and surface-form quantitative reasoning (Gordon and Schubert, 2010; Roy et al., 2015). However, it remains unclear if recent foundation models possess this ability, as they lack direct training signals. To explore this, we introduce QuRe, a crowd-sourced dataset of human-annotated generalized quantifiers in Wikipedia sentences featuring percentage-equipped predicates. We explore quantifier comprehension in language models using PRESQUE, a framework that combines natural language inference and the Rational Speech Acts framework. Experimental results on the HVD dataset and QuRe illustrate that PRESQUE, employing pragmatic reasoning, performs 20% better than a literal reasoning baseline when predicting quantifier percentage scopes, with no additional training required.

Existing efforts to improve logical reasoning ability of language models have predominantly relied on supervised fine-tuning, hindering generalization to new domains and/or tasks. The development of Large Langauge Models (LLMs) has demonstrated the capacity of compressing abundant knowledge into a single proxy, enabling them to tackle multiple tasks effectively. Our preliminary experiments, nevertheless, show that LLMs do not show capability on logical reasoning. The performance of LLMs on logical reasoning benchmarks is far behind the existing state-of-the-art baselines. In this paper, we make the first attempt to investigate the feasibility of incorporating logical knowledge through self-supervised post-training, and activating it via in-context learning, which we termed as LogicLLM. Specifically, we devise an auto-regressive objective variant of MERIt and integrate it with two LLM series, i.e., FLAN-T5 and LLaMA, with parameter size ranging from 3 billion to 13 billion. The results on two challenging logical reasoning benchmarks demonstrate the effectiveness of LogicLLM. Besides, we conduct extensive ablation studies to analyze the key factors in designing logic-oriented proxy tasks.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.

Recent advancements in Multi-Agent Systems (MAS) powered by Large Language Models (LLMs) have demonstrated tremendous potential in diverse task scenarios. Nonetheless, existing agentic systems typically rely on predefined agent-role design spaces and static communication structures, limiting their adaptability as well as flexibility in complex interaction environments and leading to subpar performance on highly specialized and expert-level tasks. To address these issues, we introduce HALO, a multi-agent collaboration framework based on a hierarchical reasoning architecture. Specifically, we incorporate a high-level planning agent for task decomposition, mid-level role-design agents for subtask-specific agent instantiation, and low-level inference agents for subtask execution. Particularly, subtask execution is reformulated as a structured workflow search problem, where Monte Carlo Tree Search (MCTS) systematically explores the agentic action space to construct optimal reasoning trajectories. Additionally, as the majority of users lack expertise in prompt engineering, we leverage an Adaptive Prompt Refinement module to transform raw queries into task-specific prompts. Empirical evaluations on Code Generation (HumanEval), General Reasoning (MMLU), and Arithmetic Reasoning (MATH) benchmark datasets highlight the effectiveness of HALO, yielding a 14.4% average improvement over state-of-the-art baselines. Notably, HALO achieves up to 13.3% performance gain on the Moral Scenarios subject in the MMLU benchmark and up to 19.6% performance gain on the Algebra subarea in the MATH benchmark, indicating its advanced proficiency in tackling highly specialized and expert-level tasks. The code repository is available at https://github.com/23japhone/HALO.

Scientific reasoning, the process through which humans apply logic, evidence, and critical thinking to explore and interpret scientific phenomena, is essential in advancing knowledge reasoning across diverse fields. However, despite significant progress, current scientific reasoning models still struggle with generalization across domains and often fall short of multimodal perception. Multimodal Large Language Models (MLLMs), which integrate text, images, and other modalities, present an exciting opportunity to overcome these limitations and enhance scientific reasoning. Therefore, this position paper argues that MLLMs can significantly advance scientific reasoning across disciplines such as mathematics, physics, chemistry, and biology. First, we propose a four-stage research roadmap of scientific reasoning capabilities, and highlight the current state of MLLM applications in scientific reasoning, noting their ability to integrate and reason over diverse data types. Second, we summarize the key challenges that remain obstacles to achieving MLLM's full potential. To address these challenges, we propose actionable insights and suggestions for the future. Overall, our work offers a novel perspective on MLLM integration with scientific reasoning, providing the LLM community with a valuable vision for achieving Artificial General Intelligence (AGI).

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

This paper presents the development of a novel ethical reasoning framework for robots. "Robots Can Feel" is the first system for robots that utilizes a combination of logic and human-like emotion simulation to make decisions in morally complex situations akin to humans. The key feature of the approach is the management of the Emotion Weight Coefficient - a customizable parameter to assign the role of emotions in robot decision-making. The system aims to serve as a tool that can equip robots of any form and purpose with ethical behavior close to human standards. Besides the platform, the system is independent of the choice of the base model. During the evaluation, the system was tested on 8 top up-to-date LLMs (Large Language Models). This list included both commercial and open-source models developed by various companies and countries. The research demonstrated that regardless of the model choice, the Emotions Weight Coefficient influences the robot's decision similarly. According to ANOVA analysis, the use of different Emotion Weight Coefficients influenced the final decision in a range of situations, such as in a request for a dietary violation F(4, 35) = 11.2, p = 0.0001 and in an animal compassion situation F(4, 35) = 8.5441, p = 0.0001. A demonstration code repository is provided at: https://github.com/TemaLykov/robots_can_feel

Recent advancements in transformer-based models have initiated research interests in investigating their ability to learn to perform reasoning tasks. However, most of the contexts used for this purpose are in practice very simple: generated from short (fragments of) first-order logic sentences with only a few logical operators and quantifiers. In this work, we construct the natural language dataset, DELTA_D, using the description logic language ALCQ. DELTA_D contains 384K examples, and increases in two dimensions: i) reasoning depth, and ii) linguistic complexity. In this way, we systematically investigate the reasoning ability of a supervised fine-tuned DeBERTa-based model and of two large language models (GPT-3.5, GPT-4) with few-shot prompting. Our results demonstrate that the DeBERTa-based model can master the reasoning task and that the performance of GPTs can improve significantly even when a small number of samples is provided (9 shots). We open-source our code and datasets.

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.

The growing popularity of neuro symbolic reasoning has led to the adoption of various forms of differentiable (i.e., fuzzy) first order logic. We introduce PyReason, a software framework based on generalized annotated logic that both captures the current cohort of differentiable logics and temporal extensions to support inference over finite periods of time with capabilities for open world reasoning. Further, PyReason is implemented to directly support reasoning over graphical structures (e.g., knowledge graphs, social networks, biological networks, etc.), produces fully explainable traces of inference, and includes various practical features such as type checking and a memory-efficient implementation. This paper reviews various extensions of generalized annotated logic integrated into our implementation, our modern, efficient Python-based implementation that conducts exact yet scalable deductive inference, and a suite of experiments. PyReason is available at: github.com/lab-v2/pyreason.

The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship remains latent potentiality until tasks impose constraints, akin to measurement. Yet, refining their sampling requires more than probabilistic selection: solutions must conform to specific structures or rules, ensuring consistency and the invocation of general principles. We present Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge. Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers. Inspired by category theory, it encodes concepts as nodes and their relationships as edges, supporting hierarchical inference and adaptive learning through isomorphic representations. Demonstrations include hypothesis generation, materials design, and creative reasoning, such as discovering relationships between mythological concepts like 'thin places' with materials science. We propose a 'knowledge garden growth' strategy that integrates insights across domains, promoting interdisciplinary connections. Results with a 3-billion-parameter Graph-PReFLexOR model show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery. It lays the groundwork for general autonomous reasoning solutions.

Despite notable advancements in multimodal reasoning, leading Multimodal Large Language Models (MLLMs) still underperform on vision-centric multimodal reasoning tasks in general scenarios. This shortfall stems from their predominant reliance on logic- and knowledge-based slow thinking strategies, while effective for domains like math and science, fail to integrate visual information effectively during reasoning. Consequently, these models often fail to adequately ground visual cues, resulting in suboptimal performance in tasks that require multiple plausible visual interpretations and inferences. To address this, we present GThinker (General Thinker), a novel reasoning MLLM excelling in multimodal reasoning across general scenarios, mathematics, and science. GThinker introduces Cue-Rethinking, a flexible reasoning pattern that grounds inferences in visual cues and iteratively reinterprets these cues to resolve inconsistencies. Building on this pattern, we further propose a two-stage training pipeline, including pattern-guided cold start and incentive reinforcement learning, designed to enable multimodal reasoning capabilities across domains. Furthermore, to support the training, we construct GThinker-11K, comprising 7K high-quality, iteratively-annotated reasoning paths and 4K curated reinforcement learning samples, filling the data gap toward general multimodal reasoning. Extensive experiments demonstrate that GThinker achieves 81.5% on the challenging comprehensive multimodal reasoning benchmark M^3CoT, surpassing the latest O4-mini model. It also shows an average improvement of 2.1% on general scenario multimodal reasoning benchmarks, while maintaining on-par performance in mathematical reasoning compared to counterpart advanced reasoning models. The code, model, and data will be released soon at https://github.com/jefferyZhan/GThinker.

Medical tasks such as diagnosis and treatment planning require precise and complex reasoning, particularly in life-critical domains. Unlike mathematical reasoning, medical reasoning demands meticulous, verifiable thought processes to ensure reliability and accuracy. However, there is a notable lack of datasets that provide transparent, step-by-step reasoning to validate and enhance the medical reasoning ability of AI models. To bridge this gap, we introduce MedReason, a large-scale high-quality medical reasoning dataset designed to enable faithful and explainable medical problem-solving in large language models (LLMs). We utilize a structured medical knowledge graph (KG) to convert clinical QA pairs into logical chains of reasoning, or ``thinking paths'', which trace connections from question elements to answers via relevant KG entities. Each path is validated for consistency with clinical logic and evidence-based medicine. Our pipeline generates detailed reasoning for various medical questions from 7 medical datasets, resulting in a dataset of 32,682 question-answer pairs, each with detailed, step-by-step explanations. Experiments demonstrate that fine-tuning with our dataset consistently boosts medical problem-solving capabilities, achieving significant gains of up to 7.7% for DeepSeek-Ditill-8B. Our top-performing model, MedReason-8B, outperforms the Huatuo-o1-8B, a state-of-the-art medical reasoning model, by up to 4.2% on the clinical benchmark MedBullets. We also engage medical professionals from diverse specialties to assess our dataset's quality, ensuring MedReason offers accurate and coherent medical reasoning. Our data, models, and code will be publicly available.

While large language models have shown impressive capabilities across a wide range of domains, they still encounter significant challenges in reasoning tasks that require gathering evidence over multiple turns and drawing logical conclusions. These challenges present significant obstacles for LLM chat user interfaces, which rely on multi-turn interactions to facilitate effective collaboration. This limitation leads to real-world issues; for example, service chatbots must gather necessary information from customers over multiple turns to diagnose and resolve problems effectively. Despite the multi-turn nature of many real-world LLM use cases, most existing benchmarks rely on carefully curated single-turn tests, which often blur the line between memorization and genuine reasoning. To address this, we introduce the Wason Inductive Logic Test (WILT), a simple yet challenging multi-turn reasoning benchmark designed to resist memorization. WILT is inspired by the Wason 2-4-6 task, where participants must infer a boolean function involving three variables (e.g., x < y < z) by proposing test cases (such as (2, 4, 6)). In WILT, each test starts from a clean slate, with only the initial instructions provided, preventing models from relying on pre-learned responses. Over several turns, models must interact with the environment by suggesting test cases to narrow the possible hypotheses and ultimately infer the hidden function based on the outcomes. Our findings reveal that LLMs struggle with this task, exhibiting distinct strengths and weaknesses: some are better at narrowing down the hypothesis space by proposing valuable test cases, while others are more adept at deducing the hidden function from observed cases. Despite these variations, the best-performing model achieves only 28% accuracy, highlighting a significant gap in LLM performance on complex multi-turn reasoning tasks.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

Large language models (LLMs) have recently achieved impressive performance across a wide range of natural language tasks and are now widely used in real-world applications. Among them, black-box LLMs--served via APIs without access to model internals--are especially dominant due to their scalability and ease of deployment. Despite their strong capabilities, these models typically produce generalized responses that overlook personal preferences and reasoning styles. This has led to growing interest in black-box LLM personalization, which aims to tailor model outputs to user-specific context without modifying model parameters. However, existing approaches primarily focus on response-level personalization, attempting to match final outputs without modeling personal thought process. To address this limitation, we propose RPM, a framework for reasoning-level personalization that aligns the model's reasoning process with a user's personalized logic. RPM first constructs statistical user-specific factors by extracting and grouping response-influential features from user history. It then builds personalized reasoning paths that reflect how these factors are used in context. In the inference stage, RPM retrieves reasoning-aligned examples for new queries via feature-level similarity and performs inference conditioned on the structured factors and retrieved reasoning paths, enabling the model to follow user-specific reasoning trajectories. This reasoning-level personalization enhances both predictive accuracy and interpretability by grounding model outputs in user-specific logic through structured information. Extensive experiments across diverse tasks show that RPM consistently outperforms response-level personalization methods, demonstrating the effectiveness of reasoning-level personalization in black-box LLMs.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

The recent success of natural language understanding (NLU) systems has been troubled by results highlighting the failure of these models to generalize in a systematic and robust way. In this work, we introduce a diagnostic benchmark suite, named CLUTRR, to clarify some key issues related to the robustness and systematicity of NLU systems. Motivated by classic work on inductive logic programming, CLUTRR requires that an NLU system infer kinship relations between characters in short stories. Successful performance on this task requires both extracting relationships between entities, as well as inferring the logical rules governing these relationships. CLUTRR allows us to precisely measure a model's ability for systematic generalization by evaluating on held-out combinations of logical rules, and it allows us to evaluate a model's robustness by adding curated noise facts. Our empirical results highlight a substantial performance gap between state-of-the-art NLU models (e.g., BERT and MAC) and a graph neural network model that works directly with symbolic inputs---with the graph-based model exhibiting both stronger generalization and greater robustness.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Recently evolved large reasoning models (LRMs) show powerful performance in solving complex tasks with long chain-of-thought (CoT) reasoning capability. As these LRMs are mostly developed by post-training on formal reasoning tasks, whether they generalize the reasoning capability to help reduce hallucination in fact-seeking tasks remains unclear and debated. For instance, DeepSeek-R1 reports increased performance on SimpleQA, a fact-seeking benchmark, while OpenAI-o3 observes even severer hallucination. This discrepancy naturally raises the following research question: Are reasoning models more prone to hallucination? This paper addresses the question from three perspectives. (1) We first conduct a holistic evaluation for the hallucination in LRMs. Our analysis reveals that LRMs undergo a full post-training pipeline with cold start supervised fine-tuning (SFT) and verifiable reward RL generally alleviate their hallucination. In contrast, both distillation alone and RL training without cold start fine-tuning introduce more nuanced hallucinations. (2) To explore why different post-training pipelines alters the impact on hallucination in LRMs, we conduct behavior analysis. We characterize two critical cognitive behaviors that directly affect the factuality of a LRM: Flaw Repetition, where the surface-level reasoning attempts repeatedly follow the same underlying flawed logic, and Think-Answer Mismatch, where the final answer fails to faithfully match the previous CoT process. (3) Further, we investigate the mechanism behind the hallucination of LRMs from the perspective of model uncertainty. We find that increased hallucination of LRMs is usually associated with the misalignment between model uncertainty and factual accuracy. Our work provides an initial understanding of the hallucination in LRMs.

Despite the impressive performance of large language models (LLMs) in general domains, they often underperform in specialized domains. Existing approaches typically rely on data synthesis methods and yield promising results by using unlabeled data to capture domain-specific features. However, these methods either incur high computational costs or suffer from performance limitations, while also demonstrating insufficient generalization across different tasks. To address these challenges, we propose AQuilt, a framework for constructing instruction-tuning data for any specialized domains from corresponding unlabeled data, including Answer, Question, Unlabeled data, Inspection, Logic, and Task type. By incorporating logic and inspection, we encourage reasoning processes and self-inspection to enhance model performance. Moreover, customizable task instructions enable high-quality data generation for any task. As a result, we construct a dataset of 703k examples to train a powerful data synthesis model. Experiments show that AQuilt is comparable to DeepSeek-V3 while utilizing just 17% of the production cost. Further analysis demonstrates that our generated data exhibits higher relevance to downstream tasks. Source code, models, and scripts are available at https://github.com/Krueske/AQuilt.

Despite rapid advancements in large language models (LLMs), the token-level autoregressive nature constrains their complex reasoning capabilities. To enhance LLM reasoning, inference-time techniques, including Chain/Tree/Graph-of-Thought(s), successfully improve the performance, as they are fairly cost-effective by guiding reasoning through sophisticated logical structures without modifying LLMs' parameters. However, these manually predefined, task-agnostic frameworks are applied uniformly across diverse tasks, lacking adaptability. To improve this, we propose RL-of-Thoughts (RLoT), where we train a lightweight navigator model with reinforcement learning (RL) to adaptively enhance LLM reasoning at inference time. Specifically, we design five basic logic blocks from the perspective of human cognition. During the reasoning process, the trained RL navigator dynamically selects the suitable logic blocks and combines them into task-specific logical structures according to problem characteristics. Experiments across multiple reasoning benchmarks (AIME, MATH, GPQA, etc.) with multiple LLMs (GPT, Llama, Qwen, and DeepSeek) illustrate that RLoT outperforms established inference-time techniques by up to 13.4%. Remarkably, with less than 3K parameters, our RL navigator is able to make sub-10B LLMs comparable to 100B-scale counterparts. Moreover, the RL navigator demonstrates strong transferability: a model trained on one specific LLM-task pair can effectively generalize to unseen LLMs and tasks. Our code is open-source at https://anonymous.4open.science/r/RL-LLM-Reasoning-1A30 for reproducibility.

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to embed entities in vector space for logical query operations, but they suffer from subpar performance on complex queries and dataset-specific representations. In this paper, we propose a novel decoupled approach, Language-guided Abstract Reasoning over Knowledge graphs (LARK), that formulates complex KG reasoning as a combination of contextual KG search and logical query reasoning, to leverage the strengths of graph extraction algorithms and large language models (LLM), respectively. Our experiments demonstrate that the proposed approach outperforms state-of-the-art KG reasoning methods on standard benchmark datasets across several logical query constructs, with significant performance gain for queries of higher complexity. Furthermore, we show that the performance of our approach improves proportionally to the increase in size of the underlying LLM, enabling the integration of the latest advancements in LLMs for logical reasoning over KGs. Our work presents a new direction for addressing the challenges of complex KG reasoning and paves the way for future research in this area.

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering, recommendation systems, and etc. According to the graph types, existing KGR models can be roughly divided into three categories, i.e., static models, temporal models, and multi-modal models. Early works in this domain mainly focus on static KGR, and recent works try to leverage the temporal and multi-modal information, which are more practical and closer to real-world. However, no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a first survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the models are reviewed based on bi-level taxonomy, i.e., top-level (graph types) and base-level (techniques and scenarios). Besides, the performances, as well as datasets, are summarized and presented. Moreover, we point out the challenges and potential opportunities to enlighten the readers. The corresponding open-source repository is shared on GitHub https://github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

We introduce Reasoning Gym (RG), a library of reasoning environments for reinforcement learning with verifiable rewards. It provides over 100 data generators and verifiers spanning multiple domains including algebra, arithmetic, computation, cognition, geometry, graph theory, logic, and various common games. Its key innovation is the ability to generate virtually infinite training data with adjustable complexity, unlike most previous reasoning datasets, which are typically fixed. This procedural generation approach allows for continuous evaluation across varying difficulty levels. Our experimental results demonstrate the efficacy of RG in both evaluating and reinforcement learning of reasoning models.

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

Spatial reasoning is a key aspect of cognitive psychology and remains a major bottleneck for current vision-language models (VLMs). While extensive research has aimed to evaluate or improve VLMs' understanding of basic spatial relations, such as distinguishing left from right, near from far, and object counting, these tasks represent only the most fundamental level of spatial reasoning. In this work, we introduce OmniSpatial, a comprehensive and challenging benchmark for spatial reasoning, grounded in cognitive psychology. OmniSpatial covers four major categories: dynamic reasoning, complex spatial logic, spatial interaction, and perspective-taking, with 50 fine-grained subcategories. Through Internet data crawling and careful manual annotation, we construct over 1.5K question-answer pairs. Extensive experiments show that both open- and closed-source VLMs, as well as existing reasoning and spatial understanding models, exhibit significant limitations in comprehensive spatial understanding. We further analyze failure cases and propose potential directions for future research.

We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. SymbolicAI enables the seamless integration of generative models with a diverse range of solvers by treating large language models (LLMs) as semantic parsers that execute tasks based on both natural and formal language instructions, thus bridging the gap between symbolic reasoning and generative AI. We leverage probabilistic programming principles to tackle complex tasks, and utilize differentiable and classical programming paradigms with their respective strengths. The framework introduces a set of polymorphic, compositional, and self-referential operations for data stream manipulation, aligning LLM outputs with user objectives. As a result, we can transition between the capabilities of various foundation models endowed with zero- and few-shot learning capabilities and specialized, fine-tuned models or solvers proficient in addressing specific problems. In turn, the framework facilitates the creation and evaluation of explainable computational graphs. We conclude by introducing a quality measure and its empirical score for evaluating these computational graphs, and propose a benchmark that compares various state-of-the-art LLMs across a set of complex workflows. We refer to the empirical score as the "Vector Embedding for Relational Trajectory Evaluation through Cross-similarity", or VERTEX score for short. The framework codebase and benchmark are linked below.

Process Reward Models (PRMs), which provide step-by-step feedback on the reasoning generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: collecting accurate step-level error labels for training typically requires costly human annotation, and existing PRMs are limited to math reasoning problems. In response to these gaps, this paper aims to address the challenges of automatic dataset creation and the generalization of PRMs to diverse reasoning tasks. To achieve this goal, we propose FoVer, an approach for training PRMs on step-level error labels automatically annotated by formal verification tools, such as Z3 for formal logic and Isabelle for theorem proof, which provide automatic and accurate verification for symbolic tasks. Using this approach, we synthesize a training dataset with error labels on LLM responses for formal logic and theorem proof tasks without human annotation. Although this data synthesis is feasible only for tasks compatible with formal verification, we observe that LLM-based PRMs trained on our dataset exhibit cross-task generalization, improving verification across diverse reasoning tasks. Specifically, PRMs trained with FoVer significantly outperform baseline PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs trained on labels annotated by humans or stronger models, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.

Designing effective reasoning-capable LLMs typically requires training using Reinforcement Learning with Verifiable Rewards (RLVR) or distillation with carefully curated Long Chain of Thoughts (CoT), both of which depend heavily on extensive training data. This creates a major challenge when the amount of quality training data is scarce. We propose a sample-efficient, two-stage training strategy to develop reasoning LLMs under limited supervision. In the first stage, we "warm up" the model by distilling Long CoTs from a toy domain, namely, Knights \& Knaves (K\&K) logic puzzles to acquire general reasoning skills. In the second stage, we apply RLVR to the warmed-up model using a limited set of target-domain examples. Our experiments demonstrate that this two-phase approach offers several benefits: (i) the warmup phase alone facilitates generalized reasoning, leading to performance improvements across a range of tasks, including MATH, HumanEval^{+}, and MMLU-Pro. (ii) When both the base model and the warmed-up model are RLVR trained on the same small dataset (leq100 examples), the warmed-up model consistently outperforms the base model; (iii) Warming up before RLVR training allows a model to maintain cross-domain generalizability even after training on a specific domain; (iv) Introducing warmup in the pipeline improves not only accuracy but also overall sample efficiency during RLVR training. The results in this paper highlight the promise of warmup for building robust reasoning LLMs in data-scarce environments.

Semantic parsing, which converts natural language questions into logic forms, plays a crucial role in reasoning within structured environments. However, existing methods encounter two significant challenges: reliance on extensive manually annotated datasets and limited generalization capability to unseen examples. To tackle these issues, we propose Targeted Synthetic Data Generation (TARGA), a practical framework that dynamically generates high-relevance synthetic data without manual annotation. Starting from the pertinent entities and relations of a given question, we probe for the potential relevant queries through layer-wise expansion and cross-layer combination. Then we generate corresponding natural language questions for these constructed queries to jointly serve as the synthetic demonstrations for in-context learning. Experiments on multiple knowledge base question answering (KBQA) datasets demonstrate that TARGA, using only a 7B-parameter model, substantially outperforms existing non-fine-tuned methods that utilize close-sourced model, achieving notable improvements in F1 scores on GrailQA(+7.7) and KBQA-Agent(+12.2). Furthermore, TARGA also exhibits superior sample efficiency, robustness, and generalization capabilities under non-I.I.D. settings.

How should one judge whether a given large language model (LLM) can reliably perform economic reasoning? Most existing LLM benchmarks focus on specific applications and fail to present the model with a rich variety of economic tasks. A notable exception is Raman et al. [2024], who offer an approach for comprehensively benchmarking strategic decision-making; however, this approach fails to address the non-strategic settings prevalent in microeconomics, such as supply-and-demand analysis. We address this gap by taxonomizing microeconomic reasoning into 58 distinct elements, focusing on the logic of supply and demand, each grounded in up to 10 distinct domains, 5 perspectives, and 3 types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. Because it offers an automated way of generating fresh questions, auto-STEER mitigates the risk that LLMs will be trained to over-fit evaluation benchmarks; we thus hope that it will serve as a useful tool both for evaluating and fine-tuning models for years to come. We demonstrate the usefulness of our benchmark via a case study on 27 LLMs, ranging from small open-source models to the current state of the art. We examined each model's ability to solve microeconomic problems across our whole taxonomy and present the results across a range of prompting strategies and scoring metrics.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.

Large language models (LLMs) have shown remarkable performance in reasoning tasks but face limitations in mathematical and complex logical reasoning. Existing methods to improve LLMs' logical capabilities either involve traceable or verifiable logical sequences that generate more reliable responses by constructing logical structures yet increase computational costs, or introduces rigid logic template rules, reducing flexibility. In this paper, we propose Reversal of Thought (RoT), a novel framework aimed at enhancing the logical reasoning abilities of LLMs. RoT utilizes a Preference-Guided Reverse Reasoning warm-up strategy, which integrates logical symbols for pseudocode planning through meta-cognitive mechanisms and pairwise preference self-evaluation to generate task-specific prompts solely through demonstrations, aligning with LLMs' cognitive preferences shaped by Reinforcement Learning with Human Feedback (RLHF). Through reverse reasoning, we ultilize a Cognitive Preference Manager to assess knowledge boundaries and further expand LLMs' reasoning capabilities by aggregating solution logic for known tasks and stylistic templates for unknown tasks. Experiments across various tasks demonstrate that RoT surpasses existing baselines in both reasoning accuracy and efficiency.

We argue that enabling human-AI dialogue, purposed to support joint reasoning (i.e., 'inquiry'), is important for ensuring that AI decision making is aligned with human values and preferences. In particular, we point to logic-based models of argumentation and dialogue, and suggest that the traditional focus on persuasion dialogues be replaced by a focus on inquiry dialogues, and the distinct challenges that joint inquiry raises. Given recent dramatic advances in the performance of large language models (LLMs), and the anticipated increase in their use for decision making, we provide a roadmap for research into inquiry dialogues for supporting joint human-LLM reasoning tasks that are ethically salient, and that thereby require that decisions are value aligned.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt to emulate human language understanding and generation, but their competency in logical reasoning remains limited. This paper seeks to address the philosophical question: How can we effectively teach logical reasoning to LLMs while maintaining a deep understanding of the intricate relationship between language and logic? By focusing on bolstering LLMs' capabilities in logical reasoning, we aim to expand their applicability in law and other logic-intensive disciplines. To this end, we propose a Reinforcement Learning from Logical Feedback (RLLF) approach, which serves as a potential framework for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation methodology, we explore new avenues for research in this domain and contribute to the development of LLMs capable of handling complex legal reasoning tasks while acknowledging the fundamental connection between language and logic.

Prompting methods such as Chain-of-Thought (CoT) have shed new light on enhancing the reasoning capabilities of large language models, and researchers have extensively explored the generation process of rationales and answers. However, they have overlooked the potential challenges posed by the poor quality of reasoning problems, which may influence the reasoning performance significantly. In this work, we propose Self-Polish (SP), a novel method that facilitates the model's problem-solving process by prompting them to progressively refine the given problems to be more comprehensible and solvable. Specifically, the method teaches models to eliminate irrelevant information, rearrange the logic structure and organize local conditions into new ones parallelly. SP is orthogonal to all other prompting methods, making it convenient to integrate with state-of-the-art techniques for further improvement. We conduct thorough experiments on five benchmarks to illustrate the effectiveness of the proposed method. For example, with Text-davinci-003, our method boosts the performance of standard few-shot prompting by 8.0% on GSM8K and 17.8% on MultiArith; it also improves the performance of CoT by 6.0% on GSM8K and 6.0% on MathQA, respectively. Furthermore, our method also showcases impressive performance on robustness evaluation.

Theory of Mind (ToM) is a critical component of intelligence, yet accurately measuring it continues to be a subject of debate. Prior research has attempted to apply human ToM assessments to natural language processing models using either human-created standardized tests or rule-based templates. However, these methods primarily focus on simplistic reasoning and require further validation. In this study, we utilize dynamic epistemic logic, which has established overlaps with ToM, to generate more intricate problems. We also introduce novel verbalization techniques to express these problems using natural language. Our findings indicate that certain language model scaling (from 70M to 6B and 350M to 174B) does not consistently yield results better than random chance. While GPT-4 demonstrates improved epistemic reasoning capabilities, there is still room for enhancement. Our code and datasets are publicly available https://github.com/antoinelrnld/modlog https://huggingface.co/datasets/sileod/mindgames

We examine how well the state-of-the-art (SOTA) models used in legal reasoning support abductive reasoning tasks. Abductive reasoning is a form of logical inference in which a hypothesis is formulated from a set of observations, and that hypothesis is used to explain the observations. The ability to formulate such hypotheses is important for lawyers and legal scholars as it helps them articulate logical arguments, interpret laws, and develop legal theories. Our motivation is to consider the belief that deep learning models, especially large language models (LLMs), will soon replace lawyers because they perform well on tasks related to legal text processing. But to do so, we believe, requires some form of abductive hypothesis formation. In other words, while LLMs become more popular and powerful, we want to investigate their capacity for abductive reasoning. To pursue this goal, we start by building a logic-augmented dataset for abductive reasoning with 498,697 samples and then use it to evaluate the performance of a SOTA model in the legal field. Our experimental results show that although these models can perform well on tasks related to some aspects of legal text processing, they still fall short in supporting abductive reasoning tasks.

Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach.

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations (or ``chain-of-thought'' (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for symbolic programming. To make progress towards understanding in-context learning, we curate synthetic datasets containing equivalent (natural, symbolic) data pairs, where symbolic examples contain first-order logic rules and predicates from knowledge bases (KBs). Then we revisit neuro-symbolic approaches and use Language Models as Logic Programmer (LMLP) that learns from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs, recovering Prolog's backward chaining algorithm. Comprehensive experiments are included to systematically compare LMLP with CoT in deductive reasoning settings, showing that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks even with fewer parameters.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Reinforcement learning (RL) has emerged as a promising approach to improve large language model (LLM) reasoning, yet most open efforts focus narrowly on math and code, limiting our understanding of its broader applicability to general reasoning. A key challenge lies in the lack of reliable, scalable RL reward signals across diverse reasoning domains. We introduce Guru, a curated RL reasoning corpus of 92K verifiable examples spanning six reasoning domains--Math, Code, Science, Logic, Simulation, and Tabular--each built through domain-specific reward design, deduplication, and filtering to ensure reliability and effectiveness for RL training. Based on Guru, we systematically revisit established findings in RL for LLM reasoning and observe significant variation across domains. For example, while prior work suggests that RL primarily elicits existing knowledge from pretrained models, our results reveal a more nuanced pattern: domains frequently seen during pretraining (Math, Code, Science) easily benefit from cross-domain RL training, while domains with limited pretraining exposure (Logic, Simulation, and Tabular) require in-domain training to achieve meaningful performance gains, suggesting that RL is likely to facilitate genuine skill acquisition. Finally, we present Guru-7B and Guru-32B, two models that achieve state-of-the-art performance among open models RL-trained with publicly available data, outperforming best baselines by 7.9% and 6.7% on our 17-task evaluation suite across six reasoning domains. We also show that our models effectively improve the Pass@k performance of their base models, particularly on complex tasks less likely to appear in pretraining data. We release data, models, training and evaluation code to facilitate general-purpose reasoning at: https://github.com/LLM360/Reasoning360

Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter - we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought reasoning not only for logic and arithmetic tasks, but also for semantic ones (and in particular, those that are a mix of both). For example, consider prompting an LM to write code that counts the number of times it detects sarcasm in an essay: the LM may struggle to write an implementation for "detect_sarcasm(string)" that can be executed by the interpreter (handling the edge cases would be insurmountable). However, LMs may still produce a valid solution if they not only write code, but also selectively "emulate" the interpreter by generating the expected output of "detect_sarcasm(string)". In this work, we propose Chain of Code (CoC), a simple yet surprisingly effective extension that improves LM code-driven reasoning. The key idea is to encourage LMs to format semantic sub-tasks in a program as flexible pseudocode that the interpreter can explicitly catch undefined behaviors and hand off to simulate with an LM (as an "LMulator"). Experiments demonstrate that Chain of Code outperforms Chain of Thought and other baselines across a variety of benchmarks; on BIG-Bench Hard, Chain of Code achieves 84%, a gain of 12% over Chain of Thought. In a nutshell, CoC broadens the scope of reasoning questions that LMs can answer by "thinking in code".

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

Current Vision-Language Models (VLMs) struggle with fine-grained spatial reasoning, particularly when multi-step logic and precise spatial alignment are required. In this work, we introduce SpatialReasoner-R1, a vision-language reasoning model designed to address these limitations. To construct high-quality supervision for spatial reasoning, we design a Multi-Model Monte Carlo Tree Search (M3CTS) method that generates diverse, logically consistent Long Chain-of-Thought (LongCoT) reasoning trajectories. In addition, we propose fine-grained Direct Preference Optimization (fDPO), which introduces segment-specific preference granularity for descriptive grounding and logical reasoning, guided by a spatial reward mechanism that evaluates candidate responses based on visual consistency, spatial grounding, and logical coherence. Experimental results demonstrate that fDPO achieves an average improvement of 4.1% over standard DPO across spatial quality tasks, and a 9.0% gain in spatial quantity tasks. SpatialReasoner-R1, trained with fDPO, sets a new SoTA on SPATIALRGPT-Bench, outperforming the strongest baseline by 9.8% in average accuracy, while maintaining competitive performance on general vision-language tasks.

Existing retrieval benchmarks primarily consist of information-seeking queries (e.g., aggregated questions from search engines) where keyword or semantic-based retrieval is usually sufficient. However, many complex real-world queries require in-depth reasoning to identify relevant documents that go beyond surface form matching. For example, finding documentation for a coding question requires understanding the logic and syntax of the functions involved. To better benchmark retrieval on such challenging queries, we introduce BRIGHT, the first text retrieval benchmark that requires intensive reasoning to retrieve relevant documents. BRIGHT is constructed from the 1,398 real-world queries collected from diverse domains (such as economics, psychology, robotics, software engineering, earth sciences, etc.), sourced from naturally occurring or carefully curated human data. Extensive evaluation reveals that even state-of-the-art retrieval models perform poorly on BRIGHT. The leading model on the MTEB leaderboard [38 ], which achieves a score of 59.0 nDCG@10,2 produces a score of nDCG@10 of 18.0 on BRIGHT. We further demonstrate that augmenting queries with Chain-of-Thought reasoning generated by large language models (LLMs) improves performance by up to 12.2 points. Moreover, BRIGHT is robust against data leakage during pretraining of the benchmarked models as we validate by showing similar performance even when documents from the benchmark are included in the training data. We believe that BRIGHT paves the way for future research on retrieval systems in more realistic and challenging settings. Our code and data are available at https://brightbenchmark.github.io.

This paper introduces RuleArena, a novel and challenging benchmark designed to evaluate the ability of large language models (LLMs) to follow complex, real-world rules in reasoning. Covering three practical domains -- airline baggage fees, NBA transactions, and tax regulations -- RuleArena assesses LLMs' proficiency in handling intricate natural language instructions that demand long-context understanding, logical reasoning, and accurate mathematical computation. Two key attributes distinguish RuleArena from traditional rule-based reasoning benchmarks: (1) it extends beyond standard first-order logic representations, and (2) it is grounded in authentic, practical scenarios, providing insights into the suitability and reliability of LLMs for real-world applications. Our findings reveal several notable limitations in LLMs: (1) they struggle to identify and apply the appropriate rules, frequently becoming confused by similar but distinct regulations, (2) they cannot consistently perform accurate mathematical computations, even when they correctly identify the relevant rules, and (3) in general, they perform poorly in the benchmark. These results highlight significant challenges in advancing LLMs' rule-guided reasoning capabilities in real-life applications.

The rapid evolution of code largelanguage models underscores the need for effective and transparent benchmarking of their reasoning capabilities. However, the current benchmarking approach heavily depends on publicly available, human-created datasets. The widespread use of these fixed benchmark datasets makes the benchmarking process to be static and thus particularly susceptible to data contamination, an unavoidable consequence of the extensive data collection processes used to train Code LLMs. Existing approaches that address data contamination often suffer from human effort limitations and imbalanced problem complexity. To tackle these challenges, we propose \tool, a novel benchmarking suite for evaluating Code LLMs under potential data contamination. Given a seed programming problem, \tool employs multiple agents to extract and modify the context without altering the core logic, generating semantically equivalent variations. We introduce a dynamic data generation methods and conduct empirical studies on two seed datasets across 21 Code LLMs. Results show that \tool effectively benchmarks reasoning capabilities under contamination risks while generating diverse problem sets to ensure consistent and reliable evaluations.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Reasoning models are large language models that emit a long chain-of-thought before answering, providing both higher accuracy and explicit reasoning for their response. A major question has been whether language model reasoning generalizes beyond mathematics, programming, and logic, where most previous work has focused. We demonstrate that reasoning models can be post-trained for chemistry without additional domain pretraining, and require substantially less data compared to contemporary domain-specific models. We report ether0, a 24B parameter LLM (based on Mistral-Small-24B) that can reason in natural language and respond with chemical structures. This reasoning model was trained with reinforcement learning on 640,730 experimentally-grounded chemistry problems across 375 tasks ranging from synthesizability, to blood-brain barrier permeability, to human receptor activity, to scent. Our model exceeds general-purpose chemistry models, frontier models, and human experts on molecular design tasks. It is also more data efficient relative to specialized models. We anticipate that this method can be applied to train data-efficient language models specialized for tasks across a wide variety of scientific domains.

While chain-of-thought (CoT) reasoning improves the performance of large language models (LLMs) in complex tasks, it still has two main challenges: the low reliability of relying solely on LLMs to generate reasoning chains and the interference of natural language reasoning chains on the inference logic of LLMs. To address these issues, we propose CoT-RAG, a novel reasoning framework with three key designs: (i) Knowledge Graph-driven CoT Generation, featuring knowledge graphs to modulate reasoning chain generation of LLMs, thereby enhancing reasoning credibility; (ii) Learnable Knowledge Case-aware RAG, which incorporates retrieval-augmented generation (RAG) into knowledge graphs to retrieve relevant sub-cases and sub-descriptions, providing LLMs with learnable information; (iii) Pseudo-Program Prompting Execution, which encourages LLMs to execute reasoning tasks in pseudo-programs with greater logical rigor. We conduct a comprehensive evaluation on nine public datasets, covering three reasoning problems. Compared with the-state-of-the-art methods, CoT-RAG exhibits a significant accuracy improvement, ranging from 4.0% to 23.0%. Furthermore, testing on four domain-specific datasets, CoT-RAG shows remarkable accuracy and efficient execution, highlighting its strong practical applicability and scalability.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable multimodal understanding and generation capabilities. However, their understanding of synthetic charts is limited, while existing benchmarks are simplistic and the charts deviate significantly from real-world examples, making it challenging to accurately assess MLLMs' chart comprehension abilities. Hence, a challenging benchmark is essential for investigating progress and uncovering the limitations of current MLLMs on chart data. In this work, we propose to examine chart comprehension through more complex visual logic and introduce ChartBench, a comprehensive chart benchmark to accurately measure MLLMs' fundamental chart comprehension and data reliability. Specifically, ChartBench consists of 41 categories, 2K charts, and 16K QA annotations. While significantly expanding chart types, ChartBench avoids direct labelling of data points, which requires MLLMs to infer values akin to humans by leveraging elements like color, legends, and coordinate systems. We also introduce an improved metric, Acc+, which accurately reflects MLLMs' chart comprehension abilities while avoiding labor-intensive manual evaluations or costly GPT-based evaluations. We conduct evaluations on 12 mainstream open-source models and 2 outstanding proprietary models. Through extensive experiments, we reveal the limitations of MLLMs on charts and provide insights to inspire the community to pay closer attention to MLLMs' chart comprehension abilities. The benchmark and code will be publicly available for research.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

Large language models (LLMs) have demonstrated remarkable capabilities in natural language understanding and task generalization. However, their application to structured data analysis remains fragile due to inconsistencies in schema interpretation, misalignment between user intent and model output, and limited mechanisms for self-correction when failures occur. This paper introduces the STROT Framework (Structured Task Reasoning and Output Transformation), a method for structured prompting and feedback-driven transformation logic generation aimed at improving the reliability and semantic alignment of LLM-based analytical workflows. STROT begins with lightweight schema introspection and sample-based field classification, enabling dynamic context construction that captures both the structure and statistical profile of the input data. This contextual information is embedded in structured prompts that guide the model toward generating task-specific, interpretable outputs. To address common failure modes in complex queries, STROT incorporates a refinement mechanism in which the model iteratively revises its outputs based on execution feedback and validation signals. Unlike conventional approaches that rely on static prompts or single-shot inference, STROT treats the LLM as a reasoning agent embedded within a controlled analysis loop -- capable of adjusting its output trajectory through planning and correction. The result is a robust and reproducible framework for reasoning over structured data with LLMs, applicable to diverse data exploration and analysis tasks where interpretability, stability, and correctness are essential.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Large language models (LLMs) have shown increasing capability in problem-solving and decision-making, largely based on the step-by-step chain-of-thought reasoning processes. However, it has been increasingly challenging to evaluate the reasoning capability of LLMs. Concretely, existing outcome-based benchmarks begin to saturate and become less sufficient to monitor the progress. To this end, we present a process-based benchmark MR-BEN that demands a meta reasoning skill, where LMs are asked to locate and analyse potential errors in automatically generated reasoning steps. MR-BEN is a comprehensive benchmark comprising 5,975 questions collected from human experts, covering various subjects such as physics, chemistry, logic, coding, and more. Through our designed metrics for assessing meta-reasoning on this benchmark, we identify interesting limitations and weaknesses of current LLMs (open-source and closed-source models). For example, open-source models are seemingly comparable to GPT-4 on outcome-based benchmarks, but they lag far behind on our benchmark, revealing the underlying reasoning capability gap between them. Our dataset and codes are available on https://randolph-zeng.github.io/Mr-Ben.github.io/.

With the continuous advancement of large language models (LLMs), it is essential to create new benchmarks to effectively evaluate their expanding capabilities and identify areas for improvement. This work focuses on multi-image reasoning, an emerging capability in state-of-the-art LLMs. We introduce ReMI, a dataset designed to assess LLMs' ability to Reason with Multiple Images. This dataset encompasses a diverse range of tasks, spanning various reasoning domains such as math, physics, logic, code, table/chart understanding, and spatial and temporal reasoning. It also covers a broad spectrum of characteristics found in multi-image reasoning scenarios. We have benchmarked several cutting-edge LLMs using ReMI and found a substantial gap between their performance and human-level proficiency. This highlights the challenges in multi-image reasoning and the need for further research. Our analysis also reveals the strengths and weaknesses of different models, shedding light on the types of reasoning that are currently attainable and areas where future models require improvement. To foster further research in this area, we are releasing ReMI publicly: https://huggingface.co/datasets/mehrankazemi/ReMI.

Recently, diffusion models have garnered significant interest in the field of text processing due to their many potential advantages compared to conventional autoregressive models. In this work, we propose Diffusion-of-Thought (DoT), a novel approach that integrates diffusion models with Chain-of-Thought, a well-established technique for improving the reasoning ability of autoregressive language models. In contrast to autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT allows reasoning steps to diffuse over time through a diffusion language model and offers greater flexibility in trading-off computation for reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication, boolean logic, and grade school math problems, with a small diffusion model outperforming a much larger autoregressive model in both efficiency and accuracy. In addition to that, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning with diffusion language models.

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

Extensive studies have been devoted to privatizing general-domain Large Language Models (LLMs) as Domain-Specific LLMs via feeding specific-domain data. However, these privatization efforts often ignored a critical aspect: Dual Logic Ability, which is a core reasoning ability for LLMs. The dual logic ability of LLMs ensures that they can maintain a consistent stance when confronted with both positive and negative statements about the same fact. Our study focuses on how the dual logic ability of LLMs is affected during the privatization process in the medical domain. We conduct several experiments to analyze the dual logic ability of LLMs by examining the consistency of the stance in responses to paired questions about the same fact. In our experiments, interestingly, we observed a significant decrease in the dual logic ability of existing LLMs after privatization. Besides, our results indicate that incorporating general domain dual logic data into LLMs not only enhances LLMs' dual logic ability but also further improves their accuracy. These findings underscore the importance of prioritizing LLMs' dual logic ability during the privatization process. Our study establishes a benchmark for future research aimed at exploring LLMs' dual logic ability during the privatization process and offers valuable guidance for privatization efforts in real-world applications.

This paper introduces a novel approach to evaluating deep learning models' capacity for in-diagram logic interpretation. Leveraging the intriguing realm of visual illusions, we establish a unique dataset, InDL, designed to rigorously test and benchmark these models. Deep learning has witnessed remarkable progress in domains such as computer vision and natural language processing. However, models often stumble in tasks requiring logical reasoning due to their inherent 'black box' characteristics, which obscure the decision-making process. Our work presents a new lens to understand these models better by focusing on their handling of visual illusions -- a complex interplay of perception and logic. We utilize six classic geometric optical illusions to create a comparative framework between human and machine visual perception. This methodology offers a quantifiable measure to rank models, elucidating potential weaknesses and providing actionable insights for model improvements. Our experimental results affirm the efficacy of our benchmarking strategy, demonstrating its ability to effectively rank models based on their logic interpretation ability. As part of our commitment to reproducible research, the source code and datasets will be made publicly available at https://github.com/rabbit-magic-wh/InDL

Large language models (LLMs) have demonstrated remarkable reasoning capabilities in math and coding, often bolstered by post-training on the chain-of-thoughts (CoTs) generated by stronger models. However, existing strategies for curating such training data predominantly rely on heuristics, limiting generalizability and failing to capture subtleties underlying in data. To address these limitations, we leverage influence functions to systematically attribute LLMs' reasoning ability on math and coding to individual training examples, sequences, and tokens, enabling deeper insights into effective data characteristics. Our Influence-based Reasoning Attribution (Infra) uncovers nontrivial cross-domain effects across math and coding tasks: high-difficulty math examples improve both math and code reasoning, while low-difficulty code tasks most effectively benefit code reasoning. Based on these findings, we introduce a simple yet effective dataset reweighting strategy by flipping task difficulty, which doubles AIME24 accuracy from 10\% to 20\% and boosts LiveCodeBench accuracy from 33.8\% to 35.3\% for Qwen2.5-7B-Instruct. Moreover, our fine-grained attribution reveals that the sequence-level exploratory behaviors enhance reasoning performance in both math and code, and the token-level influence patterns are distinct for math and code reasoning: the former prefers natural language logic connectors and the latter emphasizes structural syntax.

This work explores enabling Chain-of-Thought (CoT) reasoning to link visual cues across multiple images. A straightforward solution is to adapt rule-based reinforcement learning for Vision-Language Models (VLMs). However, such methods typically rely on manually curated question-answer pairs, which can be particularly challenging when dealing with fine grained visual details and complex logic across images. Inspired by self-supervised visual representation learning, we observe that images contain inherent constraints that can serve as supervision. Based on this insight, we construct image triplets comprising two augmented views of the same image and a third, similar but distinct image. During training, the model is prompted to generate a reasoning process to compare these images (i.e., determine same or different). Then we optimize the model with rule-based reinforcement learning. Due to the high visual similarity and the presence of augmentations, the model must attend to subtle visual changes and perform logical reasoning to succeed. Experiments show that, although trained solely on visual comparison tasks, the learned reasoning ability generalizes effectively to a wide range of questions. Without relying on any human-annotated question-answer pairs, our method achieves significant improvements on multi-image reasoning benchmarks and shows strong performance on general vision tasks.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

The ability of Large Language Models (LLMs) to critique and refine their reasoning is crucial for their application in evaluation, feedback provision, and self-improvement. This paper introduces CriticBench, a comprehensive benchmark designed to assess LLMs' abilities to critique and rectify their reasoning across a variety of tasks. CriticBench encompasses five reasoning domains: mathematical, commonsense, symbolic, coding, and algorithmic. It compiles 15 datasets and incorporates responses from three LLM families. Utilizing CriticBench, we evaluate and dissect the performance of 17 LLMs in generation, critique, and correction reasoning, i.e., GQC reasoning. Our findings reveal: (1) a linear relationship in GQC capabilities, with critique-focused training markedly enhancing performance; (2) a task-dependent variation in correction effectiveness, with logic-oriented tasks being more amenable to correction; (3) GQC knowledge inconsistencies that decrease as model size increases; and (4) an intriguing inter-model critiquing dynamic, where stronger models are better at critiquing weaker ones, while weaker models can surprisingly surpass stronger ones in their self-critique. We hope these insights into the nuanced critique-correct reasoning of LLMs will foster further research in LLM critique and self-improvement.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Legal judgment prediction (LJP) aims to function as a judge by making final rulings based on case claims and facts, which plays a vital role in the judicial domain for supporting court decision-making and improving judicial efficiency. However, existing methods often struggle with logical errors when conducting complex legal reasoning. We propose LegalReasoner, which enhances LJP reliability through step-wise verification and correction of the reasoning process. Specifically, it first identifies dispute points to decompose complex cases, and then conducts step-wise reasoning while employing a process verifier to validate each step's logic from correctness, progressiveness, and potential perspectives. When errors are detected, expert-designed attribution and resolution strategies are applied for correction. To fine-tune LegalReasoner, we release the LegalHK dataset, containing 58,130 Hong Kong court cases with detailed annotations of dispute points, step-by-step reasoning chains, and process verification labels. Experiments demonstrate that LegalReasoner significantly improves concordance with court decisions from 72.37 to 80.27 on LLAMA-3.1-70B. The data is available at https://huggingface.co/datasets/weijiezz/LegalHK.

Large language models (LLMs) have notably progressed in multi-step and long-chain reasoning. However, extending their reasoning capabilities to encompass deep interactions with search remains a non-trivial challenge, as models often fail to identify optimal reasoning-search interaction trajectories, resulting in suboptimal responses. We propose R-Search, a novel reinforcement learning framework for Reasoning-Search integration, designed to enable LLMs to autonomously execute multi-step reasoning with deep search interaction, and learn optimal reasoning search interaction trajectories via multi-reward signals, improving response quality in complex logic- and knowledge-intensive tasks. R-Search guides the LLM to dynamically decide when to retrieve or reason, while globally integrating key evidence to enhance deep knowledge interaction between reasoning and search. During RL training, R-Search provides multi-stage, multi-type rewards to jointly optimize the reasoning-search trajectory. Experiments on seven datasets show that R-Search outperforms advanced RAG baselines by up to 32.2% (in-domain) and 25.1% (out-of-domain). The code and data are available at https://github.com/QingFei1/R-Search.

While large language models (LLMs) with Chain-of-Thought (CoT) reasoning excel in mathematics and coding, their potential for systematic reasoning in chemistry, a domain demanding rigorous structural analysis for real-world tasks like drug design and reaction engineering, remains untapped. Current benchmarks focus on simple knowledge retrieval, neglecting step-by-step reasoning required for complex tasks such as molecular optimization and reaction prediction. To address this, we introduce ChemCoTBench, a reasoning framework that bridges molecular structure understanding with arithmetic-inspired operations, including addition, deletion, and substitution, to formalize chemical problem-solving into transparent, step-by-step workflows. By treating molecular transformations as modular "chemical operations", the framework enables slow-thinking reasoning, mirroring the logic of mathematical proofs while grounding solutions in real-world chemical constraints. We evaluate models on two high-impact tasks: Molecular Property Optimization and Chemical Reaction Prediction. These tasks mirror real-world challenges while providing structured evaluability. By providing annotated datasets, a reasoning taxonomy, and baseline evaluations, ChemCoTBench bridges the gap between abstract reasoning methods and practical chemical discovery, establishing a foundation for advancing LLMs as tools for AI-driven scientific innovation.

In this paper, we introduce EconLogicQA, a rigorous benchmark designed to assess the sequential reasoning capabilities of large language models (LLMs) within the intricate realms of economics, business, and supply chain management. Diverging from traditional benchmarks that predict subsequent events individually, EconLogicQA poses a more challenging task: it requires models to discern and sequence multiple interconnected events, capturing the complexity of economic logics. EconLogicQA comprises an array of multi-event scenarios derived from economic articles, which necessitate an insightful understanding of both temporal and logical event relationships. Through comprehensive evaluations, we exhibit that EconLogicQA effectively gauges a LLM's proficiency in navigating the sequential complexities inherent in economic contexts. We provide a detailed description of EconLogicQA dataset and shows the outcomes from evaluating the benchmark across various leading-edge LLMs, thereby offering a thorough perspective on their sequential reasoning potential in economic contexts. Our benchmark dataset is available at https://huggingface.co/datasets/yinzhu-quan/econ_logic_qa.

Logical reasoning is of vital importance to natural language understanding. Previous studies either employ graph-based models to incorporate prior knowledge about logical relations, or introduce symbolic logic into neural models through data augmentation. These methods, however, heavily depend on annotated training data, and thus suffer from over-fitting and poor generalization problems due to the dataset sparsity. To address these two problems, in this paper, we propose MERIt, a MEta-path guided contrastive learning method for logical ReasonIng of text, to perform self-supervised pre-training on abundant unlabeled text data. Two novel strategies serve as indispensable components of our method. In particular, a strategy based on meta-path is devised to discover the logical structure in natural texts, followed by a counterfactual data augmentation strategy to eliminate the information shortcut induced by pre-training. The experimental results on two challenging logical reasoning benchmarks, i.e., ReClor and LogiQA, demonstrate that our method outperforms the SOTA baselines with significant improvements.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Reinforcement learning has proven its effectiveness in enhancing the reasoning capabilities of large language models. Recent research efforts have progressively extended this paradigm to multimodal reasoning tasks. Due to the inherent complexity and diversity of multimodal tasks, especially in semantic content and problem formulations, existing models often exhibit unstable performance across various domains and difficulty levels. To address these limitations, we propose VL-Cogito, an advanced multimodal reasoning model trained via a novel multi-stage Progressive Curriculum Reinforcement Learning (PCuRL) framework. PCuRL systematically guides the model through tasks of gradually increasing difficulty, substantially improving its reasoning abilities across diverse multimodal contexts. The framework introduces two key innovations: (1) an online difficulty soft weighting mechanism, dynamically adjusting training difficulty across successive RL training stages; and (2) a dynamic length reward mechanism, which encourages the model to adaptively regulate its reasoning path length according to task complexity, thus balancing reasoning efficiency with correctness. Experimental evaluations demonstrate that VL-Cogito consistently matches or surpasses existing reasoning-oriented models across mainstream multimodal benchmarks spanning mathematics, science, logic, and general understanding, validating the effectiveness of our approach.

Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a quantitative meta-analysis covering over 100 papers using CoT and ran our own evaluations of 20 datasets across 14 models. Our results show that CoT gives strong performance benefits primarily on tasks involving math or logic, with much smaller gains on other types of tasks. On MMLU, directly generating the answer without CoT leads to almost identical accuracy as CoT unless the question or model's response contains an equals sign, indicating symbolic operations and reasoning. Following this finding, we analyze the behavior of CoT on these problems by separating planning and execution and comparing against tool-augmented LLMs. Much of CoT's gain comes from improving symbolic execution, but it underperforms relative to using a symbolic solver. Our results indicate that CoT can be applied selectively, maintaining performance while saving inference costs. Furthermore, they suggest a need to move beyond prompt-based CoT to new paradigms that better leverage intermediate computation across the whole range of LLM applications.

Humans often use visual aids, for example diagrams or sketches, when solving complex problems. Training multimodal models to do the same, known as Visual Chain of Thought (Visual CoT), is challenging due to: (1) poor off-the-shelf visual CoT performance, which hinders reinforcement learning, and (2) the lack of high-quality visual CoT training data. We introduce Zebra-CoT, a diverse large-scale dataset with 182,384 samples, containing logically coherent interleaved text-image reasoning traces. We focus on four categories of tasks where sketching or visual reasoning is especially natural, spanning scientific questions such as geometry, physics, and algorithms; 2D visual reasoning tasks like visual search and jigsaw puzzles; 3D reasoning tasks including 3D multi-hop inference, embodied and robot planning; visual logic problems and strategic games like chess. Fine-tuning the Anole-7B model on the Zebra-CoT training corpus results in an improvement of +12% in our test-set accuracy and yields up to +13% performance gain on standard VLM benchmark evaluations. Fine-tuning Bagel-7B yields a model that generates high-quality interleaved visual reasoning chains, underscoring Zebra-CoT's effectiveness for developing multimodal reasoning abilities. We open-source our dataset and models to support development and evaluation of visual CoT.

Answering questions with Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs), yet its impact on Large Multimodal Models (LMMs) still lacks a systematic assessment and in-depth investigation. In this paper, we introduce MME-CoT, a specialized benchmark evaluating the CoT reasoning performance of LMMs, spanning six domains: math, science, OCR, logic, space-time, and general scenes. As the first comprehensive study in this area, we propose a thorough evaluation suite incorporating three novel metrics that assess the reasoning quality, robustness, and efficiency at a fine-grained level. Leveraging curated high-quality data and a unique evaluation strategy, we conduct an in-depth analysis of state-of-the-art LMMs, uncovering several key insights: 1) Models with reflection mechanism demonstrate a superior CoT quality, with Kimi k1.5 outperforming GPT-4o and demonstrating the highest quality results; 2) CoT prompting often degrades LMM performance on perception-heavy tasks, suggesting a potentially harmful overthinking behavior; and 3) Although the CoT quality is high, LMMs with reflection exhibit significant inefficiency in both normal response and self-correction phases. We hope MME-CoT serves as a foundation for advancing multimodal reasoning in LMMs. Project Page: https://mmecot.github.io/

Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based reasoning solutions usually suffer from significant performance degradation on huge evidence (tables). In addition, most existing methods struggle to reason over complex questions since the required information is scattered in different places. To alleviate the above challenges, we exploit large language models (LLMs) as decomposers for effective table-based reasoning, which (i) decompose huge evidence (a huge table) into sub-evidence (a small table) to mitigate the interference of useless information for table reasoning; and (ii) decompose complex questions into simpler sub-questions for text reasoning. Specifically, we first use the LLMs to break down the evidence (tables) involved in the current question, retaining the relevant evidence and excluding the remaining irrelevant evidence from the huge table. In addition, we propose a "parsing-execution-filling" strategy to alleviate the hallucination dilemma of the chain of thought by decoupling logic and numerical computation in each step. Extensive experiments show that our method can effectively leverage decomposed evidence and questions and outperforms the strong baselines on TabFact, WikiTableQuestion, and FetaQA datasets. Notably, our model outperforms human performance for the first time on the TabFact dataset.

Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.

In large language models (LLMs), code and reasoning reinforce each other: code offers an abstract, modular, and logic-driven structure that supports reasoning, while reasoning translates high-level goals into smaller, executable steps that drive more advanced code intelligence. In this study, we examine how code serves as a structured medium for enhancing reasoning: it provides verifiable execution paths, enforces logical decomposition, and enables runtime validation. We also explore how improvements in reasoning have transformed code intelligence from basic completion to advanced capabilities, enabling models to address complex software engineering tasks through planning and debugging. Finally, we identify key challenges and propose future research directions to strengthen this synergy, ultimately improving LLM's performance in both areas.

Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped to correct FOL rules predicted by GPT-3.5, and can achieve similar performance as GPT-4 with a fraction of the cost. This correction ability was achieved by a novel supervised fine-tuning (SFT) + reinforcement learning with human feedback (RLHF) framework, which initially trains on synthetically perturbed NL-FOL pairs to encourage chain-of-thought reasoning and then fine-tunes with RLHF on GPT-3.5 outputs using a FOL verifier as the reward model. To train LogicLLaMA, we present MALLS (large language Model generAted NL-FOL pairS), a dataset of 34K high-quality and diverse sentence-level NL-FOL pairs collected from GPT-4. The dataset was created by implementing a pipeline that prompts GPT-4 for pairs, and dynamically adjusts the prompts to ensure the collection of pairs with rich and diverse contexts at different levels of complexity, and verifies the validity of the generated FOL rules. Codes, weights, and data are available at https://github.com/gblackout/LogicLLaMA{{small https://github.com/gblackout/LogicLLaMA}}.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

Language is not monolithic. While many benchmarks are used as proxies to systematically estimate Large Language Models' (LLM) performance in real-life tasks, they tend to ignore the nuances of within-language variation and thus fail to model the experience of speakers of minority dialects. Focusing on African American Vernacular English (AAVE), we present the first study on LLMs' fairness and robustness to a dialect in canonical reasoning tasks (algorithm, math, logic, and comprehensive reasoning). We hire AAVE speakers, including experts with computer science backgrounds, to rewrite seven popular benchmarks, such as HumanEval and GSM8K. The result of this effort is ReDial, a dialectal benchmark comprising 1.2K+ parallel query pairs in Standardized English and AAVE. We use ReDial to evaluate state-of-the-art LLMs, including GPT-4o/4/3.5-turbo, LLaMA-3.1/3, Mistral, and Phi-3. We find that, compared to Standardized English, almost all of these widely used models show significant brittleness and unfairness to queries in AAVE. Furthermore, AAVE queries can degrade performance more substantially than misspelled texts in Standardized English, even when LLMs are more familiar with the AAVE queries. Finally, asking models to rephrase questions in Standardized English does not close the performance gap but generally introduces higher costs. Overall, our findings indicate that LLMs provide unfair service to dialect users in complex reasoning tasks. Code can be found at https://github.com/fangru-lin/redial_dialect_robustness_fairness.git.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large language models perform poorly on this task. In contrast, we show that a simple structure-aware classifier outperforms the best language model by 5.46% on Logic and 4.51% on LogicClimate. We encourage future work to explore this task as (a) it can serve as a new reasoning challenge for language models, and (b) it can have potential applications in tackling the spread of misinformation. Our dataset and code are available at https://github.com/causalNLP/logical-fallacy

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, their reasoning can be unsound, inconsistent, or rely on undesirable prior assumptions. To tackle these issues, we introduce a class of tools for language models called guides that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call LogicGuide. Given a reasoning problem in natural language, a model can formalize its assumptions for LogicGuide and then guarantee that its reasoning steps are sound. In experiments with the PrOntoQA and ProofWriter reasoning datasets, LogicGuide significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35%). LogicGuide also drastically reduces content effects: the interference of prior and current assumptions that both humans and language models have been shown to suffer from. Finally, we explore bootstrapping LLaMA 13B from its own reasoning and find that LogicGuide is critical: by training only on certified self-generated reasoning, LLaMA can self-improve, avoiding learning from its own hallucinations.

Deductive reasoning is a crucial logical capability that assists us in solving complex problems based on existing knowledge. Although augmented by Chain-of-Thought prompts, Large Language Models (LLMs) might not follow the correct reasoning paths. Enhancing the deductive reasoning abilities of LLMs, and leveraging their extensive built-in knowledge for various reasoning tasks, remains an open question. Attempting to mimic the human deductive reasoning paradigm, we propose a multi-stage Syllogistic-Reasoning Framework of Thought (SR-FoT) that enables LLMs to perform syllogistic deductive reasoning to handle complex knowledge-based reasoning tasks. Our SR-FoT begins by interpreting the question and then uses the interpretation and the original question to propose a suitable major premise. It proceeds by generating and answering minor premise questions in two stages to match the minor premises. Finally, it guides LLMs to use the previously generated major and minor premises to perform syllogistic deductive reasoning to derive the answer to the original question. Extensive and thorough experiments on knowledge-based reasoning tasks have demonstrated the effectiveness and advantages of our SR-FoT.

Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs' capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs' LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) is a challenging task. Recently, a line of message-passing-based research has been proposed to solve CQA. However, they perform unsatisfactorily on negative queries and fail to address the noisy messages between variable nodes in the query graph. Moreover, they offer little interpretability and require complex query data and resource-intensive training. In this paper, we propose a Neural-Symbolic Message Passing (NSMP) framework based on pre-trained neural link predictors. By introducing symbolic reasoning and fuzzy logic, NSMP can generalize to arbitrary existential first order logic queries without requiring training while providing interpretable answers. Furthermore, we introduce a dynamic pruning strategy to filter out noisy messages between variable nodes. Experimental results show that NSMP achieves a strong performance. Additionally, through complexity analysis and empirical verification, we demonstrate the superiority of NSMP in inference time over the current state-of-the-art neural-symbolic method. Compared to this approach, NSMP demonstrates faster inference times across all query types on benchmark datasets, with speedup ranging from 2times to over 150times.

The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

Large language models (LLMs) trained on code completion have been shown to be capable of synthesizing simple Python programs from docstrings [1]. We find that these code-writing LLMs can be re-purposed to write robot policy code, given natural language commands. Specifically, policy code can express functions or feedback loops that process perception outputs (e.g.,from object detectors [2], [3]) and parameterize control primitive APIs. When provided as input several example language commands (formatted as comments) followed by corresponding policy code (via few-shot prompting), LLMs can take in new commands and autonomously re-compose API calls to generate new policy code respectively. By chaining classic logic structures and referencing third-party libraries (e.g., NumPy, Shapely) to perform arithmetic, LLMs used in this way can write robot policies that (i) exhibit spatial-geometric reasoning, (ii) generalize to new instructions, and (iii) prescribe precise values (e.g., velocities) to ambiguous descriptions ("faster") depending on context (i.e., behavioral commonsense). This paper presents code as policies: a robot-centric formulation of language model generated programs (LMPs) that can represent reactive policies (e.g., impedance controllers), as well as waypoint-based policies (vision-based pick and place, trajectory-based control), demonstrated across multiple real robot platforms. Central to our approach is prompting hierarchical code-gen (recursively defining undefined functions), which can write more complex code and also improves state-of-the-art to solve 39.8% of problems on the HumanEval [1] benchmark. Code and videos are available at https://code-as-policies.github.io

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if P and Q, then R" for some propositions P, Q, and R. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.

This paper investigates the rational thinking capability of Large Language Models (LLMs) in multi-round argumentative debates by exploring the impact of fallacious arguments on their logical reasoning performance. More specifically, we present Logic Competence Measurement Benchmark (LOGICOM), a diagnostic benchmark to assess the robustness of LLMs against logical fallacies. LOGICOM involves two agents: a persuader and a debater engaging in a multi-round debate on a controversial topic, where the persuader tries to convince the debater of the correctness of its claim. First, LOGICOM assesses the potential of LLMs to change their opinions through reasoning. Then, it evaluates the debater's performance in logical reasoning by contrasting the scenario where the persuader employs logical fallacies against one where logical reasoning is used. We use this benchmark to evaluate the performance of GPT-3.5 and GPT-4 using a dataset containing controversial topics, claims, and reasons supporting them. Our findings indicate that both GPT-3.5 and GPT-4 can adjust their opinion through reasoning. However, when presented with logical fallacies, GPT-3.5 and GPT-4 are erroneously convinced 41% and 69% more often, respectively, compared to when logical reasoning is used. Finally, we introduce a new dataset containing over 5k pairs of logical vs. fallacious arguments. The source code and dataset of this work are made publicly available.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Spatial intelligence is essential for multimodal large language models (MLLMs) operating in the complex physical world. Existing benchmarks, however, probe only single-image relations and thus fail to assess the multi-image spatial reasoning that real-world deployments demand. We introduce MMSI-Bench, a VQA benchmark dedicated to multi-image spatial intelligence. Six 3D-vision researchers spent more than 300 hours meticulously crafting 1,000 challenging, unambiguous multiple-choice questions from over 120,000 images, each paired with carefully designed distractors and a step-by-step reasoning process. We conduct extensive experiments and thoroughly evaluate 34 open-source and proprietary MLLMs, observing a wide gap: the strongest open-source model attains roughly 30% accuracy and OpenAI's o3 reasoning model reaches 40%, while humans score 97%. These results underscore the challenging nature of MMSI-Bench and the substantial headroom for future research. Leveraging the annotated reasoning processes, we also provide an automated error analysis pipeline that diagnoses four dominant failure modes, including (1) grounding errors, (2) overlap-matching and scene-reconstruction errors, (3) situation-transformation reasoning errors, and (4) spatial-logic errors, offering valuable insights for advancing multi-image spatial intelligence. Project page: https://runsenxu.com/projects/MMSI_Bench .

Despite the successes of recent developments in visual AI, different shortcomings still exist; from missing exact logical reasoning, to abstract generalization abilities, to understanding complex and noisy scenes. Unfortunately, existing benchmarks, were not designed to capture more than a few of these aspects. Whereas deep learning datasets focus on visually complex data but simple visual reasoning tasks, inductive logic datasets involve complex logical learning tasks, however, lack the visual component. To address this, we propose the visual logical learning dataset, V-LoL, that seamlessly combines visual and logical challenges. Notably, we introduce the first instantiation of V-LoL, V-LoL-Trains, -- a visual rendition of a classic benchmark in symbolic AI, the Michalski train problem. By incorporating intricate visual scenes and flexible logical reasoning tasks within a versatile framework, V-LoL-Trains provides a platform for investigating a wide range of visual logical learning challenges. We evaluate a variety of AI systems including traditional symbolic AI, neural AI, as well as neuro-symbolic AI. Our evaluations demonstrate that even state-of-the-art AI faces difficulties in dealing with visual logical learning challenges, highlighting unique advantages and limitations specific to each methodology. Overall, V-LoL opens up new avenues for understanding and enhancing current abilities in visual logical learning for AI systems.

Commonsense question answering (QA) research requires machines to answer questions based on commonsense knowledge. However, this research requires expensive labor costs to annotate data as the basis of research, and models that rely on fine-tuning paradigms only apply to specific tasks, rather than learn a general commonsense reasoning ability. As a more robust method, zero-shot commonsense question answering shows a good prospect. The current zero-shot framework tries to convert triples in commonsense knowledge graphs (KGs) into QA-form samples as the pre-trained data source to incorporate commonsense knowledge into the model. However, this method ignores the multi-hop relationship in the KG, which is also an important central problem in commonsense reasoning. In this paper, we propose a novel multi-hop commonsense knowledge injection framework. Specifically, it explores multi-hop reasoning paradigm in KGs that conform to linguistic logic, and we further propose two multi-hop QA generation methods based on KGs. Then, we utilize contrastive learning to pre-train the model with the synthetic QA dataset to inject multi-hop commonsense knowledge. Extensive experiments on five commonsense question answering benchmarks demonstrate that our framework achieves state-of-art performance.

In real-life scenarios, humans seek out objects in the 3D world to fulfill their daily needs or intentions. This inspires us to introduce 3D intention grounding, a new task in 3D object detection employing RGB-D, based on human intention, such as "I want something to support my back". Closely related, 3D visual grounding focuses on understanding human reference. To achieve detection based on human intention, it relies on humans to observe the scene, reason out the target that aligns with their intention ("pillow" in this case), and finally provide a reference to the AI system, such as "A pillow on the couch". Instead, 3D intention grounding challenges AI agents to automatically observe, reason and detect the desired target solely based on human intention. To tackle this challenge, we introduce the new Intent3D dataset, consisting of 44,990 intention texts associated with 209 fine-grained classes from 1,042 scenes of the ScanNet dataset. We also establish several baselines based on different language-based 3D object detection models on our benchmark. Finally, we propose IntentNet, our unique approach, designed to tackle this intention-based detection problem. It focuses on three key aspects: intention understanding, reasoning to identify object candidates, and cascaded adaptive learning that leverages the intrinsic priority logic of different losses for multiple objective optimization.

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.

Large Language Models have excelled in remarkable reasoning capabilities with advanced prompting techniques, but they fall short on tasks that require exploration, strategic foresight, and sequential decision-making. Recent works propose to utilize external programs to define search logic, such that LLMs can perform passive tree search to solve more challenging reasoning tasks. Though impressive results have been achieved, there are several fundamental limitations of these approaches. First, passive tree searches are not efficient as they usually require multiple rounds of LLM API calls to solve one single problem. Moreover, passive search methods are not flexible since they need task-specific program designs. Then a natural question arises: can we maintain the tree-search capability of LLMs without the aid of external programs, and can still generate responses that clearly demonstrate the process of a tree-structure search? To this end, we propose a new concept called autonomous tree-search ability of LLM, which can automatically generate a response containing search trajectories for the correct answer. Concretely, we perform search trajectories using capable LLM API via a fixed system prompt, allowing them to perform autonomous tree-search (ATS) right out of the box. Experiments on 4 puzzle games demonstrate our method can achieve huge improvements. The ATS-BFS method outperforms the Chain of Thought approach by achieving an average accuracy improvement of 33%. Compared to Tree of Thoughts, it requires 65.6% or 47.7% less GPT-api cost to attain a comparable level of accuracy. Moreover, we have collected data using the ATS prompt method and fine-tuned LLaMA. This approach yield a greater improvement compared to the ones fine-tuned on CoT data. Specifically, it outperforms CoT-tuned LLaMAs by an average of 40.6% and 38.5% for LLaMA2-7B and LLaMA2-13B, respectively.

The unprecedented surge in video data production in recent years necessitates efficient tools to extract meaningful frames from videos for downstream tasks. Long-term temporal reasoning is a key desideratum for frame retrieval systems. While state-of-the-art foundation models, like VideoLLaMA and ViCLIP, are proficient in short-term semantic understanding, they surprisingly fail at long-term reasoning across frames. A key reason for this failure is that they intertwine per-frame perception and temporal reasoning into a single deep network. Hence, decoupling but co-designing semantic understanding and temporal reasoning is essential for efficient scene identification. We propose a system that leverages vision-language models for semantic understanding of individual frames but effectively reasons about the long-term evolution of events using state machines and temporal logic (TL) formulae that inherently capture memory. Our TL-based reasoning improves the F1 score of complex event identification by 9-15% compared to benchmarks that use GPT4 for reasoning on state-of-the-art self-driving datasets such as Waymo and NuScenes.

The meaning of complex phrases in natural language is composed of their individual components. The task of compositional generalization evaluates a model's ability to understand new combinations of components. Previous studies trained smaller, task-specific models, which exhibited poor generalization. While large language models (LLMs) exhibit impressive generalization abilities on many tasks through in-context learning (ICL), their potential for compositional generalization remains unexplored. In this paper, we first empirically investigate prevailing ICL methods in compositional generalization. We find that they struggle with complex compositional questions due to cumulative errors in long reasoning steps and intricate logic required for tool-making. Consequently, we propose a human-guided tool manipulation framework (HTM) that generates tools for sub-questions and integrates multiple tools. Our method enhances the effectiveness of tool creation and usage with minimal human effort. Experiments show that our method achieves state-of-the-art performance on two compositional generalization benchmarks and outperforms existing methods on the most challenging test split by 70%.

Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being learned in these studies and introduce a simple domain specific language and a systematic translation from this language to first-order logic. By recasting the target representations in terms of classical logic, we aim to broaden the applicability of existing code datasets for investigating more complex natural language understanding and reasoning problems in the software domain.

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the Anchored Diffusion Language Model (ADLM), a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art performance in zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches

The advanced processing and reasoning capabilities of multimodal large language models (MLLMs) have driven substantial progress in vision-language (VL) understanding tasks. However, while effective for tasks governed by straightforward logic, MLLMs often encounter challenges when reasoning over complex, interdependent logic structures. To address this limitation, we introduce AgentPS, a novel framework that integrates Agentic Process Supervision into MLLMs via multi-round question answering during fine-tuning. AgentPS demonstrates significant performance improvements over baseline MLLMs on proprietary TikTok datasets, due to its integration of process supervision and structured sequential reasoning. Furthermore, we show that replacing human-annotated labels with LLM-generated labels retains much of the performance gain, highlighting the framework's practical scalability in industrial applications. These results position AgentPS as a highly effective and efficient architecture for multimodal classification tasks. Its adaptability and scalability, especially when enhanced by automated annotation generation, make it a powerful tool for handling large-scale, real-world challenges.

The ModelWriter platform provides a generic framework for automated traceability analysis. In this paper, we demonstrate how this framework can be used to trace the consistency and completeness of technical documents that consist of a set of System Installation Design Principles used by Airbus to ensure the correctness of aircraft system installation. We show in particular, how the platform allows the integration of two types of reasoning: reasoning about the meaning of text using semantic parsing and description logic theorem proving; and reasoning about document structure using first-order relational logic and finite model finding for traceability analysis.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Human intelligence thrives on the concept of cognitive synergy, where collaboration and information integration among different cognitive processes yield superior outcomes compared to individual cognitive processes in isolation. Although Large Language Models (LLMs) have demonstrated promising performance as general task-solving agents, they still struggle with tasks that require intensive domain knowledge and complex reasoning. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist refers to an intelligent agent that collaborates with multiple minds, combining their individual strengths and knowledge, to enhance problem-solving and overall performance in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. We have discovered that assigning multiple, fine-grained personas in LLMs elicits better problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, SPP effectively elicits internal knowledge acquisition abilities, reduces hallucination, and maintains strong reasoning capabilities. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Traditional autonomous driving systems often struggle to connect high-level reasoning with low-level control, leading to suboptimal and sometimes unsafe behaviors. Recent advances in multimodal large language models (MLLMs), which process both visual and textual data, offer an opportunity to unify perception and reasoning. However, effectively embedding precise safety knowledge into MLLMs for autonomous driving remains a significant challenge. To address this, we propose SafeAuto, a framework that enhances MLLM-based autonomous driving by incorporating both unstructured and structured knowledge. First, we introduce a Position-Dependent Cross-Entropy (PDCE) loss to improve low-level control signal predictions when values are represented as text. Second, to explicitly integrate safety knowledge, we develop a reasoning component that translates traffic rules into first-order logic (e.g., "red light implies stop") and embeds them into a probabilistic graphical model (e.g., Markov Logic Network) to verify predicted actions using recognized environmental attributes. Additionally, our Multimodal Retrieval-Augmented Generation (RAG) model leverages video, control signals, and environmental attributes to learn from past driving experiences. Integrating PDCE, MLN, and Multimodal RAG, SafeAuto outperforms existing baselines across multiple datasets, enabling more accurate, reliable, and safer autonomous driving. The code is available at https://github.com/AI-secure/SafeAuto.

Program-of-Thought (PoT) replaces natural language-based Chain-of-Thought (CoT) as the most popular method in Large Language Models (LLMs) mathematical reasoning tasks by utilizing external tool calls to circumvent computational errors. However, our evaluation of the GPT-4 and Llama series reveals that using PoT introduces more reasoning errors, such as incorrect formulas or flawed logic, compared to CoT. To address this issue, we propose Human-Think Language (HTL), which leverages a suite of strategies that help integrate PoT and CoT, encompassing: (1) a new generation paradigm that uses full CoT reasoning to control code generation. (2) Focus Attention, that directs model attention to the CoT reasoning during PoT to generate more logical code. (3) reinforcement learning that utilizes the accuracy of both CoT and PoT responses as rewards to prevent repetitive reasoning steps in LLMs when solving difficult math problems. Our method achieves an average improvement of 6.5% on the Llama-Base model and 4.3% on the Mistral-Base model across 8 mathematical calculation datasets. It also shows significant effectiveness on five out-of-domain datasets by controlling the model's information flow, exhibiting strong transferability. Additionally, HTL shows the most significant improvement in non-mathematical natural language inference task, contributing to a unified reasoning task framework

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Large Language Models (LLMs) perform well on familiar queries but struggle with specialized or emerging topics. Graph-based Retrieval-Augmented Generation (GraphRAG) addresses this by structuring domain knowledge as a graph for dynamic retrieval. However, existing pipelines involve complex engineering workflows, making it difficult to isolate the impact of individual components. Evaluating retrieval effectiveness is also challenging due to dataset overlap with LLM pretraining data. In this work, we introduce HuixiangDou2, a robustly optimized GraphRAG framework. Specifically, we leverage the effectiveness of dual-level retrieval and optimize its performance in a 32k context for maximum precision, and compare logic-based retrieval and dual-level retrieval to enhance overall functionality. Our implementation includes comparative experiments on a test set, where Qwen2.5-7B-Instruct initially underperformed. With our approach, the score improved significantly from 60 to 74.5, as illustrated in the Figure. Experiments on domain-specific datasets reveal that dual-level retrieval enhances fuzzy matching, while logic-form retrieval improves structured reasoning. Furthermore, we propose a multi-stage verification mechanism to improve retrieval robustness without increasing computational cost. Empirical results show significant accuracy gains over baselines, highlighting the importance of adaptive retrieval. To support research and adoption, we release HuixiangDou2 as an open-source resource https://github.com/tpoisonooo/huixiangdou2.

While text-to-visual models now produce photo-realistic images and videos, they struggle with compositional text prompts involving attributes, relationships, and higher-order reasoning such as logic and comparison. In this work, we conduct an extensive human study on GenAI-Bench to evaluate the performance of leading image and video generation models in various aspects of compositional text-to-visual generation. We also compare automated evaluation metrics against our collected human ratings and find that VQAScore -- a metric measuring the likelihood that a VQA model views an image as accurately depicting the prompt -- significantly outperforms previous metrics such as CLIPScore. In addition, VQAScore can improve generation in a black-box manner (without finetuning) via simply ranking a few (3 to 9) candidate images. Ranking by VQAScore is 2x to 3x more effective than other scoring methods like PickScore, HPSv2, and ImageReward at improving human alignment ratings for DALL-E 3 and Stable Diffusion, especially on compositional prompts that require advanced visio-linguistic reasoning. We will release a new GenAI-Rank benchmark with over 40,000 human ratings to evaluate scoring metrics on ranking images generated from the same prompt. Lastly, we discuss promising areas for improvement in VQAScore, such as addressing fine-grained visual details. We will release all human ratings (over 80,000) to facilitate scientific benchmarking of both generative models and automated metrics.

This article reports the results of a study examining the ability of legal and non-legal Large Language Models to perform legal analysis using the Issue-Rule-Application-Conclusion framework. LLMs were tested on legal reasoning tasks involving rule analysis and analogical reasoning. The results show that LLMs can conduct basic IRAC analysis, but are limited by brief responses lacking detail, an inability to commit to answers, false confidence, and hallucinations. The study compares legal and nonlegal LLMs, identifies shortcomings, and explores traits that may hinder their ability to think like a lawyer. It also discusses the implications for legal education and practice, highlighting the need for critical thinking skills in future lawyers and the potential pitfalls of overreliance on artificial intelligence AI resulting in a loss of logic, reasoning, and critical thinking skills.

The recently developed retrieval-augmented generation (RAG) technology has enabled the efficient construction of domain-specific applications. However, it also has limitations, including the gap between vector similarity and the relevance of knowledge reasoning, as well as insensitivity to knowledge logic, such as numerical values, temporal relations, expert rules, and others, which hinder the effectiveness of professional knowledge services. In this work, we introduce a professional domain knowledge service framework called Knowledge Augmented Generation (KAG). KAG is designed to address the aforementioned challenges with the motivation of making full use of the advantages of knowledge graph(KG) and vector retrieval, and to improve generation and reasoning performance by bidirectionally enhancing large language models (LLMs) and KGs through five key aspects: (1) LLM-friendly knowledge representation, (2) mutual-indexing between knowledge graphs and original chunks, (3) logical-form-guided hybrid reasoning engine, (4) knowledge alignment with semantic reasoning, and (5) model capability enhancement for KAG. We compared KAG with existing RAG methods in multihop question answering and found that it significantly outperforms state-of-theart methods, achieving a relative improvement of 19.6% on 2wiki and 33.5% on hotpotQA in terms of F1 score. We have successfully applied KAG to two professional knowledge Q&A tasks of Ant Group, including E-Government Q&A and E-Health Q&A, achieving significant improvement in professionalism compared to RAG methods.

Research has a long history of discussing what is superior in predicting certain outcomes: statistical methods or the human brain. This debate has repeatedly been sparked off by the remarkable technological advances in the field of artificial intelligence (AI), such as solving tasks like object and speech recognition, achieving significant improvements in accuracy through deep-learning algorithms (Goodfellow et al. 2016), or combining various methods of computational intelligence, such as fuzzy logic, genetic algorithms, and case-based reasoning (Medsker 2012). One of the implicit promises that underlie these advancements is that machines will 1 day be capable of performing complex tasks or may even supersede humans in performing these tasks. This triggers new heated debates of when machines will ultimately replace humans (McAfee and Brynjolfsson 2017). While previous research has proved that AI performs well in some clearly defined tasks such as playing chess, playing Go or identifying objects on images, it is doubted that the development of an artificial general intelligence (AGI) which is able to solve multiple tasks at the same time can be achieved in the near future (e.g., Russell and Norvig 2016). Moreover, the use of AI to solve complex business problems in organizational contexts occurs scarcely, and applications for AI that solve complex problems remain mainly in laboratory settings instead of being implemented in practice. Since the road to AGI is still a long one, we argue that the most likely paradigm for the division of labor between humans and machines in the next decades is Hybrid Intelligence. This concept aims at using the complementary strengths of human intelligence and AI, so that they can perform better than each of the two could separately (e.g., Kamar 2016).

Solving complex reasoning tasks is a key real-world application of agents. Thanks to the pretraining of Large Language Models (LLMs) on code data, recent approaches like CodeAct successfully use code as LLM agents' action, achieving good results. However, CodeAct greedily generates the next action's code block by relying on fragmented thoughts, resulting in inconsistency and instability. Moreover, CodeAct lacks action-related ground-truth (GT), making its supervision signals and termination conditions questionable in multi-turn interactions. To address these issues, we first introduce a simple yet effective end-to-end code generation paradigm, CodeProgram, which leverages code's systematic logic to align with global reasoning and enable cohesive problem-solving. Then, we propose Tree-of-Code (ToC), which self-grows CodeProgram nodes based on the executable nature of the code and enables self-supervision in a GT-free scenario. Experimental results on two datasets using ten popular zero-shot LLMs show ToC remarkably boosts accuracy by nearly 20% over CodeAct with less than 1/4 turns. Several LLMs even perform better on one-turn CodeProgram than on multi-turn CodeAct. To further investigate the trade-off between efficacy and efficiency, we test different ToC tree sizes and exploration mechanisms. We also highlight the potential of ToC's end-to-end data generation for supervised and reinforced fine-tuning.

The rapid evolution of large language models (LLMs) has transformed the competitive landscape in natural language processing (NLP), particularly for English and other data-rich languages. However, underrepresented languages like Cantonese, spoken by over 85 million people, face significant development gaps, which is particularly concerning given the economic significance of the Guangdong-Hong Kong-Macau Greater Bay Area, and in substantial Cantonese-speaking populations in places like Singapore and North America. Despite its wide use, Cantonese has scant representation in NLP research, especially compared to other languages from similarly developed regions. To bridge these gaps, we outline current Cantonese NLP methods and introduce new benchmarks designed to evaluate LLM performance in factual generation, mathematical logic, complex reasoning, and general knowledge in Cantonese, which aim to advance open-source Cantonese LLM technology. We also propose future research directions and recommended models to enhance Cantonese LLM development.

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.

Recent advances in zero-shot and few-shot learning have shown promise for a scope of research and practical purposes. However, this fast-growing area lacks standardized evaluation suites for non-English languages, hindering progress outside the Anglo-centric paradigm. To address this line of research, we propose TAPE (Text Attack and Perturbation Evaluation), a novel benchmark that includes six more complex NLU tasks for Russian, covering multi-hop reasoning, ethical concepts, logic and commonsense knowledge. The TAPE's design focuses on systematic zero-shot and few-shot NLU evaluation: (i) linguistic-oriented adversarial attacks and perturbations for analyzing robustness, and (ii) subpopulations for nuanced interpretation. The detailed analysis of testing the autoregressive baselines indicates that simple spelling-based perturbations affect the performance the most, while paraphrasing the input has a more negligible effect. At the same time, the results demonstrate a significant gap between the neural and human baselines for most tasks. We publicly release TAPE (tape-benchmark.com) to foster research on robust LMs that can generalize to new tasks when little to no supervision is available.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

In precision-oriented tasks like answer ranking, it is more important to rank many relevant answers highly than to retrieve all relevant answers. It follows that a good ranking strategy would be to learn how to identify the easiest correct answers first (i.e., assign a high ranking score to answers that have characteristics that usually indicate relevance, and a low ranking score to those with characteristics that do not), before incorporating more complex logic to handle difficult cases (e.g., semantic matching or reasoning). In this work, we apply this idea to the training of neural answer rankers using curriculum learning. We propose several heuristics to estimate the difficulty of a given training sample. We show that the proposed heuristics can be used to build a training curriculum that down-weights difficult samples early in the training process. As the training process progresses, our approach gradually shifts to weighting all samples equally, regardless of difficulty. We present a comprehensive evaluation of our proposed idea on three answer ranking datasets. Results show that our approach leads to superior performance of two leading neural ranking architectures, namely BERT and ConvKNRM, using both pointwise and pairwise losses. When applied to a BERT-based ranker, our method yields up to a 4% improvement in MRR and a 9% improvement in P@1 (compared to the model trained without a curriculum). This results in models that can achieve comparable performance to more expensive state-of-the-art techniques.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.