Daily Papers

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

Pretraining datasets for large language models (LLMs) have grown to trillions of tokens composed of large amounts of CommonCrawl (CC) web scrape along with smaller, domain-specific datasets. It is expensive to understand the impact of these domain-specific datasets on model capabilities as training at large FLOP scales is required to reveal significant changes to difficult and emergent benchmarks. Given the increasing cost of experimenting with pretraining data, how does one determine the optimal balance between the diversity in general web scrapes and the information density of domain specific data? In this work, we show how to leverage the smaller domain specific datasets by upsampling them relative to CC at the end of training to drive performance improvements on difficult benchmarks. This simple technique allows us to improve up to 6.90 pp on MMLU, 8.26 pp on GSM8K, and 6.17 pp on HumanEval relative to the base data mix for a 7B model trained for 1 trillion (T) tokens, thus rivaling Llama-2 (7B)x2014a model trained for twice as long. We experiment with ablating the duration of domain upsampling from 5% to 30% of training and find that 10% to 20% percent is optimal for navigating the tradeoff between general language modeling capabilities and targeted benchmarks. We also use domain upsampling to characterize at scale the utility of individual datasets for improving various benchmarks by removing them during this final phase of training. This tool opens up the ability to experiment with the impact of different pretraining datasets at scale, but at an order of magnitude lower cost compared to full pretraining runs.

Human preference plays a crucial role in the refinement of large language models (LLMs). However, collecting human preference feedback is costly and most existing datasets neglect the correlation between personalization and preferences. To address this issue, we introduce Fair-PP, a synthetic dataset of personalized preferences targeting social equity, derived from real-world social survey data, which includes 28 social groups, 98 equity topics, and 5 personal preference dimensions. Leveraging GPT-4o-mini, we engage in role-playing based on seven representative persona portrayals guided by existing social survey data, yielding a total of 238,623 preference records. Through Fair-PP, we also contribute (i) An automated framework for generating preference data, along with a more fine-grained dataset of personalized preferences; (ii) analysis of the positioning of the existing mainstream LLMs across five major global regions within the personalized preference space; and (iii) a sample reweighting method for personalized preference alignment, enabling alignment with a target persona while maximizing the divergence from other personas. Empirical experiments show our method outperforms the baselines.

Vision-and-Language Navigation (VLN) in large-scale urban environments requires embodied agents to ground linguistic instructions in complex scenes and recall relevant experiences over extended time horizons. Prior modular pipelines offer interpretability but lack unified memory, while end-to-end (M)LLM agents excel at fusing vision and language yet remain constrained by fixed context windows and implicit spatial reasoning. We introduce Mem4Nav, a hierarchical spatial-cognition long-short memory system that can augment any VLN backbone. Mem4Nav fuses a sparse octree for fine-grained voxel indexing with a semantic topology graph for high-level landmark connectivity, storing both in trainable memory tokens embedded via a reversible Transformer. Long-term memory (LTM) compresses and retains historical observations at both octree and graph nodes, while short-term memory (STM) caches recent multimodal entries in relative coordinates for real-time obstacle avoidance and local planning. At each step, STM retrieval sharply prunes dynamic context, and, when deeper history is needed, LTM tokens are decoded losslessly to reconstruct past embeddings. Evaluated on Touchdown and Map2Seq across three backbones (modular, state-of-the-art VLN with prompt-based LLM, and state-of-the-art VLN with strided-attention MLLM), Mem4Nav yields 7-13 pp gains in Task Completion, sufficient SPD reduction, and >10 pp nDTW improvement. Ablations confirm the indispensability of both the hierarchical map and dual memory modules. Our codes are open-sourced via https://github.com/tsinghua-fib-lab/Mem4Nav.

Recent advances in large language model (LLM) pretraining have shown that simply scaling data quantity eventually leads to diminishing returns, hitting a data wall. In response, the use of synthetic data for pretraining has emerged as a promising paradigm for pushing the frontier of performance. Despite this, the factors affecting synthetic data quality remain poorly understood. In this work, we introduce BeyondWeb, a synthetic data generation framework that produces high-quality synthetic data for pretraining. BeyondWeb significantly extends the capabilities of traditional web-scale datasets, outperforming state-of-the-art synthetic pretraining datasets such as Cosmopedia and Nemotron-CC's high-quality synthetic subset (Nemotron-Synth) by up to 5.1 percentage points (pp) and 2.6pp, respectively, when averaged across a suite of 14 benchmark evaluations. It delivers up to 7.7x faster training than open web data and 2.7x faster than Nemotron-Synth. Remarkably, a 3B model trained for 180B tokens on BeyondWeb outperforms an 8B model trained for the same token budget on Cosmopedia. We also present several insights from BeyondWeb on synthetic data for pretraining: what drives its benefits, which data to rephrase and how, and the impact of model size and family on data quality. Overall, our work shows that there's no silver bullet for generating high-quality synthetic pretraining data. The best outcomes require jointly optimizing many factors, a challenging task that requires rigorous science and practical expertise. Naive approaches can yield modest improvements, potentially at great cost, while well-executed methods can yield transformative improvements, as exemplified by BeyondWeb.