Zhengyu Chen

Ruochen Zhou, Minrui Xu, Shiqi Chen et al.

There has been a growing interest in enhancing the mathematical problem-solving (MPS) capabilities of large language models. While the majority of research efforts concentrate on creating specialized models to solve mathematical problems, it remains unknown how learning mathematical problem-solving generalizes to help develop other reasoning abilities. In this paper, we present an empirical investigation into the generalization potential of various MPS training approaches, such as continual pretraining, instruction tuning, and rule-based reinforcement learning across various data sources, including both short and long chain-of-thought (CoT) samples. Evaluation on 5 mathematical and 8 general reasoning benchmarks show that continual pretraining on math text is able to generalize to general reasoning tasks to some extent. In constrast, instruction tuning on conventional, short MPS samples provides limited benefits and, in many cases, even impairs generalization performance. Notably, training with long CoT responses for MPS samples and incorporating rule-based reinforcement learning on MPS queries exhibit distinct behavior, significantly enhancing generalization by extending the model's reasoning processes into other domains. These results suggest that traditional approaches to learning MPS with short reasoning chains largely fail to achieve robust generalization. However, the emerging paradigm of longer reasoning chains, coupled with self-reflection, offers a promising direction for improving generalized reasoning abilities through learning from specialized domains.

Xiangyu Xi, Deyang Kong, Jian Yang et al.

Existing pretraining data mixing methods for large language models (LLMs) typically follow a domain-wise methodology, a top-down process that first determines domain weights and then performs uniform data sampling across each domain. However, these approaches neglect significant inter-domain overlaps and commonalities, failing to control the global diversity of the constructed training dataset. Further, uniform sampling within domains ignores fine-grained sample-specific features, potentially leading to suboptimal data distribution. To address these shortcomings, we propose a novel sample-wise data mixture approach based on a bottom-up paradigm. This method performs global cross-domain sampling by systematically evaluating the quality and diversity of each sample, thereby dynamically determining the optimal domain distribution. Comprehensive experiments across multiple downstream tasks and perplexity assessments demonstrate that SampleMix surpasses existing domain-based methods. Meanwhile, SampleMix requires 1.4x to 2.1x training steps to achieves the baselines' performance, highlighting the substantial potential of SampleMix to optimize pre-training data.