Xin Yao

Xinhao Yao, Ruifeng Ren, Yun Liao et al.

The integration of explicit Chain-of-Thought (CoT) reasoning into training large language models (LLMs) has advanced their reasoning capabilities, yet the mechanisms by which CoT enhances generalization remain poorly understood. This work investigates (1) \textit{how} CoT training reshapes internal model representations and (2) \textit{why} it improves both in-distribution (ID) and out-of-distribution (OOD) reasoning generalization. Through controlled experiments and theoretical analysis, we derive the following key insights. \textbf{1)} Structural Advantage: CoT training internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Notably, CoT-trained models resolve intermediate results at shallower layers compared to non-CoT counterparts, freeing up deeper layers to specialize in subsequent reasoning steps. \textbf{2)} Theoretical Analysis: the information-theoretic generalization bounds via distributional divergence can be decomposed into ID and OOD components. While ID error diminishes with sufficient training regardless of CoT, OOD error critically depends on CoT: Non-CoT training fails to generalize to OOD samples due to unseen reasoning patterns, whereas CoT training achieves near-perfect OOD generalization by mastering subtasks and reasoning compositions during training. The identified mechanisms explain our experimental results: CoT training accelerates convergence and enhances generalization from ID to both ID and OOD scenarios while maintaining robust performance even with tolerable noise. These findings are further validated on complex real-world datasets. This paper offers valuable insights for designing CoT strategies to enhance LLM reasoning robustness.

Xinhao Yao, Lu Yu, Xiaolin Hu et al.

The ongoing debate on whether reinforcement learning with verifiable rewards (RLVR) expands or shrinks the reasoning capabilities of large language models (LLMs) remains unresolved. Some studies contend that RLVR mainly improves sampling efficiency but at the expense of diversity and exploratory capacity, resulting in capability boundary shrinkage. In contrast, others demonstrate that prolonged training can lead to the emergence of novel reasoning strategies, suggesting capability boundary expansion. To reconcile these contradictory findings, we theoretically and empirically show that both perspectives are partially valid-each aligning with a separate phase in an inherent two-stage probability mass dynamic: (1) Exploitation stage: initially, the model primarily samples explored high-reward and low-reward tokens, while rarely selecting the potentially optimal token. Positive advantage estimates increase the probability of high-reward tokens and decrease those of low-reward tokens, yet the optimal token's probability remains largely unchanged during this stage. (2) Exploration stage: as training advances, the growth rate of previously acquired high-reward tokens slows as their probabilities approach saturation. When a potentially optimal token-now receiving positive advantage estimates-is occasionally sampled, its probability increases, while those of the originally high-reward tokens decrease. This dynamic suggests that over-exploitation during the exploitation stage may lead to capability boundary shrinkage, whereas prolonged training into the exploration stage can promote an expansion of the reasoning capability boundary. Building upon our insights, we revisit the potential of only using relative negative gradients for prolonging training, providing a theoretical and empirical foundation for the development of more advanced reasoning capabilities.