← 研踪 PaperTrailarXiv:2601.15158 · v5
Outcome-Based RL Provably Leads Transformers to Reason, but Only With the Right Data
首次提交 2026-01-22 00:36
版本更新 2026-11-06 21:58
雷达观测 2026-11-09 11:19
摘要
Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive policy gradient to discover such systematic reasoning remains poorly understood. We address this by analyzing the policy gradient dynamics of single-layer linear Transformers on a synthetic graph traversal task that cannot be solved without Chain-of-Thought but admits a simple iterative solution. We prove that despite training solely on final-answer correctness, policy gradient drives the Transformer to converge to a structured, interpretable algorithm that iteratively traverses the graph vertex-by-vertex. We characterize the distributional properties required for this emergence, identifying the critical role of "simple examples": instances requiring fewer reasoning steps. When the training distribution places sufficient mass on these simpler examples, the Transformer learns a generalizable traversal strategy that extrapolates to longer chains; when this mass vanishes, policy gradient learning becomes infeasible. We corroborate our theoretical results through experiments on synthetic data and with real-world language models on mathematical reasoning tasks, validating that our theoretical findings carry over to practical settings.
作者备注：94 pages, 7 figures
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v5 · 2026-11-06 21:58 · 最新观测版本
Outcome-Based RL Provably Leads Transformers to Reason, but Only With the Right Data
Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive policy gradient to discover such systematic reasoning remains poorly understood. We address this by analyzing the policy gradient dynamics of single-layer linear Transformers on a synthetic graph traversal task that cannot be solved without Chain-of-Thought but admits a simple iterative solution. We prove that despite training solely on final-answer correctness, policy gradient drives the Transformer to converge to a structured, interpretable algorithm that iteratively traverses the graph vertex-by-vertex. We characterize the distributional properties required for this emergence, identifying the critical role of "simple examples": instances requiring fewer reasoning steps. When the training distribution places sufficient mass on these simpler examples, the Transformer learns a generalizable traversal strategy that extrapolates to longer chains; when this mass vanishes, policy gradient learning becomes infeasible. We corroborate our theoretical results through experiments on synthetic data and with real-world language models on mathematical reasoning tasks, validating that our theoretical findings carry over to practical settings.
查看此版本解读 →查看此版本原文 ↗