arXiv:2607.26119cs.AIcs.CL2026-07

对比强化学习与监督微调模型,发现前者在数学推理中拥有更优的内部表示结构。

Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models

论文配图:Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models
图 1 · 摘自论文原文
  • 通过线性探针分析隐藏状态,发现强化学习模型的表示更线性可分。
  • 深度层重要性呈递进分布,而监督微调模型各层贡献均匀。
  • 揭示了强化学习模型在推理策略上的稳定性差异,适合研究模型机制者阅读。

通过强化学习(RL)训练的大规模推理模型在数学推理任务上表现优于监督微调(SFT)模型,但其内在机制仍不清晰。本文提出两条相互印证的证据:第一,对各层隐藏状态进行线性探针分析显示,RL模型在预测答案正确性方面准确率更高,表明其表征更具线性可分性和结构性;第二,均值消融研究表明,RL模型形成层次化架构,深层逐渐变得更为关键,而SFT模型则在各层间均匀分配重要性。这两项结果共同说明,强化学习从根本上重构了模型处理推理问题的方式。最后,通过重复采样下的词元数量变化分析自适应计算分配,发现部分RL模型表现出更高的变异性,而另一些则高度一致,表明词元分配可能更多取决于整体训练流程而非仅由训练方式决定。该变异性揭示了合理策略的分布,有助于识别具有稳定策略的模型与那些未充分确定、不可识别解法行为的模型。

原文摘要 · Abstract (English)

Large reasoning models trained via reinforcement learning (RL) have been increasingly shown to outperform their supervised fine-tuned (SFT) counterparts on mathematical reasoning tasks; Yet the mechanistic basis for this advantage remains unclear. We therefore ask, what internal representational differences enable RL models' superior performance? Our work presents two converging lines of evidence: First, linear probes trained on layer-wise hidden states reveal that RL models tend to achieve higher accuracy in predicting answer correctness compared to SFT models, indicating more linearly separable and structured representations. Second, mean ablation studies show that RL models develop a hierarchical architecture where deeper layers become progressively more critical, whereas SFT models distribute importance uniformly across layers. Together, these findings demonstrate that RL training fundamentally restructures how models represent and process reasoning problems. Finally, we analyze token-count variability under repeated sampling across problems to assess adaptive compute allocation. While we observe higher variability in some RL-tuned models than in their SFT counterparts, we see strong consistency in others, suggesting that token allocation may depend more on the overall training pipeline than on RL versus SFT alone. We believe this token-allocation variability reveals the spread of plausible on-policy reasoning, highlighting which models exhibit stable policies versus those that are under-determined, potentially non-identifiable solution behaviour.

强化学习模型表征数学推理

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