aiqbench analysis
This study investigates why reinforcement learning (RL) outperforms supervised fine-tuning in mathematical reasoning, revealing that RL induces more structured internal representations and a hierarchical layer architecture critical for deep processing. The findings suggest these representational shifts are fundamental to superior performance rather than incidental effects of the training pipeline alone. For researchers focused on model interpretability and optimization strategies, this work clarifies how different training objectives reshape the underlying computational mechanisms required for complex problem-solving.
Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models
arXiv:2607.26119v1 Announce Type: new Abstract: 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.
Title:Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models
Abstract: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.
Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
arXiv:2607.26119 [cs.AI]
(or arXiv:2607.26119v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.26119 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 322 words
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