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

Abstract

Large language models trained with reinforcement learning (RL) to reason step by step have been increasingly shown to outperform their supervised fine-tuned (SFT) counterparts on mathematical reasoning tasks. Yet the mechanistic basis for this improvement remains unclear. We therefore ask, what internal representational differences enable RL-trained reasoning language models to reason better? Our work presents two primary lines of evidence: First, layer-wise linear probes tend to predict answer correctness more accurately in RL-trained reasoning language models than in instruction-tuned models on synthetic math problems, although output length alone matches the DeepSeek-Math-RL probe on two templates. Second, mean ablation studies suggest that accuracy drop rises with layer depth in DeepSeek-Math-RL but not in DeepSeek-Math-Instruct. Finally, we analyse token-count variability across accuracy bins for RL-trained reasoning language models and instruction-tuned models to measure whether token counts vary more on harder problems. Token counts tend to vary more on lower-accuracy problems, although in DeepSeek-Math-Instruct only with truncated responses included. At high accuracy, we observe lower variability in DeepSeek-Math-RL than in DeepSeek-Math-Instruct, and we observe higher variability in Olmo-3-Think than in Olmo-3-Instruct.

arXiv commentSecond Workshop on XAI4Science, AAAI 2026