Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs

Researchers mechanistically analyze how sample difficulty affects Reinforcement Learning with Verifiable Reward (RLVR) training in large language models, discovering that medium-difficulty problems yield optimal reasoning improvements while overly hard problems degrade performance. The study proposes difficulty-adaptive strategies using backward-reasoning reformulation and sparse autoencoders to optimize reward signals during training.

This research addresses a fundamental gap in understanding how reinforcement learning training dynamics affect LLM reasoning capabilities. The non-monotonic relationship between problem difficulty and learning efficacy challenges conventional assumptions that harder problems always drive better model development. The finding that easy and medium-difficulty samples produce the strongest improvements suggests that training regimes should prioritize balanced curricula rather than exclusively hard-problem exposure, which can induce failure modes like answer repetition and capability degradation.

The mechanistic analysis using Temporal Sparse Autoencoders provides granular insight into how different difficulty levels activate distinct feature representations. Easy problems reinforce computational shortcuts while suppressing deeper reasoning, whereas hard problems activate reasoning features only when successful trajectories exist—a critical distinction for practitioners designing training pipelines. This framework moves beyond black-box empirical observations toward interpretable understanding of representation learning in RL contexts.

The proposed difficulty-adaptive strategies leverage these insights through backward-reasoning reformulation and T-SAE-guided credit assignment, directly addressing the reward density problem in hard-sample training. For AI developers optimizing LLM reasoning systems, these findings suggest that curriculum learning approaches with adaptive difficulty scaling could substantially improve both training efficiency and final model capability. The research establishes sample difficulty as a critical hyperparameter deserving systematic optimization rather than arbitrary selection.

• →Medium-difficulty problems provide the most stable reasoning improvements in RLVR training, outperforming both easy and hard samples
• →Overly hard problems activate reasoning features but induce degenerate behaviors and can degrade pre-trained capabilities without successful trajectory sampling
• →Temporal Sparse Autoencoders reveal that different difficulty levels produce distinct feature activation patterns in model internals
• →Difficulty-adaptive strategies using backward-reasoning reformulation and T-SAE-guided signals improve reward density and credit assignment
• →Sample difficulty fundamentally governs both optimization dynamics and representation evolution in reinforcement learning for language models