arXiv:2605.28388v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Reward (RLVR) is empirically shown to notably enhance the reasoning performance of large language models (LLMs), particularly in mathematics and programming. However, the mechanistic role of Sample Difficulty in RLVR remains poorly understood. In this paper, we investigate RLVR through the lens of difficulty-wise and one-sample analysis. We find that sample difficulty has a non-monotonic effect on RLVR: easy and medium-difficulty problems yield the strongest and most stable reasoning improvements, whereas ov
The rapid advancement of LLMs necessitates more sophisticated training methodologies, and understanding the nuances of RLVR is critical for optimizing their performance.
This research provides a mechanistic understanding of how sample difficulty impacts LLM reasoning, directly informing the development of more effective and robust AI systems.
Our understanding of optimal training data and difficulty scaling for LLMs is refined, potentially leading to more targeted and efficient AI development strategies.
- · AI developers
- · LLM researchers
- · Mathematics education platforms
- · Programming education platforms
- · Inefficient LLM training methodologies
Improved performance of LLMs in complex reasoning tasks, particularly mathematics and programming.
Accelerated development of AI agents capable of higher-fidelity problem-solving in specialized domains.
Enhanced automation of expert-level tasks, as LLMs become more reliable in difficult cognitive domains.
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Read at arXiv cs.AI