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arXiv · 2601.15609

When Sharpening Becomes Collapse: Sampling Bias and Semantic Coupling in RL with Verifiable Rewards

Mingyuan Fan·Weiguang Han·Daixin Wang·Cen Chen·Zhiqiang Zhang·Jun Zhou
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Abstract

Reinforcement Learning with Verifiable Rewards (RLVR) is a central paradigm for turning large language models (LLMs) into reliable problem solvers, especially in logic-heavy domains. Despite its empirical success, it remains unclear whether RLVR elicits novel capabilities or merely sharpens the distribution over existing knowledge. We study this by formalizing over-sharpening, a phenomenon where the policy collapses onto limited modes, suppressing valid alternatives. At a high level, we discover finite-batch updates intrinsically bias learning toward sampled modes, triggering a collapse that propagates globally via semantic coupling. To mitigate this, we propose inverse-success advantage calibration to prioritize difficult queries and distribution-level calibration to diversify sampling via a memory network. Empirical evaluations validate that our strategies can effectively improve generalization.

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Mingyuan Fan, Weiguang Han, Daixin Wang, Cen Chen, Zhiqiang Zhang, Jun Zhou. 2026-01-22. When Sharpening Becomes Collapse: Sampling Bias and Semantic Coupling in RL with Verifiable Rewards. https://arxiv.org/abs/2601.15609

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