Title: Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning
Primary area: foundation or frontier models, including LLMs
Keywords: Mathematical Reasoning, LLM, RLVR, Advantage Estimation

Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has shown significant promise for enhancing the reasoning capabilities of large language models (LLMs). However, prevailing algorithms like GRPO broadcast a uniform advantage signal across all tokens in a sequence. This coarse-grained approach overlooks the pivotal role of uncertain, high-stakes decisions during reasoning, leading to inefficient exploration and the well-documented problem of entropy collapse. To address this, we introduce $\textbf{U}$n$\textbf{C}$ertainty-aware $\textbf{A}$dvantage $\textbf{S}$haping ($\textbf{UCAS}$), a model-free method that refines credit assignment by leveraging the model's internal uncertainty signals. UCAS operates in two stages: it first modulates the response-level advantage using the model's overall self-confidence, and then applies a token-level penalty based on raw logit certainty. This dual mechanism encourages exploration of high-uncertainty paths that yield correct answers while penalizing overconfident yet erroneous reasoning, effectively balancing the exploration-exploitation trade-off. Extensive experiments on five mathematical reasoning benchmarks show that UCAS significantly outperforms strong RLVR baselines across multiple model scales, including 1.5B and 7B. Our analysis confirms that UCAS not only achieves higher rewards but also promotes greater reasoning diversity and successfully mitigates entropy collapse.