# Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning

arXiv: https://arxiv.org/abs/2510.10649 · HTML: https://mlsanity.com/paper/2510.10649/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 34)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [OlympicArena: Benchmarking Multi-discipline Cognitive Reasoning for Superintelligent AI](https://mlsanity.com/paper/2406.12753/) (2024)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)

## Built on by (most cited first, 30 of 34)

- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [AMO-Bench: Large Language Models Still Struggle in High School Math Competitions](https://mlsanity.com/paper/2510.26768/) (2025)
- [Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical Reasoning](https://mlsanity.com/paper/2601.07408/) (2026)
- [Reinforcement Learning from Rich Feedback with Distributional DAgger](https://mlsanity.com/paper/2606.05152/) (2026)
- [ATTNPO: Attention-Guided Process Supervision for Efficient Reasoning](https://mlsanity.com/paper/2602.09953/) (2026)
- [SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards](https://mlsanity.com/paper/2602.21158/) (2026)
- [Reinforced Efficient Reasoning via Semantically Diverse Exploration](https://mlsanity.com/paper/2601.05053/) (2026)
- [FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models](https://mlsanity.com/paper/2604.02967/) (2026)
- [Self-Distilled Policy Gradient](https://mlsanity.com/paper/2606.04036/) (2026)
- [Not All Tokens See Equally: Perception-Grounded Policy Optimization for Large Vision-Language Models](https://mlsanity.com/paper/2604.01840/) (2026)
- [One Refiner to Unlock Them All: Inference-Time Reasoning Elicitation via Reinforcement Query Refinement](https://mlsanity.com/paper/2604.25444/) (2026)
- [Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning](https://mlsanity.com/paper/2603.01221/) (2026)
- [Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2606.18810/) (2026)
- [Leveraging Error Diversity in Group Rollouts for Reinforcement Learning](https://mlsanity.com/paper/2605.17333/) (2026)
- [SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs](https://mlsanity.com/paper/2605.18864/) (2026)
- [Discounted Beta-Bernoulli Reward Estimation for Sample-Efficient Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2603.18444/) (2026)
- [AMR-SD: Asymmetric Meta-Reflective Self-Distillation for Token-Level Credit Assignment](https://mlsanity.com/paper/2605.18529/) (2026)
- [GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2606.04889/) (2026)
- [EDGE: Experience-Distillation for Guided Exploration in Agentic Reinforcement Learning](https://mlsanity.com/paper/2608.21946/) (2026)
- [AWM: Answerable Working Memory for Long-Document VQA Agents](https://mlsanity.com/paper/2608.25618/) (2026)
- [Distributional Clarity: The Hidden Driver of RL-Friendliness in Large Language Models](https://mlsanity.com/paper/2601.06911/) (2026)
- [Think in Latent Thoughts: A New Paradigm for Gloss-Free Sign Language Translation](https://mlsanity.com/paper/2604.15301/) (2026)
- [Confidence Laundering in Agent Systems: Why Uncertainty Needs a Latent Carrier](https://mlsanity.com/paper/2606.20662/) (2026)
- [When Implausible Tokens Get Reinforced: Tail-Aware Credit Calibration for LLM Reinforcement Learning](https://mlsanity.com/paper/2607.07976/) (2026)
- [Miner:Mining Intrinsic Mastery for Data-Efficient RL in Large Reasoning Models](https://mlsanity.com/paper/2601.04731/) (2026)
- [OGER: A Robust Offline-Guided Exploration Reward for Hybrid Reinforcement Learning](https://mlsanity.com/paper/2604.18530/) (2026)
- [Reasoning Portability: Guiding Continual Learning for MLLMs in the RLVR Era](https://mlsanity.com/paper/2605.18903/) (2026)
- [EAPO: Entropy-Driven Adaptive Positive-Negative Sample Weighting for Policy Optimization in Open-Ended QA](https://mlsanity.com/paper/2605.27846/) (2026)
- [Guidance Contrastive Token Credit Assignment for Discrete Policy Optimization](https://mlsanity.com/paper/2605.29198/) (2026)
- [Customer-Agent: Overcoming Context Limitations in Ultra-Long Shopping Trajectories via Tool-Augmented Agents and RLVR](https://mlsanity.com/paper/2606.07995/) (2026)

## Abstract (arXiv)

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 UnCertainty-aware Advantage Shaping (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 a logit-space self-confidence proxy, and then applies an asymmetric 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. Code is available at https://github.com/xvolcano02/UCAS.