# Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs

arXiv: https://arxiv.org/abs/2512.00908 · HTML: https://mlsanity.com/paper/2512.00908/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 34 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Placed in

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

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

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [MedGemma Technical Report](https://mlsanity.com/paper/2507.05201/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [SWE-RL: Advancing LLM Reasoning via Reinforcement Learning on Open Software Evolution](https://mlsanity.com/paper/2502.18449/) (2025)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Dense Reward for Free in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2402.00782/) (2024)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [Baichuan-M2: Scaling Medical Capability with Large Verifier System](https://mlsanity.com/paper/2509.02208/) (2025)
- [First Return, Entropy-Eliciting Explore](https://mlsanity.com/paper/2507.07017/) (2025)
- [Agent-RLVR: Training Software Engineering Agents via Guidance and Environment Rewards](https://mlsanity.com/paper/2506.11425/) (2025)
- [EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity](https://mlsanity.com/paper/2507.21848/) (2025)
- [On Entropy Control in LLM-RL Algorithms](https://mlsanity.com/paper/2509.03493/) (2025)
- [GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2507.10628/) (2025)
- [CAPO: Towards Enhancing LLM Reasoning through Generative Credit Assignment](https://mlsanity.com/paper/2508.02298/) (2025)
- [Not Everything is All You Need: Toward Low-Redundant Optimization for Large Language Model Alignment](https://mlsanity.com/paper/2406.12606/) (2024)
- [SSPO: Subsentence-level Policy Optimization](https://mlsanity.com/paper/2511.04256/) (2025)
- [Reason Like a Radiologist: Chain-of-Thought and Reinforcement Learning for Verifiable Report Generation](https://mlsanity.com/paper/2504.18453/) (2025)

## Built on by (most cited first, 10 of 10)

- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical Reasoning](https://mlsanity.com/paper/2601.07408/) (2026)
- [What and When to Distill: Selective Hindsight Distillation for Multi-Turn Agents](https://mlsanity.com/paper/2605.19447/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)
- [Reinforcement Learning from Rich Feedback with Distributional DAgger](https://mlsanity.com/paper/2606.05152/) (2026)
- [Where Hindsight Credit Can Reside: A Signed-Capacity View of Token Updates in RLVR](https://mlsanity.com/paper/2604.11056/) (2026)
- [Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control](https://mlsanity.com/paper/2605.11775/) (2026)
- [GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2606.04889/) (2026)
- [CurveRL: Principled Distribution-Aware Context Reweighting for LLM Reasoning](https://mlsanity.com/paper/2605.24331/) (2026)
- [Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning](https://mlsanity.com/paper/2609.33781/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of the popular GRPO, LESS consistently improves accuracy over strong RL baselines across three backbones and six math benchmarks, achieves stronger robustness of the performance floor.