# Revisiting Entropy in Reinforcement Learning for Large Reasoning Models

arXiv: https://arxiv.org/abs/2511.05993 · HTML: https://mlsanity.com/paper/2511.05993/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 8 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 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [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)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [Evaluating Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2310.19736/) (2023)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [Large Language Model Safety: A Holistic Survey](https://mlsanity.com/paper/2412.17686/) (2024)
- [Harnessing Uncertainty: Entropy-Modulated Policy Gradients for Long-Horizon LLM Agents](https://mlsanity.com/paper/2509.09265/) (2025)
- [On Entropy Control in LLM-RL Algorithms](https://mlsanity.com/paper/2509.03493/) (2025)
- [CE-GPPO: Coordinating Entropy via Gradient-Preserving Clipping Policy Optimization in Reinforcement Learning](https://mlsanity.com/paper/2509.20712/) (2025)
- [Uncalibrated Reasoning: GRPO Induces Overconfidence for Stochastic Outcomes](https://mlsanity.com/paper/2508.11800/) (2025)

## Built on by (most cited first, 21 of 21)

- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [Small Generalizable Prompt Predictive Models Can Steer Efficient RL Post-Training of Large Reasoning Models](https://mlsanity.com/paper/2602.01970/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance](https://mlsanity.com/paper/2604.12627/) (2026)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [Reaching Beyond the Mode: RL for Distributional Reasoning in Language Models](https://mlsanity.com/paper/2603.24844/) (2026)
- [EfficientRollout: System-Aware Self-Speculative Decoding for RL Rollouts](https://mlsanity.com/paper/2606.18967/) (2026)
- [Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective](https://mlsanity.com/paper/2602.09782/) (2026)
- [The Unlearnability Phenomenon in RLVR for Language Models](https://mlsanity.com/paper/2605.16787/) (2026)
- [STARE: Surprisal-Guided Token-Level Advantage Reweighting for Policy Entropy Stability](https://mlsanity.com/paper/2606.19236/) (2026)
- [BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?](https://mlsanity.com/paper/2608.02867/) (2026)
- [Smaller Models are Natural Explorers for Policy-Level Diversity in GRPO](https://mlsanity.com/paper/2605.30789/) (2026)
- [Tool-Aware Optimization with Entropy Guidance for Efficient Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03762/) (2026)
- [Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning](https://mlsanity.com/paper/2606.19771/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [ARC: Fair Relative Advantage Comparison in Open-Ended Real-World Interaction](https://mlsanity.com/paper/2608.13622/) (2026)
- [RLVR landscapes for iterated multiplications can be benign: Insights from spin-glass theory](https://mlsanity.com/paper/2609.28625/) (2026)
- [Initialization Improves LLM-Driven Discovery](https://mlsanity.com/paper/2610.00707/) (2026)
- [Tropical Reinforcement Learning](https://mlsanity.com/paper/2610.02478/) (2026)
- [Credit Where It Matters: Dependency-Aware Policy Optimization for Terminal Agents](https://mlsanity.com/paper/2610.03634/) (2026)
- [Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains](https://mlsanity.com/paper/2610.20328/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has emerged as a prominent paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, the entropy of LLMs usually collapses during RLVR training, leading to premature convergence to suboptimal local minima and hindering further performance improvement. Although various approaches have been proposed to mitigate entropy collapse, a comprehensive study of entropy in RLVR remains lacking. To bridge this gap, we conduct extensive experiments to investigate the entropy dynamics of LLMs trained with RLVR and analyze how model entropy correlates with response diversity, calibration, and performance across various benchmarks. Our results identify three key factors that influence entropy: the clipping thresholds in the optimization objective, the number of off-policy updates, and the diversity of the training data. Furthermore, through both theoretical analysis and empirical validation, we demonstrate that tokens with positive advantages are the primary drivers of entropy collapse. Motivated by this insight, we propose Positive-Advantage Reweighting, a simple yet effective approach that regulates model entropy by adjusting the loss weights assigned to tokens with positive advantages during RLVR training, while maintaining competitive performance.