# Efficient Reinforcement Learning with Semantic and Token Entropy for LLM Reasoning

arXiv: https://arxiv.org/abs/2512.04359 · HTML: https://mlsanity.com/paper/2512.04359/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [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)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [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)
- [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)
- [Hi Robot: Open-Ended Instruction Following with Hierarchical Vision-Language-Action Models](https://mlsanity.com/paper/2502.19417/) (2025)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Survey on Large Language Model-Enhanced Reinforcement Learning: Concept, Taxonomy, and Methods](https://mlsanity.com/paper/2404.00282/) (2024)
- [NavCoT: Boosting LLM-Based Vision-and-Language Navigation via Learning Disentangled Reasoning](https://mlsanity.com/paper/2403.07376/) (2024)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [Pangu Embedded: An Efficient Dual-system LLM Reasoner with Metacognition](https://mlsanity.com/paper/2505.22375/) (2025)
- [Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2405.13629/) (2024)
- [Enhancing Efficiency and Exploration in Reinforcement Learning for LLMs](https://mlsanity.com/paper/2505.18573/) (2025)

## Built on by (most cited first, 6 of 6)

- [VI-CuRL: Stabilizing Verifier-Independent RL Reasoning via Confidence-Guided Variance Reduction](https://mlsanity.com/paper/2602.12579/) (2026)
- [Offline Exploration-Aware Fine-Tuning for Long-Chain Mathematical Reasoning](https://mlsanity.com/paper/2603.16206/) (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)
- [UP: Unbounded Positive Asymmetric Optimization for Breaking the Exploration-Stability Dilemma](https://mlsanity.com/paper/2607.06987/) (2026)
- [Learning from Hard Prompts: Difficulty-aware Advantage Amplification in Dynamic Sampling](https://mlsanity.com/paper/2608.27982/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has demonstrated superior performance in enhancing the reasoning capability of large language models (LLMs). However, this accuracy-oriented learning paradigm often suffers from entropy collapse, which reduces policy exploration and limits reasoning capabilities. To address this challenge, we propose an efficient reinforcement learning framework that leverages entropy signals at both the semantic and token levels to improve reasoning. From the data perspective, we introduce semantic entropy-guided curriculum learning, organizing training data from low to high semantic entropy to guide progressive optimization from easier to more challenging tasks. For the algorithmic design, we adopt non-uniform token treatment by imposing KL regularization on low-entropy tokens that critically impact policy exploration and applying stronger constraints on high-covariance portions within these tokens. By jointly optimizing data organization and algorithmic design, our method effectively mitigates entropy collapse and enhances LLM reasoning. Experimental results across 6 benchmarks with 3 different parameter-scale base models demonstrate that our method outperforms other entropy-based approaches in improving reasoning.