# Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control

arXiv: https://arxiv.org/abs/2605.11775 · HTML: https://mlsanity.com/paper/2605.11775/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 12 May 2026.

## 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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)
- [ACEBench: Who Wins the Match Point in Tool Usage?](https://mlsanity.com/paper/2501.12851/) (2025)
- [Nemotron-Research-Tool-N1: Exploring Tool-Using Language Models with Reinforced Reasoning](https://mlsanity.com/paper/2505.00024/) (2025)
- [JustRL: Scaling a 1.5B LLM with a Simple RL Recipe](https://mlsanity.com/paper/2512.16649/) (2025)
- [Decoupling Exploration and Exploitation for Meta-Reinforcement Learning without Sacrifices](https://mlsanity.com/paper/2008.02790/) (2020)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [On Entropy Control in LLM-RL Algorithms](https://mlsanity.com/paper/2509.03493/) (2025)
- [Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward](https://mlsanity.com/paper/2512.16912/) (2025)
- [CE-GPPO: Coordinating Entropy via Gradient-Preserving Clipping Policy Optimization in Reinforcement Learning](https://mlsanity.com/paper/2509.20712/) (2025)
- [Sparse but Critical: A Token-Level Analysis of Distributional Shifts in RLVR Fine-Tuning of LLMs](https://mlsanity.com/paper/2603.22446/) (2026)
- [Rethinking Sample Polarity in Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2512.21625/) (2025)
- [AgentV-RL: Scaling Reward Modeling with Agentic Verifier](https://mlsanity.com/paper/2604.16004/) (2026)
- [Why Reinforcement Fine-Tuning Enables MLLMs Preserve Prior Knowledge Better: A Data Perspective](https://mlsanity.com/paper/2506.23508/) (2025)
- [Entropy-Preserving Reinforcement Learning](https://mlsanity.com/paper/2603.11682/) (2026)
- [Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs](https://mlsanity.com/paper/2512.00908/) (2025)

## Built on by (most cited first, 3 of 3)

- [Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning](https://mlsanity.com/paper/2609.33781/) (2026)
- [Exploration-Preserving Policy Optimization](https://mlsanity.com/paper/2610.04011/) (2026)
- [GRPODropout: Less is More for Online Reinforcement Learning Rollouts](https://mlsanity.com/paper/2610.11854/) (2026)

## Abstract (arXiv)

Policy entropy has emerged as a fundamental measure for understanding and controlling exploration in reinforcement learning with verifiable rewards (RLVR) for LLMs. However, existing entropy-aware methods mainly regulate entropy through global objectives, while the token-level mechanism by which sampled policy updates reshape policy entropy remains underexplored. In this work, we develop a theoretical framework of entropy mechanics in RLVR. Our analysis yields a first-order approximation of the entropy change, giving rise to entropy polarity, a signed token-level quantity that predicts how much a sampled update expands or contracts entropy. This analysis further reveals a structural asymmetry: reinforcing frequent high-probability tokens triggers contraction tendencies, whereas expansive tendencies typically require lower-probability samples or stronger distributional correction. Empirically, we show that entropy polarity reliably predicts entropy changes, and that positive and negative polarity branches play complementary roles in preserving exploration while strengthening exploitation. Building on these insights, we propose Polarity-Aware Policy Optimization (PAPO), which preserves both polarity branches and implements entropy control through advantage reweighting. With the empirical entropy trajectory as an online phase signal, PAPO adaptively reallocates optimization pressure between entropy-expanding and entropy-contracting updates. Experiments on mathematical reasoning and agentic benchmarks show that PAPO consistently outperforms competitive baselines, while delivering superior training efficiency and substantial reward improvements.