# EntroPIC: Towards Stable Long-Term Training of LLMs via Entropy Stabilization with Proportional-Integral Control

arXiv: https://arxiv.org/abs/2511.15248 · HTML: https://mlsanity.com/paper/2511.15248/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 53 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 30 of 43)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [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)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Pretraining Language Models with Human Preferences](https://mlsanity.com/paper/2302.08582/) (2023)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (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)
- [Entropy Law: The Story Behind Data Compression and LLM Performance](https://mlsanity.com/paper/2407.06645/) (2024)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [Maximum Entropy-Regularized Multi-Goal Reinforcement Learning](https://mlsanity.com/paper/1905.08786/) (2019)

## Built on by (most cited first, 13 of 13)

- [AdaptVision: Efficient Vision-Language Models via Adaptive Visual Acquisition](https://mlsanity.com/paper/2512.03794/) (2025)
- [d-TreeRPO: Towards More Reliable Policy Optimization for Diffusion Language Models](https://mlsanity.com/paper/2512.09675/) (2025)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [STAPO: Stabilizing Reinforcement Learning for LLMs by Silencing Rare Spurious Tokens](https://mlsanity.com/paper/2602.15620/) (2026)
- [Composition-RL: Compose Your Verifiable Prompts for Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2602.12036/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [Intern-S2-Preview: Scientific Agentic Foundation Model](https://mlsanity.com/paper/2608.13505/) (2026)
- [STARE: Surprisal-Guided Token-Level Advantage Reweighting for Policy Entropy Stability](https://mlsanity.com/paper/2606.19236/) (2026)
- [Group Entropy-Controlled Policy Optimization](https://mlsanity.com/paper/2607.16850/) (2026)
- [Boosting LLM Reasoning via Human-Inspired Reward Shaping](https://mlsanity.com/paper/2602.04265/) (2026)
- [Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control](https://mlsanity.com/paper/2604.26326/) (2026)
- [Read the Trace, Steer the Path: Trajectory-Aware Reinforcement Learning for Diffusion Language Models](https://mlsanity.com/paper/2606.04396/) (2026)
- [Stable-MM-R1: Anchoring Multimodal Reasoning Dynamics via Entropy-Guided Stratification](https://mlsanity.com/paper/2609.07148/) (2026)

## Abstract (arXiv)

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stabilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.