# Look Inward to Explore Outward: Learning Temperature Policy from LLM Internal States via Hierarchical RL

arXiv: https://arxiv.org/abs/2602.13035 · HTML: https://mlsanity.com/paper/2602.13035/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 59 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 30 of 49)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [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)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Process Reward Models for LLM Agents: Practical Framework and Directions](https://mlsanity.com/paper/2502.10325/) (2025)
- [Enhancing Code LLMs with Reinforcement Learning in Code Generation: A Survey](https://mlsanity.com/paper/2412.20367/) (2024)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)

## Built on by (most cited first, 27 of 27)

- [ROSD: Reflective On-Policy Self-Distillation for Language Model Reasoning across Domains](https://mlsanity.com/paper/2605.28014/) (2026)
- [Not All Directions Matter: Towards Structured and Task-Aware Low-Rank Model Adaptation](https://mlsanity.com/paper/2603.14228/) (2026)
- [Seeing with You: Perception-Reasoning Coevolution for Multimodal Reasoning](https://mlsanity.com/paper/2603.28618/) (2026)
- [When Models Learn to Ask Why: Adaptive Causal Reasoning for Trustworthy Medical Vision-Language Models](https://mlsanity.com/paper/2603.23085/) (2026)
- [One Refiner to Unlock Them All: Inference-Time Reasoning Elicitation via Reinforcement Query Refinement](https://mlsanity.com/paper/2604.25444/) (2026)
- [DyJR: Preserving Diversity in Reinforcement Learning with Verifiable Rewards via Dynamic Jensen-Shannon Replay](https://mlsanity.com/paper/2603.16157/) (2026)
- [PaperMind: Benchmarking Agentic Reasoning and Critique over Scientific Papers in Multimodal LLMs](https://mlsanity.com/paper/2604.21304/) (2026)
- [SQL-ASTRA: Alleviating Sparse Feedback in Agentic SQL via Column-Set Matching and Trajectory Aggregation](https://mlsanity.com/paper/2603.16161/) (2026)
- [VistaHop: Benchmarking Long-Horizon Visual DeepSearch](https://mlsanity.com/paper/2606.03273/) (2026)
- [Rubric-Guided Process Reward for Stepwise Model Routing](https://mlsanity.com/paper/2605.29310/) (2026)
- [AWM: Answerable Working Memory for Long-Document VQA Agents](https://mlsanity.com/paper/2608.25618/) (2026)
- [AgenticRag-R1: Agentic Reinforcement Learning with Stack Memory for Multi-Step Reasoning, Retrieval and Memorizing](https://mlsanity.com/paper/2608.29622/) (2026)
- [Frequency-Modulated Visual Restoration for Matryoshka Large Multimodal Models](https://mlsanity.com/paper/2603.11220/) (2026)
- [Unleashing Implicit Rewards: Prefix-Value Learning for Distribution-Level Optimization](https://mlsanity.com/paper/2604.13197/) (2026)
- [CAP-CoT: Cycle Adversarial Prompt for Improving Chain of Thoughts in LLM Reasoning](https://mlsanity.com/paper/2604.23270/) (2026)
- [Internalize the Temperature: On-Policy Self-Distillation as Policy Reheater for Reinforcement Learning](https://mlsanity.com/paper/2606.00755/) (2026)
- [Placing Puzzle Pieces Where They Matter: A Question Augmentation Framework for Reinforcement Learning](https://mlsanity.com/paper/2604.15830/) (2026)
- [Small Language Model Helps Resolve Semantic Ambiguity of LLM Prompt](https://mlsanity.com/paper/2604.23263/) (2026)
- [EmoDistill: Offline Emotion Skill Distillation for Language Model Agents in Adversarial Negotiation](https://mlsanity.com/paper/2605.26785/) (2026)
- [Micro-Macro Retrieval: Reducing Long-Form Hallucination in Large Language Models](https://mlsanity.com/paper/2605.28828/) (2026)
- [Self-Correction Can Amplify Hallucinations: Fact-Level Repair with Graph-Based Evidence Routing in Multimodal Generation](https://mlsanity.com/paper/2606.00232/) (2026)
- [Efficient RAG with Intent-Aware Retrieval and Semantics-Preserving Chunking](https://mlsanity.com/paper/2606.01240/) (2026)
- [Shattering the Autoregressive Curse: Dynamic Epistemic Entropy Orchestrated Erasable Reinforcement Learning for LLMs](https://mlsanity.com/paper/2606.17735/) (2026)
- [BV-Blend: Uncertainty-Weighted Historical Baselines for Stable Critic-Free RL with Verifiable Rewards](https://mlsanity.com/paper/2606.28707/) (2026)
- [TGRL: Temperature-Grouped Reinforcement Learning for Efficient Exploration in LLMs](https://mlsanity.com/paper/2609.33589/) (2026)
- [Cool the Sampler, Not the Learner: Sampling Temperature Moves the Staleness Cliff of Importance-Corrected GRPO](https://mlsanity.com/paper/2609.36953/) (2026)
- [Soft Spatial Reasoning](https://mlsanity.com/paper/2609.38717/) (2026)

## Abstract (arXiv)

Reinforcement Learning from Verifiable Rewards (RLVR) trains large language models (LLMs) from sampled trajectories, making decoding strategy a core component of learning rather than a purely inference-time choice. Sampling temperature directly controls the exploration--exploitation trade-off by modulating policy entropy, yet existing methods rely on static values or heuristic adaptations that are decoupled from task-level rewards. We propose Introspective LLM, a hierarchical reinforcement learning framework that learns to control sampling temperature during generation. At each decoding step, the model selects a temperature based on its hidden state and samples the next token from the resulting distribution. Temperature and token policies are jointly optimized from downstream rewards using a coordinate ascent scheme. Experiments on mathematical reasoning benchmarks show that learned temperature policies outperform fixed and heuristic baselines, while exhibiting interpretable exploration behaviors aligned with reasoning uncertainty.