# Explore with Memory, Learn without It: In-Context Exploration and Self-Distillation for LLM Reasoning

arXiv: https://arxiv.org/abs/2610.17734 · HTML: https://mlsanity.com/paper/2610.17734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

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

- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [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)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction](https://mlsanity.com/paper/2410.09008/) (2024)
- [SEED: Self-Evolving On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.14777/) (2026)
- [Reward Is Enough: LLMs Are In-Context Reinforcement Learners](https://mlsanity.com/paper/2506.06303/) (2025)
- [Multi-Turn Code Generation Through Single-Step Rewards](https://mlsanity.com/paper/2502.20380/) (2025)
- [Exploratory Memory-Augmented LLM Agent via Hybrid On- and Off-Policy Optimization](https://mlsanity.com/paper/2602.23008/) (2026)
- [Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL](https://mlsanity.com/paper/2602.03773/) (2026)
- [Beyond Markovian: Reflective Exploration via Bayes-Adaptive RL for LLM Reasoning](https://mlsanity.com/paper/2505.20561/) (2025)
- [Think Thrice Before You Act: Progressive Thought Refinement in Large Language Models](https://mlsanity.com/paper/2410.13413/) (2024)
- [Procedural Memory Distillation: Online Reflection for Self-Improving Language Models](https://mlsanity.com/paper/2607.01480/) (2026)
- [MURPHY: Feedback-Aware GRPO with Retrospective Credit Assignment for Multi-Turn Code Generation](https://mlsanity.com/paper/2511.07833/) (2025)

## Abstract (arXiv)

Exploration bounds learning efficiency in reinforcement learning with verifiable rewards (RLVR). Current methods explore mostly through independent sampling, without fully using the information gathered along the way, such as known wrong answers and environment feedback. We propose LEAF, which injects a dynamic, problem-specific memory into the context before every rollout. The memory contains the most recent response, its reward, and other environment feedback. It is updated after every verifier call. We decouple policy updates from rollouts and update the policy through self-distillation. On four benchmarks and two open models, LEAF accelerates exploration by about 4x compared with a random sampling baseline. On unseen test sets, it improves accuracy over the strongest baseline by 1.59 and 1.83 percentage points on the two models, while using less compute than any RL baseline. These results highlight the potential of LEAF in improving both exploration and learning efficiency. Code is available at: https://github.com/on1262/LEAF