# MILES: Modular Instruction Memory with Learnable Selection for Self-Improving LLM Reasoning

arXiv: https://arxiv.org/abs/2607.06974 · HTML: https://mlsanity.com/paper/2607.06974/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 33 of its 56 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memory](https://mlsanity.com/paper/2509.25140/) (2025)
- [Dynamic Cheatsheet: Test-Time Learning with Adaptive Memory](https://mlsanity.com/paper/2504.07952/) (2025)
- [Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers](https://mlsanity.com/paper/2408.06195/) (2024)
- [Memento: Fine-tuning LLM Agents without Fine-tuning LLMs](https://mlsanity.com/paper/2508.16153/) (2025)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [Atom of Thoughts for Markov LLM Test-Time Scaling](https://mlsanity.com/paper/2502.12018/) (2025)
- [FLEX: Continuous Agent Evolution via Forward Learning from Experience](https://mlsanity.com/paper/2511.06449/) (2025)
- [Metacognitive Reuse: Turning Recurring LLM Reasoning Into Concise Behaviors](https://mlsanity.com/paper/2509.13237/) (2025)
- [B-STaR: Monitoring and Balancing Exploration and Exploitation in Self-Taught Reasoners](https://mlsanity.com/paper/2412.17256/) (2024)
- [ArcMemo: Abstract Reasoning Composition with Lifelong LLM Memory](https://mlsanity.com/paper/2509.04439/) (2025)
- [From Few to Many: Self-Improving Many-Shot Reasoners Through Iterative Optimization and Generation](https://mlsanity.com/paper/2502.00330/) (2025)
- [MCTS-RAG: Enhancing Retrieval-Augmented Generation with Monte Carlo Tree Search](https://mlsanity.com/paper/2503.20757/) (2025)
- [RL of Thoughts: Navigating LLM Reasoning with Inference-time Reinforcement Learning](https://mlsanity.com/paper/2505.14140/) (2025)
- [Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling](https://mlsanity.com/paper/2506.15707/) (2025)
- [Retrieval-of-Thought: Efficient Reasoning via Reusing Thoughts](https://mlsanity.com/paper/2509.21743/) (2025)
- [Policy Guided Tree Search for Enhanced LLM Reasoning](https://mlsanity.com/paper/2502.06813/) (2025)
- [Enhancing Test-Time Scaling of Large Language Models with Hierarchical Retrieval-Augmented MCTS](https://mlsanity.com/paper/2507.05557/) (2025)
- [Experience-Guided Adaptation of Inference-Time Reasoning Strategies](https://mlsanity.com/paper/2511.11519/) (2025)

## Built on by (most cited first, 1 of 1)

- [Test-Time Adaptation of Reasoning Strategies with Bayesian Nonparametric Memory](https://mlsanity.com/paper/2610.06516/) (2026)

## Abstract (arXiv)

Large language models (LLMs) increasingly improve their reasoning at test time via additional computation, yet most existing works treat each problem in isolation. When problems arrive sequentially, accumulating reusable experience across them can further improve performance. Existing memory-based methods either store whole-solution templates that generalize poorly to novel problems or use heuristic step-level selection that is not optimized for final-answer correctness. Learning selection policies requires large-scale training data and fixed action spaces, making such approaches unsuitable for test-time settings where memory expands incrementally and only limited supervision is available. We propose MILES (Modular Instruction Memory with LEarnable Selection for self-improving LLM reasoning), a framework that dynamically expands step-wise memory and applies correctness-optimized memory composition under realistic test-time constraints. MILES maintains modular memory units consisting of asymmetric pairs of sub-goal embeddings and sub-instructions, each associated with a learnable selection head. This memory structure enables a coarse-to-fine retrieval mechanism: The coarse level enables memory expansion and collects supervision for training selection heads from confident samples, while the fine stage applies learned selection heads to rerank coarse-level candidates and guide reasoning for uncertain samples. MILES consistently matches or outperforms prior methods while achieving superior accuracy-efficiency tradeoffs. Extensive experiments demonstrate its effectiveness, robustness, and transferability.