# ISM:Self-Improving Strategy Memory for Continual Mathematical Reasoning

arXiv: https://arxiv.org/abs/2606.31191 · HTML: https://mlsanity.com/paper/2606.31191/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- 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, 10 of 10)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [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)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Graph Memory: A Structured and Interpretable Framework for Modality-Agnostic Embedding-Based Inference](https://mlsanity.com/paper/2511.14961/) (2025)

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

- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Continual Graph Memory for Mathematical Research Agents](https://mlsanity.com/paper/2610.02945/) (2026)
- [From Existing Methods to New Research Ideas: Two Perspectives on Recursive Self-Improvement](https://mlsanity.com/paper/2610.14625/) (2026)

## Abstract (arXiv)

We propose Intelligent Schema Memory (ISM), a self-evolving memory-augmented system that improves mathematical reasoning for a frozen LLM under continual learning with hard episodic resets. ISM maintains a compact, self-refined bank of strategy schemas learned from both successful and failed episodes, with symbolic tools that check intermediate steps and certify answers. Without updating model parameters, ISM outperforms passive, retrieval, and reflection baselines on MATH-Hard and OlympiadBench, using 64% and 86% fewer schemas respectively than the strongest passive baseline. These results show that small, actively maintained, and verified strategy memories can support reliable continual mathematical reasoning under strict episodic isolation. The codebase is available at https://github.com/pdx97/ISM .