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Self-Improving Strategy Memory Boosts LLM Math Reasoning

Prakhar Dixit, Tim Oates· July 1, 2026 View original

Summary

Researchers propose Intelligent Schema Memory (ISM), a self-evolving memory system that enhances a frozen large language model's mathematical reasoning under continual learning. ISM maintains a compact bank of refined strategy schemas from successful and failed attempts, using symbolic tools for step-by-step verification.

A new system called Intelligent Schema Memory (ISM) has been introduced to significantly improve the mathematical reasoning capabilities of large language models (LLMs) without requiring any updates to the LLM's core parameters. This system operates as a self-evolving memory, continually refining a collection of strategy schemas. These schemas are derived from both successful problem-solving attempts and instances where the LLM failed, allowing for adaptive learning. ISM incorporates symbolic tools to rigorously check intermediate steps and verify final answers, ensuring accuracy and reliability. The research demonstrates that ISM outperforms other baseline methods, including passive, retrieval, and reflection-based approaches, on challenging mathematical benchmarks like MATH-Hard and OlympiadBench. Notably, ISM achieves these superior results while utilizing significantly fewer schemas than its strongest passive counterpart, highlighting its efficiency and effectiveness in supporting robust continual mathematical reasoning, even under strict episodic isolation.

Why it matters

This offers a path to significantly enhance the reliability and accuracy of LLMs for complex reasoning tasks, particularly in domains requiring precise, verifiable steps like mathematics, without costly model retraining.

How to implement this in your domain

  1. 1Evaluate current LLM performance on mathematical or logical reasoning tasks within your organization.
  2. 2Explore integrating a schema-based memory system to augment existing LLM applications.
  3. 3Develop a feedback loop for LLM outputs to identify successful and failed reasoning strategies.
  4. 4Pilot the use of symbolic verification tools to validate intermediate steps in critical LLM-generated solutions.

Who benefits

EdTechFinanceResearch & DevelopmentSoftware Development

Key takeaways

  • Intelligent Schema Memory (ISM) improves LLM mathematical reasoning without model parameter updates.
  • ISM uses a self-refined bank of strategy schemas from successful and failed attempts.
  • Symbolic tools within ISM verify intermediate steps and certify answers.
  • It outperforms baselines on hard math benchmarks, using fewer schemas.

Original post by Prakhar Dixit, Tim Oates

"arXiv:2606.31191v1 Announce Type: new Abstract: 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…"

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