ISM:Self-Improving Strategy Memory for Continual Mathematical Reasoning

2026-06-30

AI Summary

This work addresses the challenge of sustaining mathematical reasoning in large language models with frozen parameters under strict phase-wise resets. To this end, the authors propose Intelligent Strategy Memory (ISM), a mechanism that constructs a compact strategy repository distilled from both successful and failed reasoning experiences. Without updating model parameters, ISM integrates symbolic tools to verify reasoning trajectories, enabling self-evolution of reasoning capabilities through an external, self-improving strategy memory. Notably, this is the first approach to demonstrate continuous performance gains under stringent phase isolation using only memory augmentation. Experiments show that ISM significantly outperforms passive, retrieval-based, and reflection-based baselines on MATH-Hard and OlympiadBench, achieving superior results with 64% and 86% fewer stored strategies, respectively.

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 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.

Problem

• continual learning
• mathematical reasoning
• episodic resets
• frozen LLM
• strategy memory

Innovation

• Intelligent Schema Memory
• continual learning
• mathematical reasoning
• memory-augmented system
• episodic reset