Self-Improving Strategy Memory Boosts LLM Math Reasoning

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.