让冻结模型持续学数学，靠自我优化的策略记忆库提升推理能力
ISM:Self-Improving Strategy Memory for Continual Mathematical Reasoning
- 构建可自更新的策略记忆库，记录成功与失败案例
- 在两个基准上表现超越基线，用更少策略达成更高准确率
- 适合需要长期数学推理且不能改模型参数的场景
我们提出智能模式记忆（ISM），一种自演化记忆增强系统，在严格周期性重置的持续学习中提升冻结大模型的数学推理能力。ISM维护一个紧凑、自我优化的策略模式库，内容来自成功与失败的推理过程，并通过符号工具验证中间步骤和最终答案。不更新模型参数的情况下，ISM在MATH-Hard和OlympiadBench上优于被动检索与反思基线，分别仅需64%和86%的策略数量即可达到最强被动基线的性能。结果表明，在严格的周期性隔离下，小规模、主动维护且经过验证的策略记忆可支撑可靠的持续数学推理。代码已开源：https://github.com/pdx97/ISM。
原文摘要 · Abstract (English)
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 .
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