用大模型驱动的遗传算法自动发现数学问题的有趣例子。
Generative Modeling for Mathematical Discovery
- 用大语言模型生成候选解，遗传算法筛选优化，无需机器学习经验。
- 在三个组合与数论问题上成功找到新例子，部分发现具泛化能力。
- 适合数学研究者快速探索新猜想，代码修改少，可云端部署。
我们提出一种新的大语言模型驱动的遗传算法 funsearch 实现，旨在为数学家生成有研究价值的实例，已在极值组合学问题中取得成效。该实现面向实际应用，无需机器学习知识或高性能计算资源。使用 funsearch 解决新问题只需修改少量 Python 代码，并从第三方服务商选择一个大语言模型。我们在三个不同问题上进行了基准测试，获得了可用于指导未来应用的量化指标。结果表明，funsearch 在多种组合与数论场景中均能有效学习，并在某些情况下习得可泛化的原理，超越原始训练问题。
原文摘要 · Abstract (English)
We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying {\it funsearch} to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of {\it funsearch} to new problems. Our results demonstrate that {\it funsearch} successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.
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