Mathematical discoveries from program search with large language models

The article discusses the development of FunSearch, an evolutionary procedure that pairs a pre-trained Large Language Model (LLM) with a systematic evaluator to overcome the issue of confabulations or hallucinations in LLMs. The authors demonstrate the effectiveness of FunSearch in surpassing the best known results in important problems and making new discoveries in established open problems. The procedure was applied to the cap set problem in extremal combinatorics and an algorithmic problem, online bin packing, resulting in new heuristics and constructions of large cap sets.

FunSearch differs from most computer search approaches as it searches for programs that describe how to solve a problem, rather than what the solution is. The discovered programs are more interpretable than raw solutions, enabling feedback loops between domain experts and FunSearch, and the deployment of such programs in real-world applications. The authors suggest that FunSearch represents a scalable strategy for pushing the boundaries of existing LLM-based approaches.

Key takeaways:

The article introduces a new evolutionary procedure called FunSearch, which pairs a pre-trained Large Language Model (LLM) with a systematic evaluator to improve results in complex tasks.
FunSearch has been applied to the cap set problem in extremal combinatorics, leading to new discoveries that surpass previous best-known results.
The procedure has also been applied to an algorithmic problem, online bin packing, where it found new heuristics that improve upon widely used baselines.
Unlike most computer search approaches, FunSearch focuses on finding programs that describe how to solve a problem, rather than what the solution is, leading to more interpretable results and enabling feedback loops between domain experts and FunSearch.

Mathematical discoveries from program search with large language models

Key takeaways:

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