# \[PAPER\] Mathematical discoveries from program search with large language models **URL:** \ **Category:** Community\ **Tags:** api\ **Created:** [December 15, 2023, 8:53pm UTC](https://community.openai.com/t/paper-mathematical-discoveries-from-program-search-with-large-language-models/560495 "2023-12-15T20:53:24Z")\ **Posts on this page:** 1\ **Showing post:** 1
**Author:** ![PaulBellow](https://sea2.discourse-cdn.com/openai1/user_avatar/community.openai.com/paulbellow/32/597962_2.png) [@PaulBellow](https://community.openai.com/u/PaulBellow)\ **Post date:** [December 15, 2023, 8:53pm UTC](https://community.openai.com/t/paper-mathematical-discoveries-from-program-search-with-large-language-models/560495/1 "2023-12-15T20:53:24Z")
> Large Language Models (LLMs) have demonstrated tremendous capabilities in solving complex tasks, from quantitative reasoning to understanding natural language. However, LLMs sometimes suffer from confabulations (or hallucinations) which can result in them making plausible but incorrect statements [1,2]. This hinders the use of current large models in scientific discovery. Here we introduce _FunSearch_ (short for _search_ing in the _fun_ction space), an evolutionary procedure based on pairing a pre-trained LLM with a systematic evaluator. We demonstrate the effectiveness of this approach to surpass the best known results in important problems, pushing the boundary of existing LLM-based approaches [3]. Applying _FunSearch_ to a central problem in extremal combinatorics — the cap set problem — we discover new constructions of large cap sets going beyond the best known ones, both in finite dimensional and asymptotic cases. This represents the first discoveries made for established open problems using LLMs. We showcase the generality of _FunSearch_ by applying it to an algorithmic problem, online bin packing, finding new heuristics that improve upon widely used baselines. In contrast to most computer search approaches, _FunSearch_ searches for programs that describe _how_ to solve a problem, rather than _what_ the solution is. Beyond being an effective and scalable strategy, discovered programs tend to be more interpretable than raw solutions, enabling feedback loops between domain experts and _FunSearch_, and the deployment of such programs in real-world applications. [https://www.nature.com/articles/s41586-023-06924-6](https://www.nature.com/articles/s41586-023-06924-6) --- _[View the full topic](https://community.openai.com/t/paper-mathematical-discoveries-from-program-search-with-large-language-models/560495)._