Machine Learning NeEDS Mathematical Optimization with Dr Bernardino Romera Paredes

Machine Learning NeEDS Mathematical Optimization
Branding the role of OR in AI with the Support of EURO

Title: FunSearch: Discovering new mathematics and algorithms using Large Language Models

Abstract: In this talk I will present FunSearch, a method to search for new solutions in mathematics and computer science. FunSearch works by pairing a pre-trained LLM, whose goal is to provide creative solutions in the form of computer code, with an automated “evaluator”, which guards against hallucinations and incorrect ideas. By iterating back-and-forth between these two components, initial solutions “evolve” into new knowledge. I will present the application of FunSearch to a central problem in extremal combinatorics — the cap set problem — where 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. Then, I will present the application of FunSearch to an algorithmic problem, online bin packing, which showcases the generality of the method. In this use case, FunSearch finds new heuristics that improve upon widely used baselines. I will conclude the talk by discussing the implications of searching in the space of code.