Reinforcement learning and pattern finding in combinatorics 1080p

Adam Zsolt Wagner speaks to the Experimental Mathematics Seminar.
Abstract: We will look at two ways we can use tools from machine learning to help us with research in combinatorics. First we discuss reinforcement learning, a method that gives us a way to check conjectures for counterexamples efficiently. While it usually does not perform as well as other simpler methods, there have been several examples of projects in the past few years where RL was crucial for success. In the second half of the talk we will consider the following question of Ellenberg: at most how many points can we pick in the N by N grid, without creating an isosceles triangle? The best known constructions, found by computer searches for small values of N, clearly follow a pattern which we do not yet understand. We will discuss how one can train transformers to understand this pattern, and use this t rained transformer to help us find a bit better constructions for various N. This is joint work with Jordan Ellenberg, Marijn Heule, and Geordie Williamson.