In last year's AI retreat, we had lots of fun applying ML to an interesting maths problem, so this year's retreat will go all in. We will focus entirely on working with mathematical data: knots. Knot theory is an interesting area of mathematics with a lot of interesting structure, but a low barrier to entry. We will look into learning knot invariants, learning to unknot, factorizing composite knots into prime components, and many more.

We will learn about choosing the right, mathematically motivated architectures for the problems involving knots. There are several invariances that can be exploited in creative ways to make the learning problem easier, and the solutions more robust. We will explore concepts like circular convolution, convolutional transformers and more.

Several problems related to knots can be framed as Markov decision processes: similar to games like chess or go, but instead of a board, the state of the game is a knot, and instead of moves, we have mathematical transformations and operations to work with. This makes these problems an ideal playground to learn reinforcement learning algorithms, such as Monte Carlo tree search, Q-learning, and more.