Code developed for MXM Research 2023-24 as part of Jordan Ellenberg's project with the guidance of graduate student Karan Srivastava. We found the fastest ways to generate matrices in certain groups by gamifiying the process and applying reinforcement learning, then compared them to current research.
We trained several neural networks to learn the base Euclidean algorithm.
We generalized our solution to learn how to apply arbitrary randomly-generated matrices to a coordinate point in order to get closer to the origin (see here).
We also trained two neural nets using Monte Carlo Tree Search to decide state values and policies (which transformations should be applied).
We trained a tabular Q-learning model to learn the value of different moves and then trained a neural network on the output of the Q-learning model to try generalizing its output.
Additionally, we implemented BFS to explore the heisenberg group starting at the origin and trained another neural net on that optimal data.
We also did extensive data visualization on the output of BFS and Q learning to understand what these methods were suggesting about the fastest way to get back to the origin.
We investigated whether SL3(Z) could be generated by the 2 matrices described in example 11 of this paper.