We study how the Muon optimizer's parameter trajectories differ from gradient descent in matrix factorization. Muon avoids slow saddle-to-saddle dynamics, remains stable beyond the critical learning rate, and conserves a distinct matrix quantity that drives weights toward balanced solutions. Completed during a summer research internship funded by Imbue.

I'm designing a course that gives an introduction to Learning Mechanics. The course is built around the perspective paper There Will Be a Scientific Theory of Deep Learning (Simon et al., 2026).

What/why/how do deep neural networks learn? I co-authored this blog post for learningmechanics.pub to explain how a toy model (deep linear networks) can elucidate and make concrete intuition about deep learning.