Portrait of Alan Milligan

Alan Milligan

PhD - Université de Montréal
Alumni
Supervisor
Simon Lacoste-Julien
Co-supervisor
Aaron Courville
Research Topics
Deep Learning
Optimization
Website
Google Scholar
GitHub

Publications

Understanding Adam Requires Better Rotation Dependent Assumptions
Lucas Maes
Tianyue H. Zhang
Alan Milligan
Alexia Jolicoeur-Martineau
Ioannis Mitliagkas
Damien Scieur
Simon Lacoste-Julien
Charles Guille-escuret
Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This… (see more) paper investigates Adam's sensitivity to rotations of the parameter space. We observe that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis in practice. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature and find that they fall short in explaining Adam's behaviour across various rotation types. In contrast, we verify the orthogonality of the update as a promising indicator of Adam's basis sensitivity, suggesting it may be the key quantity for developing rotation-dependent theoretical frameworks that better explain its empirical success.
2025-09-17
NeurIPS.cc/2025/Conference (poster)
doi.org
openreview.net