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Noah Marshall

PhD - McGill University
Supervisor
Adam M. Oberman
Co-supervisor
Courtney Paquette
Research Topics
Deep Learning

Publications

Exact risk curves of signSGD in High-Dimensions: quantifying preconditioning and noise-compression effects
Ke Liang Xiao
Noah Marshall
Atish Agarwala
Elliot Paquette
In recent years, signSGD has garnered interest as both a practical optimizer as well as a simple model to understand adaptive optimizers lik… (see more)e Adam. Though there is a general consensus that signSGD acts to precondition optimization and reshapes noise, quantitatively understanding these effects in theoretically solvable settings remains difficult. We present an analysis of signSGD in a high dimensional limit, and derive a limiting SDE and ODE to describe the risk. Using this framework we quantify four effects of signSGD: effective learning rate, noise compression, diagonal preconditioning, and gradient noise reshaping. Our analysis is consistent with experimental observations but moves beyond that by quantifying the dependence of these effects on the data and noise distributions. We conclude with a conjecture on how these results might be extended to Adam.
2025-07-14
International Conference on Machine Learning (Accept (poster))
doi.org
proceedings.mlr.press