Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session D02: Statistical Physics Meets Machine Learning I
3:00 PM–6:00 PM,
Monday, March 6, 2023
Room: Room 125
Sponsoring
Units:
GSNP DSOFT DBIO GDS
Chair: Yuhai Tu, IBM T. J. Watson Research Center
Abstract: D02.00005 : Flatter, Faster; Scaling Momentum for Optimal Speedup of SGD*
4:12 PM–4:24 PM
Presenter:
Aditya Cowsik
(Stanford University)
Authors:
Aditya Cowsik
(Stanford University)
Tankut U Can
(The School of Natural Sciences at the Institute for Advanced Study at Princeton)
Paolo Glorioso
(Stanford University)
Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have superior training times. Momentum can help accelerate training with SGD, but so far there has been no principled way to select the momentum hyperparameter. Here we study implicit bias arising from the interplay between SGD with label noise and momentum in the training of overparametrized neural networks. We find that scaling the momentum hyperparameter $1-eta$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization. To analytically derive this result we develop an architecture-independent framework, where the main assumption is the existence of a degenerate manifold of global minimizers, as is natural in overparametrized models. Training dynamics display the emergence of two characteristic timescales that are well-separated for generic values of the hyperparameters. The maximum acceleration of training is reached when these two timescales meet, which in turn determines the scaling limit we propose. We perform experiments, including matrix sensing and ResNet on CIFAR10, which provide evidence for the robustness of these results.
*Stanford Graduate Fellowship and Xiaoliang Qi's Simons Investigator Award (ID: 560571)
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