Year: 2022
Type: preprint
Abstract: Very little is known about the training dynamics of adaptive gradient methods like Adam in deep learning. In this paper, we shed light on the behavior of these algorithms in the full-batch and sufficiently large batch settings. Specifically, we empirically demonstrate that during full-batch training, the maximum eigenvalue of the preconditioned Hessian typically equilibrates at a certain numerical value -- the stability threshold of a gradient descent algorithm. For Adam with step size $η$ and $β_1 = 0.9$, this stability threshold is $38/η$. Similar effects occur during minibatch training, especially as the batch size grows. Yet, even though adaptive methods train at the ``Adaptive Edge of Stability'' (AEoS), their behavior in this regime differs in a significant way from that of non-adaptive methods at the EoS. Whereas non-adaptive algorithms at the EoS are blocked from entering high-curvature regions of the loss landscape, adaptive gradient methods at the AEoS can keep advancing into high-curvature regions, while adapting the preconditioner to compensate. Our findings can serve as a foundation for the community's future understanding of adaptive gradient methods in deep learning.
Source: arXiv (Cornell University)
Authors: Cohen, Jeremy M., Ghorbani, Behrooz, Krishnan, Shankar, Agarwal, Naman, Medapati, Sourabh, Badura, Michal, Suo, Daniel, Cardoze, David, Nado, Zachary, Dahl, George E., Gilmer, Justin
Institution: Google (United States)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4289446290