Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability
Abstract
We empirically demonstrate that full-batch gradient descent on neural network training objectives typically operates in a regime we call the Edge of Stability. In this regime, the maximum eigenvalue of the training loss Hessian hovers just above the value $2 / \text{(step size)}$, and the training loss behaves non-monotonically over short timescales, yet consistently decreases over long timescales. Since this behavior is inconsistent with several widespread presumptions in the field of optimization, our findings raise questions as to whether these presumptions are relevant to neural network training. We hope that our findings will inspire future efforts aimed at rigorously understanding optimization at the Edge of Stability.
Cite
Text
Cohen et al. "Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability." International Conference on Learning Representations, 2021.Markdown
[Cohen et al. "Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability." International Conference on Learning Representations, 2021.](https://mlanthology.org/iclr/2021/cohen2021iclr-gradient/)BibTeX
@inproceedings{cohen2021iclr-gradient,
title = {{Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability}},
author = {Cohen, Jeremy and Kaur, Simran and Li, Yuanzhi and Kolter, J Zico and Talwalkar, Ameet},
booktitle = {International Conference on Learning Representations},
year = {2021},
url = {https://mlanthology.org/iclr/2021/cohen2021iclr-gradient/}
}