DeepAI AI Chat
Log In Sign Up

Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

by   Jeremy M Cohen, et al.

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 numerical value 2 / (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. Code is available at


page 1

page 2

page 3

page 4


Adaptive Gradient Methods at the Edge of Stability

Very little is known about the training dynamics of adaptive gradient me...

Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Recently, researchers observed that gradient descent for deep neural net...

Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Traditional analyses of gradient descent show that when the largest eige...

Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability

Recent findings (e.g., arXiv:2103.00065) demonstrate that modern neural ...

Second-order regression models exhibit progressive sharpening to the edge of stability

Recent studies of gradient descent with large step sizes have shown that...

There is a Singularity in the Loss Landscape

Despite the widespread adoption of neural networks, their training dynam...

Limited Evaluation Evolutionary Optimization of Large Neural Networks

Stochastic gradient descent is the most prevalent algorithm to train neu...