  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 $2 / \text{(step size)}$, 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. Code is
available at https://github.com/locuslab/edge-of-stability.
