The instabilities of large learning rate training: a loss landscape view

Modern neural networks are undeniably successful. Numerous works study how the curvature of loss landscapes can affect the quality of solutions. In this work we study the loss landscape by considering the Hessian matrix during network training with large learning rates - an attractive regime that is (in)famously unstable. We characterise the instabilities of gradient descent, and we observe the striking phenomena of $\mathit{\text{landscape}}\mathit{\text{flattening}}$ and $\mathit{\text{landscape}}\mathit{\text{shift}}$, both of which are intimately connected to the instabilities of training.