The large learning rate phase of deep learning: the catapult mechanism

TL;DR

This paper investigates how large learning rates induce a phase transition in deep neural network training, leading to flatter minima and often better performance, bridging theory and practical training dynamics.

Contribution

It introduces a solvable model predicting a phase transition at large learning rates and confirms these predictions empirically in deep learning applications.

Findings

Large learning rates lead to convergence to flatter minima.

Optimal performance often occurs in the large learning rate phase.

A narrow range of stable large learning rates exists.

Abstract

The choice of initial learning rate can have a profound effect on the performance of deep networks. We present a class of neural networks with solvable training dynamics, and confirm their predictions empirically in practical deep learning settings. The networks exhibit sharply distinct behaviors at small and large learning rates. The two regimes are separated by a phase transition. In the small learning rate phase, training can be understood using the existing theory of infinitely wide neural networks. At large learning rates the model captures qualitatively distinct phenomena, including the convergence of gradient descent dynamics to flatter minima. One key prediction of our model is a narrow range of large, stable learning rates. We find good agreement between our model's predictions and training dynamics in realistic deep learning settings. Furthermore, we find that the optimal performance in such settings is often found in the large learning rate phase. We believe our results shed light on characteristics of models trained at different learning rates. In particular, they fill a gap between existing wide neural network theory, and the nonlinear, large learning rate, training dynamics relevant to practice.