A Loss Curvature Perspective on Training Instability in Deep Learning

TL;DR

This paper investigates how the curvature of the loss landscape affects training stability in deep learning, revealing that strategies like warmup and normalization improve optimization by navigating to flatter regions.

Contribution

It provides a comprehensive analysis of loss Hessian evolution across various factors, unifying different mitigation strategies under a common conditioning framework.

Findings

Successful training avoids high curvature regions early on.

Warmup and normalization techniques improve stability by enhancing conditioning.

Different strategies ultimately address poor loss landscape conditioning.

Abstract

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning rates affect the loss Hessian observed during training, we also analyze the effects of model initialization, architectural choices, and common training heuristics such as gradient clipping and learning rate warmup. Our results demonstrate that successful model and hyperparameter choices allow the early optimization trajectory to either avoid -- or navigate out of -- regions of high curvature and into flatter regions that tolerate a higher learning rate. Our results suggest a unifying perspective on how disparate mitigation strategies for training instability ultimately address the same underlying failure mode of neural network optimization, namely poor conditioning. Inspired by the conditioning perspective, we show that learning rate warmup can improve training stability just as much as batch normalization, layer normalization, MetaInit, GradInit, and Fixup initialization.