A Loss Curvature Perspective on Training Instability in Deep Learning
This provides a unifying perspective on training instability for deep learning practitioners, though it is incremental in linking existing mitigation strategies.
The paper investigates how loss curvature affects training instability in deep neural networks, finding that successful hyperparameter choices help optimization avoid high-curvature regions, and shows that learning rate warmup can match the stability improvements of methods like batch normalization.
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.