Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models

TL;DR

This paper investigates why Adam outperforms gradient descent on language models, revealing that heavy-tailed class imbalance causes slow learning for infrequent words with gradient descent, while Adam mitigates this issue.

Contribution

It demonstrates that heavy-tailed class imbalance explains Adam's superior performance and provides empirical and theoretical evidence across various models and data types.

Findings

Gradient descent learns frequent words faster than infrequent ones.

Adam and sign-based methods are less affected by class imbalance.

Theoretical proof shows slow convergence of gradient descent on low-frequency classes.

Abstract

Adam has been shown to outperform gradient descent on large language models by a larger margin than on other tasks, but it is unclear why. We show that a key factor in this performance gap is the heavy-tailed class imbalance found in language tasks. When trained with gradient descent, the loss of infrequent words decreases more slowly than the loss of frequent ones. This leads to a slow decrease on the average loss as most samples come from infrequent words. On the other hand, Adam and sign-based methods are less sensitive to this problem. To establish that this behavior is caused by class imbalance, we show empirically that it can be reproduced across architectures and data types, on language transformers, vision CNNs, and linear models. On a linear model with cross-entropy loss, we show that class imbalance leads to imbalanced, correlated gradients and Hessians that have been hypothesized to benefit Adam. We also prove that, in continuous time, gradient descent converges slowly on low-frequency classes while sign descent does not.