Benign Overfitting in Single-Head Attention

TL;DR

This paper investigates benign overfitting in single-head attention models, demonstrating that under certain conditions, these models can perfectly fit noisy data yet still generalize well, with the behavior depending on the data's signal-to-noise ratio.

Contribution

It provides the first theoretical analysis of benign overfitting in a fundamental Transformer component, showing conditions for its occurrence in a simple attention model.

Findings

Benign overfitting occurs after two gradient steps under certain conditions.

A large signal-to-noise ratio is necessary and sufficient for benign overfitting.

Minimum-norm interpolators can also exhibit benign overfitting.

Abstract

The phenomenon of benign overfitting, where a trained neural network perfectly fits noisy training data but still achieves near-optimal test performance, has been extensively studied in recent years for linear models and fully-connected/convolutional networks. In this work, we study benign overfitting in a single-head softmax attention model, which is the fundamental building block of Transformers. We prove that under appropriate conditions, the model exhibits benign overfitting in a classification setting already after two steps of gradient descent. Moreover, we show conditions where a minimum-norm/maximum-margin interpolator exhibits benign overfitting. We study how the overfitting behavior depends on the signal-to-noise ratio (SNR) of the data distribution, namely, the ratio between norms of signal and noise tokens, and prove that a sufficiently large SNR is both necessary and sufficient for benign overfitting.