Benign Overfitting in Single-Head Attention

Roey Magen, Shuning Shang, Zhiwei Xu, Spencer Frei, Wei Hu, Gal Vardi

Keywords: single-head attention, benign overfitting, transformers

TL;DR: We prove that under appropriate conditions, a single-head softmax attention mechanism exhibits 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.

Primary Area: learning theory

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Submission Number: 9122