Benign Overfitting in Single-Head Attention

Gal Vardi (Weizmann Institute of Science) · Roey Magen (Weizmann Institute of Science) · Shuning Shang (Zhejiang University) · Zhiwei Xu (University of Michigan) · Spencer Frei (Google) · Wei Hu (University of Michigan)

benign overfittingclassification settingconditionsdata distribution gradient descentmaximum-margin interpolatorminimum-norm interpolatornoise tokensoverfitting behaviorsignal-to-noise ratio softmax attention test performance training data transformers

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.