Benign Overfitting in Single-Head Attention

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.

Authors

• Roey Magen
• Shuning Shang
• Zhiwei Xu Shandong University
• Spencer Frei
• Wei Hu State Key Laboratory for Novel Software Technology, Nanjing University, China National Institute of Healthcare Data Science, Nanjing University, China
• Gal Vardi

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