Benign Overfitting in Single-Head Attention

2024-10-10

arXiv.org

AI Summary

This work investigates benign overfitting in single-head Softmax attention models: despite fitting noisy training data perfectly, such models retain strong generalization performance. Leveraging gradient descent dynamics analysis, minimum-norm interpolation theory, and high-dimensional statistical learning techniques, we provide the first rigorous proof that benign overfitting occurs in single-head attention, establishing signal-to-noise ratio (SNR) as its necessary and sufficient condition. We derive a verifiable SNR threshold that quantitatively links overfitting behavior to the underlying data distribution structure. Furthermore, we demonstrate that both the minimum-norm and maximum-margin interpolators under this architecture exhibit benign generalization. Empirical results show that merely two gradient descent steps suffice to achieve perfect training fit while attaining near-optimal test performance on noisy data.

Technology Category

• Machine Learning: Learning Theory
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• Study benign overfitting in single-head attention
• Analyze conditions for benign overfitting post-gradient descent
• Examine SNR's role in benign overfitting behavior

Innovation

• Single-head softmax attention model
• Gradient descent optimization
• Signal-to-noise ratio analysis