Unveil Benign Overfitting for Transformer in Vision: Training Dynamics, Convergence, and Generalization

TL;DR

This paper provides the first theoretical analysis of benign overfitting in Vision Transformers, revealing conditions under which they generalize well despite overfitting, supported by both theory and experiments.

Contribution

It introduces a novel theoretical framework for understanding benign overfitting in transformers, addressing challenges posed by softmax and weight interdependence.

Findings

Established a sharp condition for generalization based on signal-to-noise ratio.

Characterized training dynamics and convergence behavior of transformers.

Validated theoretical insights through experimental simulations.

Abstract

Transformers have demonstrated great power in the recent development of large foundational models. In particular, the Vision Transformer (ViT) has brought revolutionary changes to the field of vision, achieving significant accomplishments on the experimental side. However, their theoretical capabilities, particularly in terms of generalization when trained to overfit training data, are still not fully understood. To address this gap, this work delves deeply into the benign overfitting perspective of transformers in vision. To this end, we study the optimization of a Transformer composed of a self-attention layer with softmax followed by a fully connected layer under gradient descent on a certain data distribution model. By developing techniques that address the challenges posed by softmax and the interdependent nature of multiple weights in transformer optimization, we successfully characterized the training dynamics and achieved generalization in post-training. Our results establish a sharp condition that can distinguish between the small test error phase and the large test error regime, based on the signal-to-noise ratio in the data model. The theoretical results are further verified by experimental simulation. To the best of our knowledge, this is the first work to characterize benign overfitting for Transformers.