Vision Transformers (ViTs) with self-attention modules have recently achieved great empirical success in many vision tasks. Due to non-convex interactions across layers, however, theoretical learning and generalization analysis is mostly elusive. Based on a data model characterizing both label-relevant and label-irrelevant tokens, this paper provides the first theoretical analysis of training a shallow ViT, i.e., one self-attention layer followed by a two-layer perceptron, for a classification task. We characterize the sample complexity to achieve a zero generalization error. Our sample complexity bound is positively correlated with the inverse of the fraction of label-relevant tokens, the token noise level, and the initial model error. We also prove that a training process using stochastic gradient descent (SGD) leads to a sparse attention map, which is a formal verification of the general intuition about the success of attention. Moreover, this paper indicates that a proper token sparsification can improve the test performance by removing label-irrelevant and/or noisy tokens, including spurious correlations. Empirical experiments on synthetic data and CIFAR-10 dataset justify our theoretical results and generalize to deeper ViTs.

翻译：视觉Transformer（ViT）凭借其自注意力模块，近期在众多视觉任务中取得了显著的实证成功。然而，由于层间非凸交互作用，其理论学习和泛化分析长期难以实现。本文基于一个描述标签相关与标签无关令牌的数据模型，首次对分类任务中浅层ViT（即一个自注意力层后接一个两层感知器）的训练进行理论分析。我们刻画了实现零泛化误差所需的样本复杂度。该样本复杂度上界与标签相关令牌占比的倒数、令牌噪声水平及初始模型误差呈正相关。我们还证明，采用随机梯度下降（SGD）的训练过程会导致稀疏注意力图，这正式验证了关于注意力机制成功原理的普遍直觉。此外，本文表明，通过移除标签无关和/或含噪令牌（包括虚假相关性），适当的令牌稀疏化可提升测试性能。基于合成数据及CIFAR-10数据集的实证实验证实了我们的理论结果，并将其推广至更深层ViT。