Vision Transformers (ViTs) have emerged as the fundamental architecture for most computer vision fields, but the considerable memory and computation costs hinders their application on resource-limited devices. As one of the most powerful compression methods, binarization reduces the computation of the neural network by quantizing the weights and activation values as $\pm$1. Although existing binarization methods have demonstrated excellent performance on Convolutional Neural Networks (CNNs), the full binarization of ViTs is still under-studied and suffering a significant performance drop. In this paper, we first argue empirically that the severe performance degradation is mainly caused by the weight oscillation in the binarization training and the information distortion in the activation of ViTs. Based on these analyses, we propose $\textbf{BinaryViT}$, an accurate full binarization scheme for ViTs, which pushes the quantization of ViTs to the limit. Specifically, we propose a novel gradient regularization scheme (GRS) for driving a bimodal distribution of the weights to reduce oscillation in binarization training. Moreover, we design an activation shift module (ASM) to adaptively tune the activation distribution to reduce the information distortion caused by binarization. Extensive experiments on ImageNet dataset show that our BinaryViT consistently surpasses the strong baseline by 2.05% and improve the accuracy of fully binarized ViTs to a usable level. Furthermore, our method achieves impressive savings of 16.2$\times$ and 17.7$\times$ in model size and OPs compared to the full-precision DeiT-S.
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