  Recently, transformer has achieved remarkable performance on a variety of
computer vision applications. Compared with mainstream convolutional neural
networks, vision transformers are often of sophisticated architectures for
extracting powerful feature representations, which are more difficult to be
developed on mobile devices. In this paper, we present an effective
post-training quantization algorithm for reducing the memory storage and
computational costs of vision transformers. Basically, the quantization task
can be regarded as finding the optimal low-bit quantization intervals for
weights and inputs, respectively. To preserve the functionality of the
attention mechanism, we introduce a ranking loss into the conventional
quantization objective that aims to keep the relative order of the
self-attention results after quantization. Moreover, we thoroughly analyze the
relationship between quantization loss of different layers and the feature
diversity, and explore a mixed-precision quantization scheme by exploiting the
nuclear norm of each attention map and output feature. The effectiveness of the
proposed method is verified on several benchmark models and datasets, which
outperforms the state-of-the-art post-training quantization algorithms. For
instance, we can obtain an 81.29\% top-1 accuracy using DeiT-B model on
ImageNet dataset with about 8-bit quantization.
