Making Vision Transformers Truly Shift-Equivariant

For computer vision tasks, Vision Transformers (ViTs) have become one of the go-to deep net architectures. Despite being inspired by Convolutional Neural Networks (CNNs), ViTs remain sensitive to small shifts in the input image. To address this, we introduce novel designs for each of the modules in ViTs, such as tokenization, self-attention, patch merging, and positional encoding. With our proposed modules, we achieve truly shift-equivariant ViTs on four well-established models, namely, Swin, SwinV2, MViTv2, and CvT, both in theory and practice. Empirically, we tested these models on image classification and semantic segmentation, achieving competitive performance across three different datasets while maintaining 100% shift consistency.

Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networks

We propose learnable polyphase sampling (LPS), a pair of learnable down/upsampling layers that enable truly shift-invariant and equivariant convolutional networks. LPS can be trained end-to-end from data and generalizes existing handcrafted downsampling layers. It is widely applicable as it can be integrated into any convolutional network by replacing down/upsampling layers. We evaluate LPS on image classification and semantic segmentation. Experiments show that LPS is on-par with or outperforms existing methods in both performance and shift consistency. For the first time, we achieve true shift-equivariance on semantic segmentation (PASCAL VOC), i.e., 100% shift consistency, outperforming baselines by an absolute 3.3%.