Title: Local-Global Shifting Vision Transformers. Abstract: Recent work has shown the potential of transformers for computer vision applications. An image is first partitioned into patches, which are then used as input tokens for the attention mechanism. Due to the expensive quadratic cost of the attention mechanism, either a large patch size is used, resulting in coarse-grained global interactions, or alternatively, attention is applied only on a local region of the image at the expense of long-range interactions.  In this work, we propose an approach that allows for both coarse global interactions and fine-grained local interactions simultaneously. At the core of our method is the application of local and global attention layers.  In the local attention layer, we apply attention to each patch and its local shifts, resulting in virtually located local patches, which are not bound to a single, specific location. These virtually located patches are then used in global attention layers, where global coarse interactions are learned, using a pyramid of attention layers applied on decreasing resolution inputs. The separation of the attention layer into local and global counterparts allows for a low computational cost in the number of patches, while still supporting data-dependent localization, as opposed to the static positioning in other visual transformers. Our method is shown to be superior to both convolutional and transformer-based methods for image classification on CIFAR10, CIFAR100, and ImageNet.