  Vision transformers have been applied successfully for image recognition
tasks. There have been either multi-headed self-attention based (ViT
\cite{dosovitskiy2020image}, DeIT, \cite{touvron2021training}) similar to the
original work in textual models or more recently based on spectral layers
(Fnet\cite{lee2021fnet}, GFNet\cite{rao2021global},
AFNO\cite{guibas2021efficient}). We hypothesize that both spectral and
multi-headed attention plays a major role. We investigate this hypothesis
through this work and observe that indeed combining spectral and multi-headed
attention layers provides a better transformer architecture. We thus propose
the novel Spectformer architecture for transformers that combines spectral and
multi-headed attention layers. We believe that the resulting representation
allows the transformer to capture the feature representation appropriately and
it yields improved performance over other transformer representations. For
instance, it improves the top-1 accuracy by 2\% on ImageNet compared to both
GFNet-H and LiT. SpectFormer-S reaches 84.25\% top-1 accuracy on ImageNet-1K
(state of the art for small version). Further, Spectformer-L achieves 85.7\%
that is the state of the art for the comparable base version of the
transformers. We further ensure that we obtain reasonable results in other
scenarios such as transfer learning on standard datasets such as CIFAR-10,
CIFAR-100, Oxford-IIIT-flower, and Standford Car datasets. We then investigate
its use in downstream tasks such of object detection and instance segmentation
on the MS-COCO dataset and observe that Spectformer shows consistent
performance that is comparable to the best backbones and can be further
optimized and improved. Hence, we believe that combined spectral and attention
layers are what are needed for vision transformers.
