On the Relationship between Self-Attention and Convolutional Layers

A BSTRACT Recent trends of incorporating attention mechanisms in vision have led researchers to reconsider the supremacy of convolutional layers as a primary building block. Beyond helping CNNs to handle long-range dependencies, Ramachan-dran et al. (2019) showed that attention can completely replace convolution and achieve state-of-the-art performance on vision tasks. This raises the question: do learned attention layers operate similarly to convolutional layers? This work provides evidence that attention layers can perform convolution and, indeed, they often learn to do so in practice. Specifically, we prove that a multi-head self-attention layer with sufficient number of heads is at least as expressive as any convolutional layer. Our numerical experiments then show that the phenomenon also occurs in practice, corroborating our analysis. Our code is publicly available 1 . 1 I NTRODUCTION Recent advances in Natural Language Processing (NLP) are largely attributed to the rise of the transformer (V aswani et al., 2017).