On the Relationship between Self Attention and Convolutional Layers

Properties
authors	Jean-Baptiste Cordonnier, Andreas Loukas, Martin Jaggi
year	2020
url	https://arxiv.org/abs/1911.03584

Abstract

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, Stand-Alone Self-Attention in Vision Models 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 self-attention layers attend to pixel-grid patterns similarly to CNN layers, corroborating our analysis.

Notes

• Note to self: fully read article, it looks fun ⏫ #personal