Phil 1.11.20

On the Relationship between Self-Attention and Convolutional Layers

  • 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, Ramachandran 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 powerful as any convolutional layer. Our numerical experiments then show that the phenomenon also occurs in practice, corroborating our analysis. Our code is publicly available.
  • I’ve just started to think about how machines and humans could serve as different attention heads, which is why we concentrate into populations with shared features. Attention, given the right conditions, may be an emergent phenomena. Need to look at Kauffman.


  • More Forward – done!
  • Dedication – done
  • Acknowledgements – started!
  • Sometime between the end of the forward and meeting with Aaron, move over to the new template