On the Relationship between Self-Attention and Convolutional Layers
This work addresses a foundational question in computer vision about the relationship between attention and convolution, potentially influencing model design for researchers and practitioners.
The paper investigates whether self-attention layers in vision models operate similarly to convolutional layers, proving that multi-head self-attention is at least as expressive as convolution and showing through experiments that they attend to pixel-grid patterns like CNNs.
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 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. Our code is publicly available.