Papers › On the Relationship between Self-Attention and Convolutional Layers
On the Relationship between Self-Attention and Convolutional Layers
Jean-Baptiste Cordonnier, Andreas Loukas, Martin Jaggi
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.
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Code
Syntology Ran 4 of 16 code samples harvested from 1 repository linked to this paper; 12 have no recorded run. Of those that ran: 1 ran · honoured contract; 3 ran · our draft was wrong.
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Code Syntology ran Syntology
16 samples harvested; 4 ran; 1 honoured the contract we drafted; 12 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 0 of the 16 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Classification | CIFAR-10 | SA quadratic embedding | Percentage correct | 93.8 | #168 of 265 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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