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Comment by Legend2440 | Hacker News Reader

Only certain types of neural networks use convolutions. It's not universal.

No, ALL machine learning architectures are convolutions https://grlearning.github.io/papers/11.pdf

Reading the paper, they're saying convolutions are powerful enough to express any possible architecture. But that's just computational universality - this does not mean they are convolutions.

Every matrix multiply can be viewed as a 1x1 convolution, just like every convolution can be viewed as an (implicit, for larger than 1x1 kernels) matrix multiply.

I'm not sure this is particularly enlightening, but it's probably one small step of understanding that is required to truly "get" the underlying math.

Edit: Should have said that every matrix multiply against weights is a convolution. The matrix multiply in the standard attention block (query times keys) really doesn't make sense to be seen as a convolution.

Integral transform is the right abstraction level. Matmul is an integral transform.

What are some examples of types that don't?

I think anything that doesn't have an explicit convolution layer? Transformer, MLP, RNN don't automatically have a convolution layer, although for many tasks you can add it in if you want.

The transformer module is currently dominating ML, and is widely used in text, vision, audio, and video models. It was introduced in 2017 and shows no real signs of being displaced. It has no convolutions.

https://en.wikipedia.org/wiki/Transformer_(deep_learning_arc... http://jalammar.github.io/illustrated-transformer/

… or does it https://grlearning.github.io/papers/11.pdf

Lots of interesting work out there; time will tell!

If they use dot products on at least one layer with fully-connected inputs, which they do, along with everything else derived from the basic MLP model, then they're technically performing convolution.

Of course, the convolution concept breaks down when nonlinear activation functions are introduced, so I'm not sure the equivalence is really all that profound.

Nonlinear activation layers are piecewise linear-ish.

I don't think a dot product between high dimensional vectors is considered a convolution? I'm familiar with convolution between continuous functions, and with kernels in neural networks providing invariance. I'd love to learn more if you have any links that expand on your statement.

Transformers, MLPs.

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