KAN for images?

[albusdemens]

Hello, first of all, congratulations for the great work! As far as you know, is it possible to extend the Kolmogorov-Arnold theorem to images? Something like "If IM is a multivariate continuous (?) [2D] function on a bounded domain, it can be written as a finite composition of continuous [2D] functions". If that holds, then KANs have the potential to take as input images too! Taking as a starting point what you observed for PDE, KANs could turn out to be more accurate and more parameter-efficient than MLPs, and potentially CNNs.

I am testing if things work, codewise.

[yingzhige00]

Hello, I don’t know how your test results are. I am also very concerned about whether KAN can be applied to images. Can you share it?

[albusdemens]

Hello, I have a deadline this friday so I didn't have any time for this. Next week should be better. I'll let you know ASAP

[epicgzs1112]

me too!@yingzhige0,@albusdemens.

[hailuu684]

I am waiting for all discussions

[lacie-life]

Me too!

[albusdemens]

@yingzhige00 @epicgzs1112 @hailuu684 @lacie-life I wrote down my thoughts, trying to explain the intuition I got, and listed the points that should be considered/tested/solved. Feel free to let me know if you have any comments :) If anyone is interested, we could team up and test things.

To be clear, there could be fundamental reasons why using KANs to process images is not possible. Anyway, it could be worth exploring further.

KAN_images.pdf

[StarostinV]

Here is the basic implementation of the convolutional layer with KAN, which seems to work just fine on the mnist dataset. https://github.com/StarostinV/convkan