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KindXiaoming / pykan

Kolmogorov Arnold Networks
MIT License
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KAN for images? #88

Open albusdemens opened 2 months ago

albusdemens commented 2 months ago

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 commented 2 months ago

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 commented 2 months ago

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 commented 2 months ago

me too!@yingzhige0,@albusdemens.

hailuu684 commented 2 months ago

I am waiting for all discussions

lacie-life commented 2 months ago

Me too!

albusdemens commented 2 months ago

@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 commented 1 month ago

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