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KindXiaoming / pykan

Kolmogorov Arnold Networks
MIT License
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Corresponding explanation #109

Closed ghost closed 2 months ago

ghost commented 4 months ago

Hello, what is the proof that kan and mlp are dual?

brayevalerien commented 4 months ago

You can read the full paper at: https://arxiv.org/abs/2404.19756 The section where they define the KANs should be sufficient

ghost commented 4 months ago

Do you use the article "Duality between two generalized.." by Wang Y. et al?

brayevalerien commented 4 months ago

I've not read the paper you are mentioning yet, but there is a discussion about this topic on Reddit. The OP has shared a notebook where they show how one can build an MLP equivalent to a given KAN.

edit: typo

ghost commented 4 months ago

Thanks!

brayevalerien commented 4 months ago

You're welcome. This is a pretty interesting topic and even thought the collab notebook only shows how they are equivalent on a piecewise linear fonction, I'm confident it can be generalized to any continous function with large enough MLPs.

AlessandroFlati commented 4 months ago

Spoiler: it can. Unfortunately, this comment is too narrow to write down the proof. (semi-quote)