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Kolmogorov-Arnold networks (KANs) in Wolfram language

Kolmogorov Arnold Networks

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POSTED BY: Andreas Hafver
7 Replies

Dear Andreas,

I implemented the MLP and KANs models using my own dataset. Please see the attached notebook.

The KANs model generated the following results: {{0.}, {0.}, {0.}, {0.}}

I’m not sure what the problem is.

Thank you for your help.

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POSTED BY: M.A. Ghorbani
Posted 2 months ago

Dear Ghobani,

I checked your Mathematica codes and found that your KAN model does not reduce the loss. It seems that only one KANlayer[2,1,15,3] is not complex enough to learn.

kan = NetTrain[NetChain[{KANlayer[2,1,15,3]},"Input"->2],training]

I added one more KANlayer, then the loss is reduced.

dataSDL = ArrayReshape[N@Range[300], {100, 3}];

Two KANlayers:

kanSDLEE = 
 NetTrain[NetChain[{KANlayer[2, 5, 15, 3], KANlayer[5, 1, 15, 3]}], 
  dataSDL[[All, 1 ;; 2]] -> Transpose@{dataSDL[[All, 3]]}].

Three KAN layers:

kanSDLEE03 = 
 NetTrain[
  NetChain[{KANlayer[2, 5, 15, 3], KANlayer[5, 5, 15, 3], 
    KANlayer[5, 1, 15, 3]}], 
  dataSDL[[All, 1 ;; 2]] -> Transpose@{dataSDL[[All, 3]]}].
POSTED BY: Sangdon Lee

Hi Sangdon,

I appreciate your help. You did awesome.:)

I’m going to start working on the problem now.

Regards

POSTED BY: M.A. Ghorbani
Posted 2 months ago
POSTED BY: Sangdon Lee

Hi, I really appreciate your time.

I got the attached message when I ran the new command.I even ran different data, but the program still gave me the same error.

Best

Attachment

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POSTED BY: M.A. Ghorbani
Posted 7 months ago

Dear Andreas: I use modification of your code for my paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4419282 (unpublished). What (pseudo-) metrics do you use to fit the polynomials -- MSE, Kullback-Leibler, something different? If you can answer, write me at pblerner18@gmail.com because I rarely use this place.

POSTED BY: Peter Lerner

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POSTED BY: EDITORIAL BOARD
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