Awesome
FourierKAN
Pytorch Layer for FourierKAN
It is a layer intended to be a substitution for Linear + non-linear activation
This is inspired by Kolmogorov-Arnold Networks but using 1d fourier coefficients instead of splines coefficients It should be easier to optimize as fourier are more dense than spline (global vs local) Once convergence is reached you can replace the 1d function with spline approximation for faster evaluation giving almost the same result The other advantage of using fourier over spline is that the function are periodic, and therefore more numerically bounded Avoiding the issues of going out of grid
Usage
put the file in the same directory then
from fftKAN import NaiveFourierKANLayer
alternatively you can run
python fftKAN.py
to see the demo.
Code runs, cpu and gpu, but is untested.
This is a naive version that use memory proportional to the gridsize, where as a fused version doesn't require temporary memory
Training
The higher frequency terms of the fourier coefficients may make the training difficult as the function will not be very smooth.
@JeremyIV suggested a brownian noise intialisation for the fourier coefficients (See PR https://github.com/GistNoesis/FourierKAN/pull/4 ), you can try it by constructing the layer with the flag smooth_initialization=True
One usual way of dealing with Fourier higher frequency terms, is adding a regularization term which penalize the higher frequencies in the way you want. The merit of that being that the function will be enforced smoothed as training progresses, and not just at initialization.
Highlight of the core :
You can either do the simple thing of materializing the product and then do the sum, or you can use einsum to do the reduction. Einsum should use less memory but be slower
License
License is MIT, but future evolutions (including fused kernels ) will be proprietary.
Fused Operations
This layer use a lot of memory, but by fusing operations we don't need any extra memory, and we can even use trigonometry tricks.