This is a Julia version of the TorchKAN. In the TorchKAN,

TorchKAN introduces a simplified KAN model and its variations, including KANvolver and KAL-Net, designed for high-performance image classification and leveraging polynomial transformations for enhanced feature detection.

In the original TorchKAN, the package uses the PyTorch. In the FluxKAN, this package uses the Flux.jl.

I rewrote the TorchKAN with the Julia language. Now this package has

• KAL-Net: Utilizing Legendre Polynomials in Kolmogorov Arnold Legendre Networks

In addition, I implemented Chebyshev polynomials in KAN.

• KAC-Net: Utilizing Chebyshev Polynomials in Kolmogorov Arnold Chebyshev Networks

I implemented the Gaussian Radial Basis Functions introduced in fastkan:

• KAG-Net: Utilizing Gaussian radial basis functions in Kolmogorov Arnold Gaussian Networks (non-trainable grids)
• KAGL-Net: (Experimental) Utilizing Gaussian radial basis functions in Kolmogorov Arnold Gaussian Networks (trainable grids)

add FluxKAN

You can use KALnet layer like Dense layer in Flux.jl. For example, the model is defined as

using FluxKAN
model = Chain(KALnet(2, 10), KALnet(10, 1))

or

using FluxKAN
model = Chain(KALnet(2, 10, polynomial_order=3), KALnet(10, 1, polynomial_order=3))

If you want to use the Chebyshev polynomials, you can use KACnet.

using FluxKAN
model = Chain(KACnet(2, 10, polynomial_order=3), KACnet(10, 1, polynomial_order=3))

If you want to use the Gaussian radial basis functions, you can use KAGnet.

using FluxKAN
model = Chain(KAGnet(2, 10, num_grids=4), KAGnet(10, 1, num_grids=4))

In the KAGnet, the grid points are fixed.

I implemented the Gaussian function with learnable grid points. But this is experimental. You can use KAGLnet.

using FluxKAN
FluxKAN.MNIST_KAN()

or

using FluxKAN
FluxKAN.MNIST_KAN(; batch_size=256, epochs=20, nhidden=64, polynomial_order=3,method= "Legendre")

We can choose Legendre, Chebyshev, or Gaussian.

With the use of the CUDA.jl, we can use the GPU. But now only KALnet and KACnet support GPU calculations. Please see the manual of Flux.jl.

Yuki Nagai, Ph. D.

Associate Professor in the Information Technology Center, The University of Tokyo.

For support, please contact: nagai.yuki@mail.u-tokyo.ac.jp

If this project is used in your research or referenced for baseline results, please use the following BibTeX entries.

@misc{torchkan,
  author = {Subhransu S. Bhattacharjee},
  title = {TorchKAN: Simplified KAN Model with Variations},
  year = {2024},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/1ssb/torchkan/}}
}

@misc{fluxkan,
  author = {Yuki Nagai},
  title = {FluxKAN: Julia version of the TorchKAN},
  year = {2024},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/cometscome/FluxKAN.jl}}
}

• [0] Ziming Liu et al., "KAN: Kolmogorov-Arnold Networks", 2024, arXiv. https://arxiv.org/abs/2404.19756
• [1] https://github.com/KindXiaoming/pykan
• [2] https://github.com/Blealtan/efficient-kan
• [3] https://github.com/1ssb/torchkan
• [4] https://github.com/ZiyaoLi/fast-kan