In this repo, we use Efficient KAN (https://github.com/Blealtan/efficient-kan/ and FAST-KAN (https://github.com/ZiyaoLi/fast-kan/) to create BSRBF_KAN, which combines B-Splines (BS) and Radial Basis Functions (RBF) for Kolmogorov-Arnold Networks (KANs).
Our paper is available at https://arxiv.org/abs/2406.11173 (BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks).
- numpy==1.26.4
- numpyencoder==0.3.0
- torch==2.3.0+cu118
- torchvision==0.18.0+cu118
- tqdm==4.66.4
We start with layer normalization of the input and then merge three outputs: base_output, bs_output, and rbf_output. Although this method appears simple, finding an optimal combined KAN that is better than the available KANs in terms of something (accuracy, speed, convergence, etc) is time-consuming. We hope our research will lead to the development of various combined KANs using mathematical functions.
def forward(self, x):
# layer normalization
x = self.layernorm(x)
# base
base_output = F.linear(self.base_activation(x), self.base_weight)
# b_splines
bs_output = self.b_splines(x).view(x.size(0), -1)
# rbf
rbf_output = self.rbf(x).view(x.size(0), -1)
# combine
bsrbf_output = bs_output + rbf_output
bsrbf_output = F.linear(bsrbf_output, self.spline_weight)
return base_output + bsrbf_output
- mode: working mode ("train" or "test").
- ds_name: dataset name ("mnist" or "fashion_mnist").
- model_name: type of model (bsrbf_kan, efficient_kan, fast_kan, faster_kan).
- epochs: the number of epochs.
- batch_size: the training batch size.
- n_input: The number of input neurons.
- n_hidden: The number of hidden neurons. We use only 1 hidden layer. You can modify the code (run.py) for more layers.
- n_output: The number of output neurons (classes). For MNIST, there are 10 classes.
- grid_size: The size of grid (default: 5). Use with bsrbf_kan and efficient_kan.
- spline_order: The order of spline (default: 3). Use with bsrbf_kan and efficient_kan.
- num_grids: The number of grids, equals grid_size + spline_order (default: 8). Use with fast_kan and faster_kan.
- device: use "cuda" or "cpu".
- n_examples: the number of examples in the training set used for training (default: -1, mean use all training data)
python run.py --mode "train" --ds_name "mnist" --model_name "bsrbf_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --grid_size 5 --spline_order 3
python run.py --mode "train" --ds_name "mnist" --model_name "efficient_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --grid_size 5 --spline_order 3
python run.py --mode "train" --ds_name "mnist" --model_name "fast_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --num_grids 8
python run.py --mode "train" --ds_name "mnist" --model_name "faster_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --num_grids 8
python run.py --mode "train" --ds_name "mnist" --model_name "gottlieb_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --spline_order 3
python run.py --mode "train" --ds_name "mnist" --model_name "mlp" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10
We trained the models on GeForce RTX 3060 Ti (with other default parameters; see Commands). The results are in our updated paper, we are working to update them.
- https://github.com/Blealtan/efficient-kan
- https://github.com/AthanasiosDelis/faster-kan
- https://github.com/ZiyaoLi/fast-kan/
- https://github.com/seydi1370/Basis_Functions
- https://github.com/KindXiaoming/pykan (the original KAN)
We especially thank the contributions of https://github.com/Blealtan/efficient-kan, https://github.com/ZiyaoLi/fast-kan/, and https://github.com/seydi1370/Basis_Functions for their great work in KANs.
@misc{ta2024bsrbfkan,
title={BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks},
author={Hoang-Thang Ta},
year={2024},
eprint={2406.11173},
archivePrefix={arXiv}
}
}
If you have any questions, please contact: [email protected]. If you want to know more about me, please visit website: https://tahoangthang.com.