- Add SKAN and LArctan-SKAN: https://github.com/chikkkit/SKAN/, https://github.com/chikkkit/LArctan-SKAN
- Add "attention" combination
In this repository, we apply function combinations in low-dimensional data to design Kolmogorov-Arnold Networks, referred to as FC-KAN (Function Combinations in Kolmogorov-Arnold Networks). The experiments demonstrate that these combinations improve the model performance.
Our paper, "FC-KAN: Function Combinations in Kolmogorov-Arnold Networks," is available at https://arxiv.org/abs/2409.01763 or https://www.researchgate.net/publication/383659216_FC-KAN_Function_Combinations_in_Kolmogorov-Arnold_Networks.
We can use some element-wise operations to combine the functions' outputs by different methods.
def forward(self, X):
device = X.device
# Layer normalization
X = self.layernorm(X)
output = torch.zeros(X.shape[0], X.shape[1], self.output_dim).to(device)
for i, f in zip(range(X.shape[0]), self.func_list):
x = X[i, :, :].squeeze(0)
if (f == 'rbf'):
x = self.rbf(x).view(x.size(0), -1)
x = F.linear(x, self.spline_weight)
elif (f == 'bs'):
x = self.b_splines(x).view(x.size(0), -1)
x = F.linear(x, self.spline_weight)
elif (f == 'dog'):
x = self.wavelet_transform(x, wavelet_type = 'dog')
elif (f == 'base'):
x = F.linear(self.base_activation(x), self.base_weight)
elif (f in ['shifted_softplus', 'arctan', 'relu', 'elu', 'gelup', 'leaky_relu', 'swish', 'softplus', 'sigmoid', 'hard_sigmoid', 'sin', 'cos']):
x = x.view(-1, 1, self.input_dim)
if self.use_bias:
x = torch.cat([x, torch.ones_like(x[..., :1])], dim=2)
if (f == 'shifted_softplus'): # shifted softplus
x = llshifted_softplus(x, self.base_weight)
elif (f == 'arctan'):
x = larctan(x, self.base_weight)
elif (f == 'relu'):
x = lrelu(x, self.base_weight)
elif (f == 'elu'):
x = lelu(x, self.base_weight)
elif (f == 'gelup'):
x = lgelup(x, self.base_weight)
elif (f == 'leaky_relu'):
x = lleaky_relu(x, self.base_weight)
elif (f == 'swish'):
x = lswish(x, self.base_weight)
elif (f == 'softplus'):
x = lsoftplus(x, self.base_weight)
elif (f == 'sigmoid'):
x = lsigmoid(x, self.base_weight)
elif (f == 'hard_sigmoid'):
x = lhard_sigmoid(x, self.base_weight)
elif (f == 'sin'):
x = lsin(x, self.base_weight)
elif (f == 'cos'):
x = lcos(x, self.base_weight)
x = torch.sum(x, dim=2)
else:
raise Exception('The function "' + f + '" does not support!')
# Write more functions here...
output[i] = x
return output
- numpy==1.26.4
- numpyencoder==0.3.0
- torch==2.3.0+cu118
- torchvision==0.18.0+cu118
- tqdm==4.66.4
- mode: working mode ("train" or "test"). Note that we did not write the test() function. =))
- ds_name: dataset name ("mnist" or "fashion_mnist").
- model_name: type of models (bsrbf_kan, efficient_kan, fast_kan, faster_kan, mlp, and fc_kan).
- epochs: the number of epochs.
- batch_size: the training batch size (default: 64).
- n_input: The number of input neurons (default: 28^2 = 784).
- 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 and Fashion-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" (default: "cuda").
- n_examples: the number of examples in the training set used for training (default: 0, mean use all training data)
- note: A note saved in the model name file.
- n_part: the part of data used to train data (default: 0, mean use all training data, 0.1 means 10%).
- func_list: the name of functions used in FC-KAN (default='dog,rbf'). Other functions are bs and base, and functions in SKAN ('shifted_softplus', 'arctan', 'relu', 'elu', 'gelup', 'leaky_relu', 'swish', 'softplus', 'sigmoid', 'hard_sigmoid', 'sin', 'cos').
- combined_type: the type of data combination used in the output (default='quadratic', others are sum, product, sum_product, concat, max, min, mean). We are developing other combinations.
See run.sh or run_fc.sh (bash run.sh or bash run_fc.sh in BASH) for details. We trained the models on GeForce RTX 3060 Ti (with other default parameters). For example, FC-KAN models (Difference of Gaussians + B-splines) can be trained on MNIST with different output combinations.
python run.py --mode "train" --model_name "fc_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --ds_name "mnist" --note "full_0" --n_part 0 --func_list "dog,bs" --combined_type "sum"
python run.py --mode "train" --model_name "fc_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --ds_name "mnist" --note "full_0" --n_part 0 --func_list "dog,bs" --combined_type "product"
python run.py --mode "train" --model_name "fc_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --ds_name "mnist" --note "full_0" --n_part 0 --func_list "dog,bs" --combined_type "sum_product"
python run.py --mode "train" --model_name "fc_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --ds_name "mnist" --note "full_0" --n_part 0 --func_list "dog,bs" --combined_type "quadratic"
python run.py --mode "train" --model_name "fc_kan" --epochs 25 --batch_size 64 --n_input 784 --n_hidden 64 --n_output 10 --ds_name "mnist" --note "full_0" --n_part 0 --func_list "dog,bs" --combined_type "concat"
- https://github.com/hoangthangta/BSRBF_KAN
- https://github.com/Blealtan/efficient-kan
- https://github.com/AthanasiosDelis/faster-kan
- https://github.com/ZiyaoLi/fast-kan/
- https://github.com/zavareh1/Wav-KAN
- https://github.com/seydi1370/Basis_Functions
- https://github.com/KindXiaoming/pykan (the original KAN)
Cite our work if this paper is helpful for you.
@misc{ta2024fckan,
title={FC-KAN: Function Combinations in Kolmogorov-Arnold Networks},
author={Hoang-Thang Ta and Duy-Quy Thai and Abu Bakar Siddiqur Rahman and Grigori Sidorov and Alexander Gelbukh},
year={2024},
eprint={2409.01763},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
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