Fractional Kolmogorov-Arnold Network (fKAN) is a novel neural network that incorporates the distinctive attributes of Kolmogorov-Arnold Networks (KANs) with a trainable adaptive fractional-orthogonal Jacobi function as its basis function. This method offers several advantages, including non-polynomial behavior, activity for both positive and negative input values, faster execution, and better accuracy.

To install fKAN, use the following command:

$ pip install fkan

The current implementation of fKAN works with both the TensorFlow and PyTorch APIs.

from tensorflow import keras
from tensorflow.keras import layers
from fkan.tensorflow import FractionalJacobiNeuralBlock as fJNB

model = keras.Sequential(
    [
        layers.InputLayer(input_shape=input_shape),
        layers.Conv2D(32, kernel_size=(3, 3)),
        fJNB(3),
        layers.MaxPooling2D(pool_size=(2, 2)),
        layers.Flatten(),
        layers.Dropout(0.5),
        layers.Dense(16),
        fJNB(2),
        layers.Dense(num_classes, activation="softmax"),
    ]
)

import torch.nn as nn
from fkan.torch import FractionalJacobiNeuralBlock as fJNB

model = nn.Sequential(
    nn.Linear(1, 16),
    fJNB(3),
    nn.Linear(16, 32),
    fJNB(6),
    nn.Linear(32, 1),
)

The example folder contains the implementation of the experiments from the paper using fKAN. These experiments include:

• Synthetic Regression
• MNIST Classification
• Fashion MNIST Image Denoising
• IMDB Sentiment Analysis

• Lane Emden Ordinary Differential Equation
• Burgers Partial Differential Equation
• Fractional Delay Differential Equation with Caputo definition

• Maximum allowed Jacobi polynomial degree is set to six.
• The current library is not compatible with other deep learning frameworks, but it can be converted easily.

We encourage the community to contribute by opening issues and submitting pull requests to help address these limitations and improve the overall functionality of fKAN.

If you have any questions or encounter any issues, please open an issue in this repository (preferred) or reach out to the author directly.

If you use fKAN in your research, please cite our paper:

@misc{aghaei2024fkan,
      title={fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions},
      author={Alireza Afzal Aghaei},
      year={2024},
      eprint={2406.07456},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}