https://github.com/alirezaafzalaghaei/fKAN

Implementation of Fractional Kolmogorov-Arnold Network (fKAN)
https://github.com/alirezaafzalaghaei/fKAN

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Implementation of Fractional Kolmogorov-Arnold Network (fKAN)

• Host: GitHub
• URL: https://github.com/alirezaafzalaghaei/fKAN
• Owner: alirezaafzalaghaei
• License: bsd-3-clause
• Created: 2024-06-11T18:24:01.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2024-06-12T01:13:04.000Z (7 months ago)
• Last Synced: 2024-10-25T02:51:04.225Z (3 months ago)
• Language: Python
• Size: 822 KB
• Stars: 16
• Watchers: 1
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

• awesome-kan - fKAN - Arnold Networks with trainable Jacobi basis functions |  (Library / Theorem)
• awesome-kan - fKAN - Arnold Networks with trainable Jacobi basis functions |  (Library / Theorem)

README

        
# Fractional Kolmogorov-Arnold Network (fKAN)

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.

## Installation

To install fKAN, use the following command:

```bash

$ pip install fkan

```

## Example Usage

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

### TensorFlow

```python

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"),

    ]

)

```

### PyTorch

```python

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),

)

```

## Experiments

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

### Deep Learning Tasks

- **Synthetic Regression**

- **MNIST Classification**

- **Fashion MNIST Image Denoising**

- **IMDB Sentiment Analysis**

### Physics Informed Deep Learning

- **Lane Emden Ordinary Differential Equation**

- **Burgers Partial Differential Equation**

- **Fractional Delay Differential Equation** with Caputo definition

## Current Limitations

-   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.

## Contribution

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.

## Contact

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

## Citation

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}

}

```