https://github.com/alirezaafzalaghaei/rKAN

Implementation of Rational Kolmogorov-Arnold Network (rKAN)
https://github.com/alirezaafzalaghaei/rKAN

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Implementation of Rational Kolmogorov-Arnold Network (rKAN)

• Host: GitHub
• URL: https://github.com/alirezaafzalaghaei/rKAN
• Owner: alirezaafzalaghaei
• License: bsd-3-clause
• Created: 2024-06-20T03:43:06.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2024-06-28T17:21:37.000Z (7 months ago)
• Last Synced: 2024-10-25T02:32:45.015Z (3 months ago)
• Language: Python
• Homepage:
• Size: 213 KB
• Stars: 13
• Watchers: 1
• Forks: 2
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

• awesome-kan - rKAN - Arnold Networks |  (Library / Theorem)

README

        
# Rational Kolmogorov-Arnold Network (rKAN)

Rational Kolmogorov-Arnold Network (rKAN) is a novel neural network that incorporates the distinctive attributes of Kolmogorov-Arnold Networks (KANs) with a trainable adaptive rational-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 rKAN, use the following command:

```bash

$ pip install rkan

```

## Example Usage

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

### TensorFlow

```python

from tensorflow import keras

from tensorflow.keras import layers

from rkan.tensorflow import JacobiRKAN, PadeRKAN

model = keras.Sequential(

    [

        layers.InputLayer(input_shape=input_shape),

        layers.Conv2D(32, kernel_size=(3, 3)),

        JacobiRKAN(3),      # Jacobi polynomial of degree 3

        layers.MaxPooling2D(pool_size=(2, 2)),

        layers.Flatten(),

        layers.Dropout(0.5),

        layers.Dense(16),

        PadeRKAN(2, 6),     # Pade [2/6]

        layers.Dense(num_classes, activation="softmax"),

    ]

)

```

### PyTorch

```python

import torch.nn as nn

from rkan.torch import JacobiRKAN, PadeRKAN

model = nn.Sequential(

    nn.Linear(1, 16),

    JacobiRKAN(3),      # Jacobi polynomial of degree 3

    nn.Linear(16, 32),

    PadeRKAN(2, 6),     # Pade [2/6]

    nn.Linear(32, 1),

)

```

## Experiments

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

### Deep Learning Tasks

- **Synthetic Regression**

- **MNIST Classification**

### Physics Informed Deep Learning

- **Lane Emden Ordinary Differential Equation**

- **Elliptic Partial Differential Equation**

## 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 rKAN.

## 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 rKAN in your research, please cite our paper:

```

@article{aghaei2024rkan,

  title={rKAN: Rational Kolmogorov-Arnold Networks},

  author={Aghaei, Alireza Afzal},

  journal={arXiv preprint arXiv:2406.14495},

  year={2024}

}

```