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:

$ pip install rkan

Example Usage

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

TensorFlow

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

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}
}