SKAN: Single-parameter Kolmogorov-Arnold Networks

This repository contains the experimental code for the paper "SKAN: Single-parameter Kolmogorov-Arnold Networks". The experiments are organized into four main folders:

Repository Structure

1. pre-experiments/

Preliminary experiments comparing different grid sizes in Spl-KAN (the original KAN variant) on the MNIST dataset. These experiments helps verify the EKE (efficient KAN expansion) principle.

2. comparision of KAN variants on MNIST/

Comprehensive comparison between our proposed SKAN and other KAN variants on the MNIST dataset:

• Different SKAN variants with various basis functions
• Classic KAN variants (FourierKAN, WaveKAN, FastKAN, etc.)
• Extensive experiments with different learning rates and architectures

3. ODE solving/

Implementation and comparison of x-SKAN-ODE (where x represents different SKAN basis functions) with:

• KAN-ODE (based on Spl-KAN)
• Neural-ODE (based on MLP)

The experiments focus on solving the Lotka-Volterra predator-prey differential equations, demonstrating SKAN's capability in scientific computing tasks.

4. medical image segmentation/

Application of SKAN in medical image segmentation tasks, comparing:

• U-x-SKAN (our model with different basis functions)
• U-KAN (based on Spl-KAN)
• U-Net (based on MLP)

Experiments were conducted on three datasets:

• BUSI: Breast ultrasound image dataset
  • Additional experiments with reduced-parameter SKAN variants
• CVC-ClinicDB: Polyp segmentation dataset
• GlaS: Gland segmentation dataset

Key Features

• Novel single-parameterized architecture (SKAN)
• Multiple basis function variants (LSS-SKAN, LSin-SKAN, LArctan-SKAN)
• Comprehensive benchmarking against existing KAN variants
• Applications in both scientific computing and computer vision tasks

Usage

Each folder contains its own README with detailed instructions for running experiments. The code is organized to be modular and easy to extend for new applications.

License

Currently, this repository contains only the LICENSE files from referenced codebases (some original repositories do not specify licenses). For double-blind review purposes, we have not included our own license to maintain anonymity. After publication, this repository will be released under the MIT License.