Official Implementation: GS-KAN (Generalized Sprecher KAN)

This repository contains the official code and implementation for the paper "GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions" by Oscar Eliasson.

It introduces GS-KAN (Generalized Sprecher KAN), a novel neural architecture grounded in Sprecher's refinement of the Kolmogorov-Arnold theorem, designed to improve parameter efficiency and computational performance.

Experiments & Evaluation

The architecture is tested and benchmarked against standard KAN, WavKAN and standard MLPs across three distinct experimental domains:

1. Synthetic Function Regression: Evaluates the model's ability to approximate complex mathematical functions with high precision.
2. Tabular Data Regression (California Housing): Tests performance on real-world tabular datasets to measure generalization in housing price prediction.
3. Multi-Class Classification (Fashion MNIST): Assesses the architecture's capability in image classification tasks compared to established baselines.

Note: Results may vary slightly due to hardware differences and GPU non-determinism, despite the use of fixed random seeds.

Project Overview

The study benchmarks the following architectures:

• GS-KAN (Ours): Utilizing layer-wise shared basis functions for enhanced efficiency.
• WavKAN: Wavelet-based KAN implementation.
• Standard KAN: The efficient-kan implementation.
• General MLP: Standard Multi-Layer Perceptron baseline with SiLU/ReLU activations.

Usage

To reproduce the results from the paper, run the following scripts:

• function_experiment.py: Synthetic function approximation (Table 1).
• housing_experiment.py: California Housing tabular regression (Table 2).
• fashion_experiment.py: Fashion-MNIST classification (Table 3).

Note: All dependencies must be installed via requirements.txt before running.

Installation

To install all dependencies, including the external efficient-kan library, run:

pip install -r requirements.txt