Double-KANs: Enhancing KANs with Simplified NURBS for Accurate Approximation of Discontinuous Signals

Abstract

Kolmogorov–Arnold Networks (KANs) have shown strong potential in scientific computing, including approximating physical equations and solving partial differential equations. While B-splines provide KAN with local control and robustness to catastrophic forgetting, the Uniform Rational B-Splines (URBS) used in vanilla KAN struggle to approximate abrupt or discontinuous signals, limiting their effectiveness. To address this issue, we introduce Double-KANs, a novel structure that expresses Non-Uniform Rational B-Splines (NURBS) as a simplified quotient of two B-spline summations. Double-KANs retains the structural simplicity of vanilla KAN while substantially enhancing the approximation of discontinuities. Furthermore, it can be seamlessly applied to existing KAN-based models and extensions. Experimental evaluations across multiple tasks demonstrate that Double-KANs achieves superior accuracy and generalization compared to multilayer perceptrons(MLP), vanilla KAN, and other improved variants, highlighting its effectiveness and broad applicability.

Highlight

• Introduce NURBS to improve KAN’s ability to approximate abrupt signals
• Maintain compatibility with KAN-based models for seamless enhancement
• Show better performance than MLPs, vanilla KANs, and their variants in multiple tasks

We propose Double-KANs, an extension of KANs that overcomes their limitations in approximating abrupt and discontinuous signals. By reformulating NURBS as a quotient of two B-spline summations, Double-KANs preserves the simplicity of vanilla KANs while significantly enhancing their approximation ability. Experiments on multiple tasks, including bladder cancer classification and staging, show that Double-KANs consistently outperforms MLPs, vanilla KANs, and other variants, achieving superior accuracy and generalization.

Environment Requirements

Python Version

• Python 3.9

Main Dependencies

# Core scientific computing
numpy=1.26.4
torch=2.7.1+cu118
torchvision>=0.22.1

# Machine learning utilities
scikit-learn>=1.1.0
pandas=2.1.4

# Visualization (optional)
matplotlib>=3.5.0

Installation

# Clone the repository
git clone https://github.com/baboonaaaa/Double-KANs.git
cd Double-KANs

# Install dependencies
pip install -r requirements.txt

# Or install manually
pip install python=3.9.23 numpy=1.26.4 torch=2.7.1+cu118 torchvision>=0.22.1 scikit-learn>=1.1.0 pandas=2.1.4 matplotlib>=3.5.0

Quick Start

# Basic training with default parameters
python train_minist_double_kan.py

# Custom training with specific parameters
python train_minist_double_kan.py \
    --epochs 100 \
    --batch_size 64 \
    --lr 1e-4 \
    --n_hidden 32 \
    --model_name "my_double_kan" \
    --note "experiment_1"

# View all available parameters
python train_minist_double_kan.py --help

Citation

If you use Double-KANs in your research, please cite our paper:

@article{2026doublekans,
title = {Double-KANs: Enhancing KANs with simplified NURBS for accurate modeling of discontinuous signals},
author = {Wei Gao and Hongtao Liu and Meixuan Li and Xingfei Li and Xuefeng Li},
journal = {Neurocomputing},
pages = {133895},
year = {2026},
publisher={Elsevier}
}