This is the github repo for the paper "KAN: Kolmogorov-Arnold Networks". Find the documentation here.
Kolmogorov-Arnold Networks (KANs) are promising alternatives of Multi-Layer Perceptrons (MLPs). KANs have strong mathematical foundations just like MLPs: MLPs are based on the universal approximation theorem, while KANs are based on Kolmogorov-Arnold representation theorem. KANs and MLPs are dual: KANs have activation functions on edges, while MLPs have activation functions on nodes. This simple change makes KANs better (sometimes much better!) than MLPs in terms of both model accuracy and interpretability. A quick intro of KANs here.
KANs have faster scaling than MLPs. KANs have better accuracy than MLPs with fewer parameters.
Example 1: fitting symbolic formulas
Example 2: fitting special functions
Example 3: PDE solving
Example 4: avoid catastrophic forgetting
KANs can be intuitively visualized. KANs offer interpretability and interactivity that MLPs cannot provide. We can use KANs to potentially discover new scientific laws.
Example 1: Symbolic formulas
Example 2: Discovering mathematical laws of knots
Example 3: Discovering physical laws of Anderson localization
Example 4: Training of a three-layer KAN
There are two ways to install pykan, through pypi or github.
Installation via github
git clone https://github.com/KindXiaoming/pykan.git
cd pykan
pip install -e .Installation via pypi
pip install pykanRequirements
# python==3.9.7
matplotlib==3.6.2
numpy==1.24.4
scikit_learn==1.1.3
setuptools==65.5.0
sympy==1.11.1
torch==2.2.2
tqdm==4.66.2To install requirements:
pip install -r requirements.txtExamples in tutorials are runnable on a single CPU typically less than 10 minutes. All examples in the paper are runnable on a single CPU in less than one day. Training KANs for PDE is the most expensive and may take hours to days on a single CPU. We use CPUs to train our models because we carried out parameter sweeps (both for MLPs and KANs) to obtain Pareto Frontiers. There are thousands of small models which is why we use CPUs rather than GPUs. Admittedly, our problem scales are smaller than typical machine learning tasks, but are typical for science-related tasks. In case the scale of your task is large, it is advisable to use GPUs.
The documenation can be found here.
Quickstart
Get started with hellokan.ipynb notebook.
More demos
More Notebook tutorials can be found in tutorials.
@misc{liu2024kan,
title={KAN: Kolmogorov-Arnold Networks},
author={Ziming Liu and Yixuan Wang and Sachin Vaidya and Fabian Ruehle and James Halverson and Marin Soljačić and Thomas Y. Hou and Max Tegmark},
year={2024},
eprint={2404.19756},
archivePrefix={arXiv},
primaryClass={cs.LG}
}If you have any questions, please contact zmliu@mit.edu