Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks

Nandi Schoots, Mattia Jacopo Villani, Niels uit de Bos
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:199-207, 2025.

Abstract

Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (Liu et al., 2024). In this paper, we explore the connection between Kolmogorov Arnold Networks (KANs) with piecewise linear (univariate real) functions and ReLU networks. We provide completely explicit constructions to convert a piecewise linear KAN into a ReLU network and vice versa.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-schoots25a, title = {Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks}, author = {Schoots, Nandi and Villani, Mattia Jacopo and uit de Bos, Niels}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {199--207}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/schoots25a/schoots25a.pdf}, url = {https://proceedings.mlr.press/v258/schoots25a.html}, abstract = {Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (Liu et al., 2024). In this paper, we explore the connection between Kolmogorov Arnold Networks (KANs) with piecewise linear (univariate real) functions and ReLU networks. We provide completely explicit constructions to convert a piecewise linear KAN into a ReLU network and vice versa.} }
Endnote
%0 Conference Paper %T Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks %A Nandi Schoots %A Mattia Jacopo Villani %A Niels uit de Bos %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-schoots25a %I PMLR %P 199--207 %U https://proceedings.mlr.press/v258/schoots25a.html %V 258 %X Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (Liu et al., 2024). In this paper, we explore the connection between Kolmogorov Arnold Networks (KANs) with piecewise linear (univariate real) functions and ReLU networks. We provide completely explicit constructions to convert a piecewise linear KAN into a ReLU network and vice versa.
APA
Schoots, N., Villani, M.J. & uit de Bos, N.. (2025). Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:199-207 Available from https://proceedings.mlr.press/v258/schoots25a.html.

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