# Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks

arXiv: https://arxiv.org/abs/2503.01702 · HTML: https://mlsanity.com/paper/2503.01702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [Hidden symmetries of ReLU networks](https://mlsanity.com/paper/2306.06179/) (2023)
- [Unwrapping The Black Box of Deep ReLU Networks: Interpretability, Diagnostics, and Simplification](https://mlsanity.com/paper/2011.04041/) (2020)
- [Empirical Bounds on Linear Regions of Deep Rectifier Networks](https://mlsanity.com/paper/1810.03370/) (2018)
- [Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networks](https://mlsanity.com/paper/2207.07696/) (2022)
- [On the Kolmogorov neural networks](https://mlsanity.com/paper/2311.00049/) (2023)
- [Polyhedral Complex Extraction from ReLU Networks using Edge Subdivision](https://mlsanity.com/paper/2306.07212/) (2023)
- [Any Deep ReLU Network is Shallow](https://mlsanity.com/paper/2306.11827/) (2023)

## Built on by (most cited first, 2 of 2)

- [PolyKAN: A Polyhedral Analysis Framework for Provable and Approximately Optimal KAN Compression](https://mlsanity.com/paper/2510.04205/) (2025)
- [Fisher Simplicity in Kolmogorov-Arnold Networks and Multilayer Perceptrons](https://mlsanity.com/paper/2609.32503/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (arXiv:2404.19756). 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.