# PolyKAN: A Polyhedral Analysis Framework for Provable and Approximately Optimal KAN Compression

arXiv: https://arxiv.org/abs/2510.04205 · HTML: https://mlsanity.com/paper/2510.04205/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 13 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU](https://mlsanity.com/paper/2406.02075/) (2024)
- [Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networks](https://mlsanity.com/paper/2503.01702/) (2025)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional Multi-Layer Perceptrons (MLPs), offering enhanced interpretability and a solid mathematical foundation. However, their parameter efficiency remains a significant challenge for practical deployment. This paper introduces PolyKAN, a novel theoretical framework for KAN compression that provides formal guarantees on both model size reduction and approximation error. By leveraging the inherent piecewise polynomial structure of KANs, we formulate the compression problem as a polyhedral region merging task. We establish a rigorous polyhedral characterization of KANs, develop a complete theory of ε-equivalent compression, and design a dynamic programming algorithm that achieves approximately optimal compression under specified error bounds. Our theoretical analysis demonstrates that PolyKAN achieves provably near-optimal compression while maintaining strict error control, with guaranteed global optimality for univariate spline functions. This framework provides the first formal foundation for KAN compression with mathematical guarantees, opening new directions for the efficient deployment of interpretable neural architectures.