PolyKAN: A Polyhedral Analysis Framework for Provable and Approximately Optimal KAN Compression
This addresses the problem of practical deployment for interpretable neural architectures, offering a formal foundation for KAN compression, though it appears incremental as it builds on existing KAN theory.
The paper tackles the parameter efficiency challenge in Kolmogorov-Arnold Networks (KANs) by introducing PolyKAN, a framework that achieves provably near-optimal compression with strict error control, including guaranteed global optimality for univariate spline functions.
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.