GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions

TL;DR

GS-KAN introduces a parameter-efficient architecture for Kolmogorov-Arnold Networks by sharing a parent function across edges, enabling high approximation performance with fewer parameters, suitable for high-dimensional tasks.

Contribution

The paper proposes GS-KAN, a novel shared basis function approach that reduces parameter count in KANs while maintaining or improving approximation capabilities.

Findings

GS-KAN outperforms standard KANs and MLPs on function approximation tasks.

GS-KAN achieves competitive results on tabular data regression.

GS-KAN is effective in high-dimensional regimes with strict parameter constraints.

Abstract

The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes. While recent implementations such as Kolmogorov-Arnold Networks (KANs) demonstrate high approximation capabilities, they suffer from significant parameter inefficiency due to the requirement of maintaining unique parameterizations for every network edge. In this work, we propose GS-KAN (Generalized Sprecher-KAN), a lightweight architecture inspired by David Sprecher's refinement of the superposition theorem. GS-KAN constructs unique edge functions by applying learnable linear transformations to a single learnable, shared parent function per layer. We evaluate GS-KAN against existing KAN architectures and MLPs across synthetic function approximation, tabular data regression and image classification tasks. Our results demonstrate that GS-KAN outperforms both MLPs and standard KAN baselines on continuous function approximation tasks while maintaining superior parameter efficiency. Additionally, GS-KAN achieves competitive performance with existing KAN architectures on tabular regression and outperforms MLPs on high-dimensional classification tasks. Crucially, the proposed architecture enables the deployment of KAN-based architectures in high-dimensional regimes under strict parameter constraints, a setting where standard implementations are typically infeasible due to parameter explosion. The source code is available at https://github.com/rambamn48/gs-impl.