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GS-KAN addresses the parameter inefficiency of standard Kolmogorov-Arnold Networks by introducing a shared basis function architecture that significantly reduces model size without sacrificing approximation accuracy. This approach enables KANs to remain competitive with MLPs on high-dimensional classification tasks while solving the parameter explosion issue in constrained regimes. The work offers a practical pathway for deploying theoretically sound Kolmogorov-Arnold architectures in resource-limited environments.
GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions
arXiv:2512.09084v3 Announce Type: replace 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.
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 this https URL.
Machine Learning (cs.LG)
arXiv:2512.09084 [cs.LG]
(or arXiv:2512.09084v3 [cs.LG] for this version)
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