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.

翻译：Kolmogorov-Arnold表示定理为多层感知机（MLP）提供了一种理论替代方案，其将可学习的单变量函数置于网络边而非节点上。尽管近期实现如Kolmogorov-Arnold网络（KAN）展现出强大的逼近能力，但由于需要为每条网络边维护独立的参数化表示，这些网络存在显著的参数低效问题。本研究提出GS-KAN（广义Sprecher-KAN），这是一种受David Sprecher对叠加定理的改进所启发的轻量级架构。GS-KAN通过对每层中单个可学习的共享母函数施加可学习的线性变换，来构建各边的独特函数。我们在合成函数逼近、表格数据回归和图像分类任务中，将GS-KAN与现有KAN架构及MLP进行对比评估。结果表明，在连续函数逼近任务上，GS-KAN在保持卓越参数效率的同时，其性能优于MLP和标准KAN基线。此外，GS-KAN在表格回归任务上与现有KAN架构性能相当，并在高维分类任务上超越MLP。至关重要的是，所提出的架构使得在严格参数约束下部署基于KAN的架构处理高维数据成为可能，而在此类场景下，标准实现通常会因参数爆炸而不可行。源代码发布于https://github.com/rambamn48/gs-impl。