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：科尔莫戈罗夫-阿诺德表示定理通过将可学习单变量函数置于网络边而非节点上，为多层感知机（MLP）提供了理论替代方案。尽管近期实现的科尔莫戈罗夫-阿诺德网络（KAN）展现出高近似能力，但由于需为每条网络边维护独立参数化，导致显著参数低效问题。本文提出GS-KAN（广义斯普雷彻-KAN），一种受大卫·斯普雷彻对叠加定理精细化研究启发的轻量架构。GS-KAN通过对每层单个可学习的共享父函数施加可学习线性变换，构造唯一的边函数。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，GS-KAN在连续函数逼近任务上优于MLP和标准KAN基线，同时保持更优的参数效率。此外，GS-KAN在表格回归任务上达到与现有KAN架构相当的竞争力，并在高维分类任务中超越MLP。关键在于，所提架构使基于KAN的架构能够在严格参数约束下的高维场景中部署——而标准实现因参数爆炸在此类场景中通常不可行。源代码见https://github.com/rambamn48/gs-impl。