GS-KAN: 通过Sprecher型共享基函数的参数高效Kolmogorov-Arnold网络
GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions
AI总结：
提出GS-KAN，通过每层共享单一父函数的线性变换构造边函数，在保持参数高效的同时，在函数逼近、表格回归和图像分类任务上优于或媲美现有KAN和MLP。
摘要：
Kolmogorov-Arnold表示定理通过在边上而非节点上放置可学习单变量函数，为多层感知器（MLP）提供了理论替代方案。尽管最近的实现如Kolmogorov-Arnold网络（KAN）展示了高逼近能力，但由于需要为每个网络边维护唯一参数化，它们存在显著的参数低效问题。在这项工作中，我们提出GS-KAN（广义Sprecher-KAN），一种受David Sprecher对叠加定理的改进启发的轻量级架构。GS-KAN通过对每层单个可学习的共享父函数应用可学习线性变换来构造唯一的边函数。我们在合成函数逼近、表格数据回归和图像分类任务上评估了GS-KAN与现有KAN架构和MLP的性能。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，同时保持优越的参数效率。此外，GS-KAN在表格回归上与现有KAN架构性能相当，在高维分类任务上优于MLP。关键的是，所提出的架构使得在严格参数约束下的高维场景中部署基于KAN的架构成为可能，而标准实现由于参数爆炸通常不可行。源代码可在https://github.com/rambamn48/gs-impl获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
