Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Design

Abstract

The landscape of Kolmogorov-Arnold Networks (KANs) is rapidly expanding, yet lacks a unified theoretical framework and a clear principle for efficient architecture design. This paper addresses these gaps with three core contributions. First, we introduce the Universal KAN (Uni-KAN) framework, a novel abstraction that formally unifies all KAN-style networks through dense and sparse representations. We prove their interchangeability and provide an open-source library for this framework, facilitating future research. Second, we propose the Efficient KAN Expansion (EKE) Hypothesis, a design philosophy positing that allocating parameters to architectural scaling rather than basis function complexity yields superior performance. Third, we present Single-Parameter KANs (SKANs), a family of ultra-lightweight networks that embody the EKE Hypothesis. Our comprehensive experiments provide the first strong empirical validation for the theoretical necessity of basis function smoothness for stable training. Furthermore, SKANs demonstrate state-of-the-art performance, improving F1 scores by up to 6.51\% and reducing test loss by 93.1\%, while achieving up to 6x faster training speeds compared to existing KAN variants. These results establish a robust framework, a guiding hypothesis, and a practical methodology for designing the next generation of efficient and powerful neural networks. The code is accessible at https://anonymous.4open.science/r/SKAN-EBBB/.