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

arXiv: https://arxiv.org/abs/2410.14951 · HTML: https://mlsanity.com/paper/2410.14951/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Medical Transformer: Gated Axial-Attention for Medical Image Segmentation](https://mlsanity.com/paper/2102.10662/) (2021)
- [Attention Gated Networks: Learning to Leverage Salient Regions in Medical Images](https://mlsanity.com/paper/1808.08114/) (2018)
- [ResUNet++: An Advanced Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1911.07067/) (2019)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [Smooth Kolmogorov Arnold networks enabling structural knowledge representation](https://mlsanity.com/paper/2405.11318/) (2024)
- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries](https://mlsanity.com/paper/2408.02950/) (2024)

## Built on by (most cited first, 6 of 6)

- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [MatrixKAN: Parallelized Kolmogorov-Arnold Network](https://mlsanity.com/paper/2502.07176/) (2025)
- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)
- [LArctan-SKAN: Simple and Efficient Single-Parameterized Kolmogorov-Arnold Networks using Learnable Trigonometric Function](https://mlsanity.com/paper/2410.19360/) (2024)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [SparseKAN: Compressing Kolmogorov--Arnold Networks Across Basis Functions, Neurons, and Bits](https://mlsanity.com/paper/2608.00859/) (2026)

## Abstract (arXiv)

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/.