# Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate

arXiv: https://arxiv.org/abs/2604.21174 · HTML: https://mlsanity.com/paper/2604.21174/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.17611/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU](https://mlsanity.com/paper/2406.02075/) (2024)
- [Kolmogorov-Arnold Fourier Networks](https://mlsanity.com/paper/2502.06018/) (2025)
- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster](https://mlsanity.com/paper/2409.14248/) (2024)
- [Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries](https://mlsanity.com/paper/2408.02950/) (2024)
- [LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behavior](https://mlsanity.com/paper/2502.17844/) (2025)
- [Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs](https://mlsanity.com/paper/2505.03595/) (2025)
- [Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study](https://mlsanity.com/paper/2509.03417/) (2025)
- [Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology](https://mlsanity.com/paper/2504.07379/) (2025)
- [Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2411.15111/) (2024)
- [CVKAN: Complex-Valued Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2502.02417/) (2025)
- [BubbleOKAN: A Physics-Informed Interpretable Neural Operator for High-Frequency Bubble Dynamics](https://mlsanity.com/paper/2508.03965/) (2025)
- [FEKAN: Feature-Enriched Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.16530/) (2026)
- [Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement](https://mlsanity.com/paper/2505.18131/) (2025)
- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks](https://mlsanity.com/paper/2603.18548/) (2026)
- [Analysis of Structured Deep Kernel Networks](https://mlsanity.com/paper/2105.07228/) (2021)

## Built on by (most cited first, 3 of 3)

- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [Partition-of-Unity Gaussian Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.23599/) (2026)
- [Kolmogorov--Arnold Networks for Small Language Models](https://mlsanity.com/paper/2607.15525/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis. Gaussian radial basis functions provide a simple and efficient alternative to splines, but their accuracy and stability are highly sensitive to the scale parameter (ε), which has not been studied systematically. We analyze this dependence through the geometry and conditioning of the first-layer feature matrix. Because the first layer is defined directly on the input domain, any loss of feature distinguishability introduced there propagates through the entire network. Based on this analysis, we identify the practical operating interval [ ε ∈ left[frac1G-1,frac2G-1right], ] where (G) is the number of Gaussian centers. This interval is proposed as a stable design rule rather than a universal optimum. Extensive experiments on function approximation and physics-informed problems confirm its reliability across different collocation densities, grid resolutions, architectures, and input dimensions. We also show how the same principle supports fixed-scale selection, variable-scale models, constrained optimization of (ε), and efficient scale search using early-stage training error. These results establish scale selection as a central design principle for reliable and accurate Gaussian KANs.