Study on Gaussian Scale Parameter in Kolmogorov-Arnold Networks
A recent study published on arXiv examines how the Gaussian scale parameter ε influences Gaussian Kolmogorov-Arnold Networks (KANs). It reveals that the selection of scale is mainly determined by the first layer, which is uniquely built on the input domain. Any loss of distinguishability that occurs at this stage cannot be rectified by subsequent layers. The researchers evaluate the feature matrix of the first layer and propose a practical range for ε: [1/(G-1), 2/(G-1)], with G representing the number of Gaussian centers. For the conventional shared-center Gaussian KAN, this range is seen not as a definitive optimality criterion but rather as a recommendation for effective scaling.
Key facts
- arXiv paper 2604.21174 studies Gaussian KANs
- Gaussian scale parameter ε is central to Gaussian KAN behavior
- Scale selection governed primarily by first layer
- First layer is only layer constructed directly on input domain
- Loss of distinguishability in first layer cannot be recovered later
- Practical operating interval for ε: [1/(G-1), 2/(G-1)]
- G denotes number of Gaussian centers
- Interval not a universal optimality result for shared-center Gaussian KAN
Entities
Institutions
- arXiv