Partition-of-Unity Gaussian Kolmogorov-Arnold Networks
Gaussian basis functions provide an efficient and flexible alternative to spline activations in KANs. In this work, we introduce the partition-of-unity Gaussian KAN (PU-GKAN), a Shepard-type normalized Gaussian KAN in which the Gaussian basis values on each edge are divided by their local sum over fixed centers. This produces a partition-of-unity feature map with trainable coefficients, while preserving the standard edge-based KAN structure. The normalized construction gives exact constant reproduction at the edge level and admits an explicit finite-feature kernel interpretation. We formulate both the standard Gaussian KAN (GKAN) and PU-GKAN from a finite-feature and additive-kernel viewp...
| Authors | Amir Noorizadegan |
|---|---|
| Primary category | cs.CE |
| Published | 26 April 2026 |
| Last updated at source | 3 May 2026 |
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