Partition-of-Unity Gaussian Kolmogorov-Arnold Networks Introduced

A recent publication on arXiv presents the partition-of-unity Gaussian KAN (PU-GKAN), which enhances traditional Gaussian KANs (GKAN) by normalizing Gaussian basis values along each edge through division by their local sum over designated centers. This method yields a partition-of-unity feature map with adjustable coefficients while maintaining the conventional edge-based KAN framework. The normalization guarantees precise constant reproduction at the edge level and allows for a clear finite-feature kernel interpretation. The authors derive both GKAN and PU-GKAN from the perspectives of finite-feature and additive-kernel, clarifying induced layer kernels and empirical feature matrices. A practical interval for epsilon selection is proposed, with the lower limit set by neighboring centers. This research is documented as arXiv:2604.23599.