Determine the appropriate univariate function family for Kolmogorov–Arnold networks

Determine which univariate function family—such as B-splines, rational functions, Padé approximants, or rational Jacobi functions—should be used for the edge functions of Kolmogorov–Arnold networks.

Background

The paper notes that Kolmogorov–Arnold networks replace the fixed activations of multilayer perceptrons with learnable univariate functions, most commonly univariate B-splines. Alternative families, including rational functions, Padé approximants, and rational Jacobi functions, have also been proposed. The comparative suitability of these families is identified as unresolved, including for applications to partial differential equations.

References

Which univariate family those edge functions are drawn from is itself an open question, and rational ones, Padé approximants and rational Jacobi functions, have been proposed in place of the splines.

— IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs  (2610.06348 - Naraghi et al., 5 Oct 2026) in Section 2.3, “Kolmogorov–Arnold networks”