Enhances Kolmogorov-Arnold Networks (KAN) with fractal interpolation to approximate non-smooth and rough functions.
March 31, 2026
Original Paper
FI-KAN: Fractal Interpolation Kolmogorov-Arnold Networks
arXiv · 2603.28288
The Takeaway
Standard KANs use B-splines which struggle with sharp singularities or rough PDE solutions. By integrating learnable fractal bases, FI-KAN achieves up to 79x improvement in accuracy on rough-coefficient diffusion problems, making KANs viable for complex physical simulations.
From the abstract
Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal Interpolation KAN (FI-KAN), which incorporates learnable fractal interpolation function (FIF) bases from iterated function system (IFS) theory into KAN. Two variants are presented: Pure FI-KAN (Barnsley, 1986) replaces B-splines entirely with FIF bases; Hybrid FI-KAN (Navascues, 2005) retains the B-spline path and add