Hybrid Parallel Bessel KAN Model: a Kolmogorov Arnold Network: integrated framework for developing a novel architecture to reconstruct the fused-basis approach via a parameter free quadratic interaction

Abstract:The Kolmogorov-Arnold Network (KAN) challenges traditional MLPs by placing learnable activation functions on network edges. However, scaling KANs to spatial data exposes limitations in default B-Splines. While hybrid architectures mix multiple basis families on a single edge to resolve this, monolithic superposition causes geometric overlap, parameter explosion, and severe numerical ill-conditioning ($\kappa(G) \approx 10^{16}$).To overcome this, we propose Parallel BesselKAN, which isolates B-Spline and low-order Bessel branches into parallel processing pipelines integrated via a parameter-free quadratic interaction. This decoupled architecture acts as an efficient internal ensemble, bypassing monolithic stability bottlenecks. It compresses the parameter footprint by $35\%$ while achieving $97.99\%$ accuracy on MNIST. Although standard MLPs retain a hardware speed advantage for pure vision tasks, Parallel BesselKAN provides a robust, parameter-efficient framework stabilizing mixed-basis networks and paving the way for scalable spatial adaptations like Convolutional KANs.

Machine Learning (cs.LG)

arXiv:2610.17779 [cs.LG]

(or arXiv:2610.17779v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.17779 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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