SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials

תקציר מקורי באנגליתarXiv:2610.00050v1 Announce Type: cross Abstract: Kolmogorov-Arnold Networks (KANs) represent a paradigmatic shift in deep learning by replacing fixed node activations with learnable univariate functions on edges, offering enhanced interpretability and parameter efficiency. While recent polynomial-based KAN variants have addressed the computational overhead of original B-spline implementations, they introduce a fundamental yet underexplored challenge: the domain mismatch between unbounded real-valued inputs and the bounded or semi-infinite support of orthogonal polynomial bases. To address this limitation, we propose the Stieltjes-Wigert Kolmogorov-Arnold Network (SW-KAN), a novel architecture that employs Stieltjes-Wigert q-orthogonal polynomials defined on the semi-infinite domain (0, in