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[Submitted on 3 Sep 2026] Title:SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials View a PDF of the paper titled SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials, by Amirhosein Azarpour and 1 other authors View PDF HTML (experimental) 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, infinity). We introduce a smooth exponential-of-tanh mapping that stably bridges the domain gap while preserving well-conditioned gradients, and leverage a numerically stable three-term recurrence that evaluates polynomial expansions in O(N) operations without special-function calls. Through comprehensive experiments spanning image classification and continuous function approximation, we demonstrate that SW-KAN achieves superior accuracy-efficiency trade-offs across diverse tasks. The log-normal weight structure and learnable q-parameter of Stieltjes-Wigert polynomials provide a distinct inductive bias that enables robust performance under resource-constrained conditions, including reduced feature dimensionality and limited training data. The proposed architecture not only outperforms established polynomial KAN baselines on standard benchmarks but also exhibits strong representational capacity for approximating complex multivariate functions with remarkably few parameters, making it a compelling alternative for efficient function approximation and classification in resource-constrained settings. Comments: 22 pages, Code and pretrained models available at: this https URL Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) ACM classes: I.2.6; I.5.1 Cite as: arXiv:2610.00050 [cs.LG] (or arXiv:2610.00050v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2610.00050 arXiv-issued DOI via DataCite Submission history From: Amirhosein Azarpour [view email] [v1] Thu, 3 Sep 2026 19:46:42 UTC (730 KB) Full-text links: Access Paper: View a PDF of the paper titled SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials, by Amirhosein Azarpour and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)