{"ID":2850854,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22021","arxiv_id":"2510.22021","title":"K-DAREK: Distance Aware Error for Kurkova Kolmogorov Networks","abstract":"Neural networks are powerful parametric function approximators, while Gaussian processes (GPs) are nonparametric probabilistic models that place distributions over functions via kernel-defined correlations but become computationally expensive for large-scale problems. Kolmogorov-Arnold networks (KANs), semi-parametric neural architectures, model complex functions efficiently using spline layers. Kurkova Kolmogorov-Arnold networks (KKANs) extend KANs by replacing the early spline layers with multi-layer perceptrons that map inputs into higher-dimensional spaces before applying spline-based transformations, which yield more stable training and provide robust architectures for system modeling. By enhancing the KKAN architecture, we develop a novel learning algorithm, distance-aware error for Kurkova-Kolmogorov networks (K-DAREK), for efficient and interpretable function approximation with uncertainty quantification. Our approach establishes robust error bounds that are distance-aware; this means they reflect the proximity of a test point to its nearest training points. In safe control case studies, we demonstrate that K-DAREK is about four times faster and ten times more computationally efficient than Ensemble of KANs, 8.6 times more scalable than GP as data size increases, and 7.2% safer than our previous work distance-aware error for Kolmogorov networks (DAREK). Moreover, on real data (e.g., Real Estate Valuation), K-DAREK's error bound achieves zero coverage violations.","short_abstract":"Neural networks are powerful parametric function approximators, while Gaussian processes (GPs) are nonparametric probabilistic models that place distributions over functions via kernel-defined correlations but become computationally expensive for large-scale problems. Kolmogorov-Arnold networks (KANs), semi-parametric...","url_abs":"https://arxiv.org/abs/2510.22021","url_pdf":"https://arxiv.org/pdf/2510.22021v2","authors":"[\"Masoud Ataei\",\"Vikas Dhiman\",\"Mohammad Javad Khojasteh\"]","published":"2025-10-24T20:49:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\",\"stat.ML\"]","methods":"[]","has_code":false}