DAREK -- Distance Aware Error for Kolmogorov Networks

In this paper, we provide distance-aware error bounds for Kolmogorov Arnold Networks (KANs). We call our new error bounds estimator DAREK -- Distance Aware Error for Kolmogorov networks. Z. Liu et al. provide error bounds, which may be loose, lack distance-awareness, and are defined only up to an un...

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Bibliographic Details
Main Authors Ataei, Masoud, Khojasteh, Mohammad Javad, Dhiman, Vikas
Format Journal Article
LanguageEnglish
Published 08.01.2025
Subjects
Computer Science - Learning
Online AccessGet full text
DOI10.48550/arxiv.2501.04757

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Summary:In this paper, we provide distance-aware error bounds for Kolmogorov Arnold Networks (KANs). We call our new error bounds estimator DAREK -- Distance Aware Error for Kolmogorov networks. Z. Liu et al. provide error bounds, which may be loose, lack distance-awareness, and are defined only up to an unknown constant of proportionality. We review the error bounds for Newton's polynomial, which is then generalized to an arbitrary spline, under Lipschitz continuity assumptions. We then extend these bounds to nested compositions of splines, arriving at error bounds for KANs. We evaluate our method by estimating an object's shape from sparse laser scan points. We use KAN to fit a smooth function to the scans and provide error bounds for the fit. We find that our method is faster than Monte Carlo approaches, and that our error bounds enclose the true obstacle shape reliably.
DOI:10.48550/arxiv.2501.04757