Input Convex Kolmogorov–Arnold Networks.
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| Title: | Input Convex Kolmogorov–Arnold Networks. |
|---|---|
| Authors: | Deschatre, Thomas1 (AUTHOR) thomas-t.deschatre@edf.fr, Warin, Xavier1 (AUTHOR) xavier.warin@edf.fr |
| Source: | SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pC579-C603. 25p. |
| Subjects: | Piecewise linear approximation, Artificial neural networks, Transportation problems (Programming), Splines, Convex functions, Approximation theory |
| Abstract: | This article presents an input convex neural network (ICNN) architecture using Kolmogorov–Arnold networks (ICKANs). Two specific networks are presented. The first is based on a low-order, piecewise-linear representation of functions, and a universal approximation theorem is provided. The second is based on cubic splines, for which only numerical results support convergence. We demonstrate through simple tests that these networks perform competitively with classical ICNNs. We then use the networks to solve optimal transport problems that require a convex approximation of functions and demonstrate their effectiveness. Cubic-ICKANs produce results similar to those of ICNNs. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 195222026 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Input Convex Kolmogorov–Arnold Networks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Deschatre%2C+Thomas%22">Deschatre, Thomas</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> thomas-t.deschatre@edf.fr</i><br /><searchLink fieldCode="AR" term="%22Warin%2C+Xavier%22">Warin, Xavier</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xavier.warin@edf.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 3, pC579-C603. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Piecewise+linear+approximation%22">Piecewise linear approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Transportation+problems+%28Programming%29%22">Transportation problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Splines%22">Splines</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This article presents an input convex neural network (ICNN) architecture using Kolmogorov–Arnold networks (ICKANs). Two specific networks are presented. The first is based on a low-order, piecewise-linear representation of functions, and a universal approximation theorem is provided. The second is based on cubic splines, for which only numerical results support convergence. We demonstrate through simple tests that these networks perform competitively with classical ICNNs. We then use the networks to solve optimal transport problems that require a convex approximation of functions and demonstrate their effectiveness. Cubic-ICKANs produce results similar to those of ICNNs. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/25M1778626 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: C579 Subjects: – SubjectFull: Piecewise linear approximation Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Transportation problems (Programming) Type: general – SubjectFull: Splines Type: general – SubjectFull: Convex functions Type: general – SubjectFull: Approximation theory Type: general Titles: – TitleFull: Input Convex Kolmogorov–Arnold Networks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Deschatre, Thomas – PersonEntity: Name: NameFull: Warin, Xavier IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10648275 Numbering: – Type: volume Value: 48 – Type: issue Value: 3 Titles: – TitleFull: SIAM Journal on Scientific Computing Type: main |
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