Optimizing the Simplicial-Map Neural Network Architecture
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be robust to adversarial attacks. In this paper,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Journal of Imaging |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2313-433X/7/9/173 |
| _version_ | 1797518662475710464 |
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| author | Eduardo Paluzo-Hidalgo Rocio Gonzalez-Diaz Miguel A. Gutiérrez-Naranjo Jónathan Heras |
| author_facet | Eduardo Paluzo-Hidalgo Rocio Gonzalez-Diaz Miguel A. Gutiérrez-Naranjo Jónathan Heras |
| author_sort | Eduardo Paluzo-Hidalgo |
| collection | DOAJ |
| description | Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be robust to adversarial attacks. In this paper, the refinement toward robustness is optimized by reducing the number of simplices (i.e., nodes) needed. We have shown experimentally that such a refined neural network is equivalent to the original network as a classification tool but requires much less storage. |
| first_indexed | 2024-03-10T07:32:53Z |
| format | Article |
| id | doaj.art-6f749f66c6744304adb822d630d59da9 |
| institution | Directory Open Access Journal |
| issn | 2313-433X |
| language | English |
| last_indexed | 2024-03-10T07:32:53Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Imaging |
| spelling | doaj.art-6f749f66c6744304adb822d630d59da92023-11-22T13:44:05ZengMDPI AGJournal of Imaging2313-433X2021-09-017917310.3390/jimaging7090173Optimizing the Simplicial-Map Neural Network ArchitectureEduardo Paluzo-Hidalgo0Rocio Gonzalez-Diaz1Miguel A. Gutiérrez-Naranjo2Jónathan Heras3Department of Applied Mathematics I, University of Sevilla, 41012 Sevilla, SpainDepartment of Applied Mathematics I, University of Sevilla, 41012 Sevilla, SpainDepartment of Computer Sciences and Artificial Intelligence, University of Sevilla, 41012 Sevilla, SpainDepartment of Mathematics and Computer Science, University of La Rioja, 26004 Logroño, SpainSimplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be robust to adversarial attacks. In this paper, the refinement toward robustness is optimized by reducing the number of simplices (i.e., nodes) needed. We have shown experimentally that such a refined neural network is equivalent to the original network as a classification tool but requires much less storage.https://www.mdpi.com/2313-433X/7/9/173simplicial-map neural networksartificial neural networkscomputational topology |
| spellingShingle | Eduardo Paluzo-Hidalgo Rocio Gonzalez-Diaz Miguel A. Gutiérrez-Naranjo Jónathan Heras Optimizing the Simplicial-Map Neural Network Architecture Journal of Imaging simplicial-map neural networks artificial neural networks computational topology |
| title | Optimizing the Simplicial-Map Neural Network Architecture |
| title_full | Optimizing the Simplicial-Map Neural Network Architecture |
| title_fullStr | Optimizing the Simplicial-Map Neural Network Architecture |
| title_full_unstemmed | Optimizing the Simplicial-Map Neural Network Architecture |
| title_short | Optimizing the Simplicial-Map Neural Network Architecture |
| title_sort | optimizing the simplicial map neural network architecture |
| topic | simplicial-map neural networks artificial neural networks computational topology |
| url | https://www.mdpi.com/2313-433X/7/9/173 |
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