Trainable and Explainable Simplicial Map Neural Networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911806075699200 |
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| author | Paluzo-Hidalgo, Eduardo Gutiérrez-Naranjo, Miguel A. Gonzalez-Diaz, Rocio |
| author_facet | Paluzo-Hidalgo, Eduardo Gutiérrez-Naranjo, Miguel A. Gonzalez-Diaz, Rocio |
| contents | Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and an effective implementation are also newly introduced in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trainable and Explainable Simplicial Map Neural Networks Paluzo-Hidalgo, Eduardo Gutiérrez-Naranjo, Miguel A. Gonzalez-Diaz, Rocio Machine Learning Artificial Intelligence Algebraic Topology Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and an effective implementation are also newly introduced in this paper. |
| title | Trainable and Explainable Simplicial Map Neural Networks |
| topic | Machine Learning Artificial Intelligence Algebraic Topology |
| url | https://arxiv.org/abs/2306.00010 |