| Title | Simplicial-Map Neural Networks Robust to Adversarial Examples |
|---|---|
| Authors | PALUZO HIDALGO, EDUARDO, Gonzalez-Diaz, Rocio , Gutierrez-Naranjo, Miguel A. , Heras, Jonathan |
| External publication | Si |
| Means | Mathematics |
| Scope | Article |
| Nature | Científica |
| JCR Quartile | 1 |
| SJR Quartile | 2 |
| JCR Impact | 2.592 |
| SJR Impact | 0.538 |
| Publication date | 01/01/2021 |
| ISI | 000611359600001 |
| DOI | 10.3390/math9020169 |
| Abstract | Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent a weakness for the safety of neural network applications, and many different solutions have been proposed for minimizing their effects. In this paper, we propose a new approach by means of a family of neural networks called simplicial-map neural networks constructed from an Algebraic Topology perspective. Our proposal is based on three main ideas. Firstly, given a classification problem, both the input dataset and its set of one-hot labels will be endowed with simplicial complex structures, and a simplicial map between such complexes will be defined. Secondly, a neural network characterizing the classification problem will be built from such a simplicial map. Finally, by considering barycentric subdivisions of the simplicial complexes, a decision boundary will be computed to make the neural network robust to adversarial attacks of a given size. |
| Keywords | algebraic topology; neural network; adversarial examples |
| Universidad Loyola members |
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