| Título |
Simplicial-Map Neural Networks Robust to Adversarial Examples |
| Autores |
PALUZO HIDALGO, EDUARDO, Gonzalez-Diaz, Rocio , Gutierrez-Naranjo, Miguel A. , Heras, Jonathan |
| Publicación externa |
Si |
| Medio |
Mathematics |
| Alcance |
Article |
| Naturaleza |
Científica |
| Cuartil JCR |
1 |
| Cuartil SJR |
2 |
| Impacto JCR |
2.592 |
| Impacto SJR |
0.538 |
| Fecha de publicacion |
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. |
| Palabras clave |
algebraic topology; neural network; adversarial examples |
| Miembros de la Universidad Loyola |
|
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