Artículo
Simplicial-Map Neural Networks Robust to Adversarial Examples
Autor/es | Paluzo Hidalgo, Eduardo
González Díaz, Rocío Gutiérrez Naranjo, Miguel Ángel Heras, Jónathan |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Fecha de publicación | 2021-01-15 |
Fecha de depósito | 2021-02-03 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Identificador del proyecto | PID2019-107339GB-100 |
Cita | Paluzo Hidalgo, E., González Díaz, R., Gutiérrez Naranjo, M.Á. y Heras, J. (2021). Simplicial-Map Neural Networks Robust to Adversarial Examples. Mathematics, 9(2) (169), 1-1-16-16. |
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