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Simplicial-Map Neural Networks Robust to Adversarial Examples
- Publication Year :
- 2021
-
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.
Details
- Database :
- OAIster
- Notes :
- Universidad de Sevilla. Departamento de Matemática Aplicada I, Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial, Ministerio de Ciencia, Innovación y Universidades (MICINN). España, European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER), Paluzo Hidalgo, Eduardo, González Díaz, Rocío, Gutiérrez Naranjo, Miguel Ángel, Heras, Jónathan
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1410782921
- Document Type :
- Electronic Resource