Canonical foliations of neural networks: application to robustness
| Autor: | Tron, Eliot, Couellan, Nicolas, Puechmorel, Stéphane |
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| Přispěvatelé: | Ecole normale supérieure de Lyon (Ens Lyon), Ecole Nationale de l'Aviation Civile (ENAC), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Mathematics - Differential Geometry Computer Science - Machine Learning Neural Networks Information Theory (cs.IT) Computer Science - Information Theory Adversarial attacks Machine Learning (stat.ML) Machine Learning (cs.LG) Differential Geometry (math.DG) [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Statistics - Machine Learning Fisher Information Metric [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] FOS: Mathematics Mathematics::Differential Geometry Robustness Information geometry Computer Science::Cryptography and Security |
| Popis: | Deep learning models are known to be vulnerable to adversarial attacks. Adversarial learning is therefore becoming a crucial task. We propose a new vision on neural network robustness using Riemannian geometry and foliation theory. The idea is illustrated by creating a new adversarial attack that takes into account the curvature of the data space. This new adversarial attack called the two-step spectral attack is a piece-wise linear approximation of a geodesic in the data space. The data space is treated as a (degenerate) Riemannian manifold equipped with the pullback of the Fisher Information Metric (FIM) of the neural network. In most cases, this metric is only semi-definite and its kernel becomes a central object to study. A canonical foliation is derived from this kernel. The curvature of transverse leaves gives the appropriate correction to get a two-step approximation of the geodesic and hence a new efficient adversarial attack. The method is first illustrated on a 2D toy example in order to visualize the neural network foliation and the corresponding attacks. Next, experiments on the MNIST dataset with the proposed technique and a state of the art attack presented in Zhao et al. (2019) are reported. The result show that the proposed attack is more efficient at all levels of available budget for the attack (norm of the attack), confirming that the curvature of the transverse neural network FIM foliation plays an important role in the robustness of neural networks. |
| Databáze: | OpenAIRE |
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