The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality

By Laurent Amsaleg, James Bailey, Dominique Barbe, Sarah Monazam Erfani, Michael E. Houle, Vinh Nguyen, Miloš Radovanović. 2017

62 citations recorded by the source corpus.

Subfields: Artificial Intelligence

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Bernt Schiele
2. Matthias Hein
3. Yoshua Bengio
4. David Lopez-Paz
5. Bo Li
6. David Stutz
7. Yisen Wang
8. Xingjun Ma

Citations in the corpus

• Adversarial Vulnerability of Neural Networks Increases With Input Dimension (2018, background): “This explanation of adversarial vulnerability is independent of the intrinsic dimensionality or geometry of the data (compare to Amsaleg et al. 2017; Gilmer et al. 2018). Incidentally, Goodfellow et al. (2015) also already relate adversarial vulnerability to large gradients of the loss L, an insight”
• Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality (2018, methodology): “Recent work in Amsaleg et al. (2017) shows that the magnitude of the perturbation required to make changes in the expected nearest neighbor ranking tends to zero as the LID and the data sample size tend to infinity.”
• Disentangling Adversarial Robustness and Generalization (2018, methodology): “Defenses: Proposed defenses include detection and rejection methods [31, 25, 54, 60, 3, 63], pre-processing, quantization and dimensionality reduction methods [12, 73, 7], manifold-projection methods [39, 72, 82, 86], methods based on stochasticity/regularization or adapted architectures [109, 7, 68”
• Dimensionality-Driven Learning with Noisy Labels (2018, background): “Recent theoretical work for adversarial perturbation in nearest-neighbor classification further supports the relationship between LID and local transformation of data, by showing that the magnitude of the perturbation required in order to subvert the classification diminishes as the local intrinsic ”
• Relating Adversarially Robust Generalization to Flat Minima (2021, methodology): “2, 6, 21 [3] Laurent Amsaleg, James Bailey, Dominique Barbe, Sarah M.”
• First-Order Adversarial Vulnerability of Neural Networks and Input Dimension (2018, methodology): “As opposed to Amsaleg et al. (2017); Gilmer et al. (2018); Shafahi et al. (2019), their (and our) explanation of the dimension dependence is data-independent. Incidentally, they also link adversarial vulnerability to loss gradients and use it to derive the FGSM adversarial augmentation defense (see ”
• Intrinsic dimension of data representations in deep neural networks (2019, background): “In [7], estimates of the ID were related to robustness properties of deep networks to adversarial attacks, showing that a low local intrinsic dimension correlates positively with robustness.”
• Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels (2019, background): “The combining weight depends on the dimensionality of the latent feature subspace (Amsaleg et al., 2017).”