A Single Gradient Step Finds Adversarial Examples on Random Two-Layers Neural Networks

Abstract

Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks. The term “undercomplete” refers to the fact that their proof only holds when the number of neurons is a vanishing fraction of the ambient dimension. We extend their result to the overcomplete case, where the number of neurons is larger than the dimension (yet also subexponential in the dimension). In fact we prove that a single step of gradient descent suffices. We also show this result for any subexponential width random neural network with smooth activation function.

PDF NeurIPS OpenReview Semantic Scholar

Cite

Text

Bubeck et al. "A Single Gradient Step Finds Adversarial Examples on Random Two-Layers Neural Networks." Neural Information Processing Systems, 2021.

Markdown

[Bubeck et al. "A Single Gradient Step Finds Adversarial Examples on Random Two-Layers Neural Networks." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/bubeck2021neurips-single/)

BibTeX

@inproceedings{bubeck2021neurips-single,
  title     = {{A Single Gradient Step Finds Adversarial Examples on Random Two-Layers Neural Networks}},
  author    = {Bubeck, Sebastien and Cherapanamjeri, Yeshwanth and Gidel, Gauthier and Combes, Remi Tachet des},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/bubeck2021neurips-single/}
}