Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{SO}(d)$

Amit Daniely
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:1368-1379, 2025.

Abstract

We show that adversarial examples exist for various random convolutional networks, and furthermore, that this is a relatively simple consequence of the isoperimetric inequality on the special orthogonal group $\mathbb{SO}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-daniely25a, title = {Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{SO}(d)$}, author = {Daniely, Amit}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {1368--1379}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/daniely25a/daniely25a.pdf}, url = {https://proceedings.mlr.press/v291/daniely25a.html}, abstract = {We show that adversarial examples exist for various random convolutional networks, and furthermore, that this is a relatively simple consequence of the isoperimetric inequality on the special orthogonal group $\mathbb{SO}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.} }
Endnote
%0 Conference Paper %T Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{SO}(d)$ %A Amit Daniely %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-daniely25a %I PMLR %P 1368--1379 %U https://proceedings.mlr.press/v291/daniely25a.html %V 291 %X We show that adversarial examples exist for various random convolutional networks, and furthermore, that this is a relatively simple consequence of the isoperimetric inequality on the special orthogonal group $\mathbb{SO}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.
APA
Daniely, A.. (2025). Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{SO}(d)$. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:1368-1379 Available from https://proceedings.mlr.press/v291/daniely25a.html.

Related Material