Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on SO(d)

Amit Daniely

Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on SO(d)

Amit Daniely^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

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 SO(d). This extends and simplifies a recent line of work (Daniely and Shacham, 2020; Bubeck et al., 2021; Bartlett et al., 2021; Montanari and Wu, 2023) which shows similar results for random fully connected networks.

Original language	English
Journal	Proceedings of Machine Learning Research
Volume	291
State	Published - 2025
Event	38th Annual Conference on Learning Theory, COLT 2025 - Lyon, France Duration: 30 Jun 2025 → 4 Jul 2025

Bibliographical note

Publisher Copyright:
© 2025 A. Daniely.

Keywords

Adversarial Examples
Convolutional Networks
Isoperimetric Inequalities

Cite this

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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 SO(d). This extends and simplifies a recent line of work (Daniely and Shacham, 2020; Bubeck et al., 2021; Bartlett et al., 2021; Montanari and Wu, 2023) which shows similar results for random fully connected networks.",

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AB - 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 SO(d). This extends and simplifies a recent line of work (Daniely and Shacham, 2020; Bubeck et al., 2021; Bartlett et al., 2021; Montanari and Wu, 2023) which shows similar results for random fully connected networks.

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KW - Convolutional Networks

KW - Isoperimetric Inequalities

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SN - 2640-3498

VL - 291

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 38th Annual Conference on Learning Theory, COLT 2025

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Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on SO(d)

Abstract

Bibliographical note

Keywords

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