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

2025/06/14 by Amit Daniely, Daniely, Amit
Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Structural Response to Dynamic Loads

paper · pdf · doi:10.48550/arxiv.2506.12613

openalex publication_date 2025/06/14 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

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 \mathbbso(d). This extends and simplifies a recent line of work which shows similar results for random fully connected networks.

Citations

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• Detecting Adversarial Samples from Artifacts
• On the (Statistical) Detection of Adversarial Examples
• Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity
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