The Role of Feature Vector Scale in the Adversarial Vulnerability of Convolutional Neural Networks

Hyun-Cheol Park and Sang-Woong Lee ()
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Hyun-Cheol Park: Department of Computer Engineering, Korea National University of Transportation, 50, Daehak-ro, Daesowon-myeon, Chungju-si 27469, Republic of Korea
Sang-Woong Lee: Department of Artificial Intelligence, Gachon University, Seongnam 13120, Republic of Korea

Mathematics, 2025, vol. 13, issue 18, 1-17

Abstract: In image classification, convolutional neural networks (CNNs) remain vulnerable to visually imperceptible perturbations, often called adversarial examples. Although various hypotheses have been proposed to explain this vulnerability, a clear cause has not been established. We hypothesize an unfair learning effect: samples are learned unevenly depending on the scale (norm) of their feature vectors in feature space. As a result, feature vectors with different scales exhibit different levels of robustness against noise. To test this hypothesis, we conduct vulnerability tests on CIFAR-10 using a standard convolutional classifier, analyzing cosine similarity between original and perturbed feature vectors, as well as error rates across scale intervals. Our experiments show that small-scale feature vectors are highly vulnerable. This is reflected in low cosine similarity and high error rates, whereas large-scale feature vectors consistently exhibit greater robustness with high cosine similarity and low error rates. These findings highlight the critical role of feature vector scale in adversarial vulnerability.

Keywords: convolutional neural networks; vulnerability; feature vector; adversarial examples; gabor noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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