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arXiv · 2503.22653

Tropical Bisectors and Carlini-Wagner Attacks

Gillian Grindstaff·Julia Lindberg·Daniela Schkoda·Miruna-Stefana Sorea·Ruriko Yoshida
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Abstract

Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner attack. This improvement occurs when the attacks are not specifically adapted to the non-differentiability of the tropical layer. Moreover, they showed that the decision boundary of a tropical CNN is defined by tropical bisectors. In this paper, we explore the combinatorics of tropical bisectors and analyze how the tropical embedding layer enhances robustness against Carlini-Wagner attacks. We prove an upper bound on the number of linear segments the decision boundary of a tropical CNN can have. We then propose a refined version of the Carlini-Wagner attack, specifically tailored for the tropical architecture. Computational experiments with MNIST and LeNet5 showcase our attacks improved success rate.

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Gillian Grindstaff, Julia Lindberg, Daniela Schkoda, Miruna-Stefana Sorea, Ruriko Yoshida. 2025-03-28. Tropical Bisectors and Carlini-Wagner Attacks. https://arxiv.org/abs/2503.22653

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