Tropical Bisectors and Carlini-Wagner Attacks
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916665181077504 |
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| author | Grindstaff, Gillian Lindberg, Julia Schkoda, Daniela Sorea, Miruna-Stefana Yoshida, Ruriko |
| author_facet | Grindstaff, Gillian Lindberg, Julia Schkoda, Daniela Sorea, Miruna-Stefana Yoshida, Ruriko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical Bisectors and Carlini-Wagner Attacks Grindstaff, Gillian Lindberg, Julia Schkoda, Daniela Sorea, Miruna-Stefana Yoshida, Ruriko Machine Learning Algebraic Geometry Combinatorics Metric Geometry Optimization and Control 14T90, 52B12, 68T07 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. |
| title | Tropical Bisectors and Carlini-Wagner Attacks |
| topic | Machine Learning Algebraic Geometry Combinatorics Metric Geometry Optimization and Control 14T90, 52B12, 68T07 |
| url | https://arxiv.org/abs/2503.22653 |