{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tropical-bisectors-and-carlini-wagner-attacks","title":"Tropical Bisectors and Carlini-Wagner Attacks","arxiv_id":"2503.22653","date":"2025-03-28","proceeding":null,"authors":["Gillian Grindstaff","Julia Lindberg","Daniela Schkoda","Miruna-Stefana Sorea","Ruriko Yoshida"],"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.","url_abs":"https://arxiv.org/abs/2503.22653v1","url_pdf":"https://arxiv.org/pdf/2503.22653v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"tropical-bisectors-and-carlini-wagner-attacks","repo_url":"https://github.com/DanielaSchkoda/TropicalCNN","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}