Title: Tropical Bisectors and Carlini-Wagner Attacks Show Chinese title

Title: 热带平分线和Carlini-Wagner攻击

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. Show Chinese abstract

Abstract: Pasque等人展示了在最后一层使用热带对称度量作为激活函数可以提高卷积神经网络（CNNs）对最先进的攻击的鲁棒性，包括Carlini-Wagner攻击。这种改进发生在攻击没有专门针对热带层的不可微性时。此外，他们展示了热带CNN的决策边界由热带平分线定义。在本文中，我们探讨了热带平分线的组合学，并分析了热带嵌入层如何增强对Carlini-Wagner攻击的鲁棒性。我们证明了热带CNN的决策边界可能拥有的线性段数的一个上界。然后，我们提出了一种改进的Carlini-Wagner攻击，专门针对热带架构。在MNIST和LeNet5上的计算实验展示了我们的攻击成功率的提高。