Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attacks
This addresses the issue of adversarial vulnerability in neural networks for applications like image recognition, though it appears incremental as it builds on existing piece-wise linear models.
The authors tackled the problem of adversarial robustness in neural networks by introducing a tropical convolutional architecture that embeds data in the tropical projective torus, resulting in demonstrated robustness against adversarial attacks in computational experiments on image datasets.
We introduce a simple, easy to implement, and computationally efficient tropical convolutional neural network architecture that is robust against adversarial attacks. We exploit the tropical nature of piece-wise linear neural networks by embedding the data in the tropical projective torus in a single hidden layer which can be added to any model. We study the geometry of its decision boundary theoretically and show its robustness against adversarial attacks on image datasets using computational experiments.