Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attacks

Artificial Neural Networks have demonstrated exceptional capability in the fields of computer vision, natural language processing, and genetics. However, they have similarly demonstrated a concerning vulnerability to adversarial attacks Huang et al. [2017], Papernot et al. [2018]. As neural networks become prevalent in critical applications such as autonomous driving, healthcare, and cybersecurity, the development of adversarial defense methodologies will become central to the reliability and ultimate success of those efforts (for example, see Madry et al. [2018], Kotyan and Vargas [2022], Carlini and Wagner [2017a], Croce et al. [2019], Croce and Hein [2020] and references