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From Notices of the AMS

An Analytical and Geometric Perspective on Adversarial Robustness

llustration of a generalized barycenter $\lambda$ for the measures $\mu_1, \mu_2, \mu_3$ and the associated perturbations $\tilde{\mu}_y$. The smaller the total mass of $\lambda$, the better for the adversary. Since $\lambda$ must lie above the $\mu_y$, the only way to reduce the mass of $\lambda$ is to make the $\tilde \mu_y$ overlap.

by Nicolás García Trillos
Communicated by Matt Jacobs

"…y luego se fueron el uno para el otro, como si fueran dos mortales enemigos. " Miguel de Cervantes, Don Quixote; Chapter 8, Part 1.

1. Introduction

In the last ten years, neural networks have made incredible strides in classifying large data sets, to the point that they can now outperform humans in raw accuracy. However, the robustness of these systems is a completely different story. Suppose you were asked to identify whether a photo contained an image of a cat or a dog. You probably would have no difficulty at all; at worst, maybe you would only be tripped up by a particularly small or unusual Shiba Inu. In contrast, it has been widely documented that an adversary can convince an otherwise well-performing neural network that a dog is actually a cat (or vice-versa) by making tiny human-imperceptible changes to an image at the pixel level. These small perturbations are known as adversarial attacks and they are a significant obstacle to the deployment of machine learning systems in security-critical applications [GSS14]. The susceptibility to adversarial attacks is not exclusive to neural network models, and many other learning systems have also been observed to be brittle when facing adversarial perturbations of data.

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