  Machine learning models are known to be vulnerable to adversarial attacks,
namely perturbations of the data that lead to wrong predictions despite being
imperceptible. However, the existence of "universal" attacks (i.e., unique
perturbations that transfer across different data points) has only been
demonstrated for images to date. Part of the reason lies in the lack of a
common domain, for geometric data such as graphs, meshes, and point clouds,
where a universal perturbation can be defined. In this paper, we offer a change
in perspective and demonstrate the existence of universal attacks for geometric
data (shapes). We introduce a computational procedure that operates entirely in
the spectral domain, where the attacks take the form of small perturbations to
short eigenvalue sequences; the resulting geometry is then synthesized via
shape-from-spectrum recovery. Our attacks are universal, in that they transfer
across different shapes, different representations (meshes and point clouds),
and generalize to previously unseen data.
