  Current approaches to novelty or anomaly detection are based on deep neural
networks. Despite their effectiveness, neural networks are also vulnerable to
imperceptible deformations of the input data. This is a serious issue in
critical applications, or when data alterations are generated by an adversarial
attack. While this is a known problem that has been studied in recent years for
the case of supervised learning, the case of novelty detection has received
very limited attention. Indeed, in this latter setting the learning is
typically unsupervised because outlier data is not available during training,
and new approaches for this case need to be investigated. We propose a new
prior that aims at learning a robust likelihood for the novelty test, as a
defense against attacks. We also integrate the same prior with a
state-of-the-art novelty detection approach. Because of the geometric
properties of that approach, the resulting robust training is computationally
very efficient. An initial evaluation of the method indicates that it is
effective at improving performance with respect to the standard models in the
absence and presence of attacks.
