CF-OOD+: Concentration-Free Out-of-Distribution Detection with multi-layer aggregation

Out-of-Distribution (OOD) detection is a task that is witnessing increasing interest in machine and deep learning, since it deals with the problem of signaling inputs coming outside of the data-generating distribution on which a certain model has been trained. Different methods have been proposed, some of which are based on network architecture design (pre-hoc), others consisting in obtaining confidence scores without retraining (post-hoc). In this work, we provide a contribution within this research line by introducing the CF-OOD (for Concentration-Free Out-of-Distribution detection) out-of-distribution post-hoc approach and its multi-layer version CF-OOD+. The approach is based on the Concentration-Free Outlier Factor (CFOF), a score relying on the concept of reverse nearest neighborhood, which has been originally designed for effective anomaly detection in the context of very high-dimensional data. Indeed, the above measure is particularly suitable for the typically large hidden representations of deep learning architectures. Specifically, CF-OOD+ exploits weighted aggregation of layer-wise scores in order to enhance ID/OOD separation. Experiments highlight that the method is able to provide state-of-the-art performances on a plurality of deep learning architectures and out-of-distribution datasets, and also on the challenging low-regime scenario. Finally, we show that the choice of the neighborhood parameter value is not critical and, moreover, that the scores can be reliably estimated by means of a sampling procedure exploiting only a small fraction of the in-distribution data.