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We present BioMetricNet: a novel framework for deep unconstrained face verification which learns a regularized metric to compare facial features. Differently from popular methods such as FaceNet, the proposed approach does not impose any specific metric on facial features; instead, it shapes the decision space by learning a latent representation in which matching and non-matching pairs are mapped onto clearly separated and well-behaved target distributions. In particular, the network jointly learns the best feature representation, and the best metric that follows the target distributions, to be used to discriminate face images. In this paper we present this general framework, first of its kind for facial verification, and tailor it to Gaussian distributions. This choice enables the use of a simple linear decision boundary that can be tuned to achieve the desired trade-off between false alarm and genuine acceptance rate, and leads to a loss function that can be written in closed form. Extensive analysis and experimentation on publicly available datasets such as Labeled Faces in the wild (LFW), Youtube faces (YTF), Celebrities in Frontal-Profile in the Wild (CFP), and challenging datasets like cross-age LFW (CALFW), cross-pose LFW (CPLFW), In-the-wild Age Dataset (AgeDB) show a significant performance improvement and confirms the effectiveness and superiority of BioMetricNet over existing state-of-the-art methods.