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Deep neural networks trained using a softmax layer at the top and thecross-entropy loss are ubiquitous tools for image classification. Yet, thisdoes not naturally enforce intra-class similarity nor inter-class margin of thelearned deep representations. To simultaneously achieve these two goals,different solutions have been proposed in the literature, such as the pairwiseor triplet losses. However, such solutions carry the extra task of selectingpairs or triplets, and the extra computational burden of computing and learningfor many combinations of them. In this paper, we propose a plug-and-play lossterm for deep networks that explicitly reduces intra-class variance andenforces inter-class margin simultaneously, in a simple and elegant geometricmanner. For each class, the deep features are collapsed into a learned linearsubspace, or union of them, and inter-class subspaces are pushed to be asorthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OL\'E) doesnot require carefully crafting pairs or triplets of samples for training, andworks standalone as a classification loss, being the first reported deep metriclearning framework of its kind. Because of the improved margin between featuresof different classes, the resulting deep networks generalize better, are morediscriminative, and more robust. We demonstrate improved classificationperformance in general object recognition, plugging the proposed loss term intoexisting off-the-shelf architectures. In particular, we show the advantage ofthe proposed loss in the small data/model scenario, and we significantlyadvance the state-of-the-art on the Stanford STL-10 benchmark.

OL\'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning