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We study the problem of learning similarity functions over very large corporausing neural network embedding models. These models are typically trained usingSGD with sampling of random observed and unobserved pairs, with a number ofsamples that grows quadratically with the corpus size, making it expensive toscale to very large corpora. We propose new efficient methods to train thesemodels without having to sample unobserved pairs. Inspired by matrixfactorization, our approach relies on adding a global quadratic penalty to allpairs of examples and expressing this term as the matrix-inner-product of twogeneralized Gramians. We show that the gradient of this term can be efficientlycomputed by maintaining estimates of the Gramians, and develop variancereduction schemes to improve the quality of the estimates. We conductlarge-scale experiments that show a significant improvement in training timeand generalization quality compared to traditional sampling methods.

Efficient Training on Very Large Corpora via Gramian Estimation