Task: Summarization
Input (English): We study the problem of learning similarity functions over very large corpora using neural network embedding models. These models are typically trained using SGD with random sampling of unobserved pairs, with a sample size that grows quadratically with the corpus size, making it expensive to scale.
 We propose new efficient methods to train these models without having to sample unobserved pairs. Inspired by matrix factorization, our approach relies on adding a global quadratic penalty and expressing this term as the inner-product of two generalized Gramians. We show that the gradient of this term can be efficiently computed by maintaining estimates of the Gramians, and develop variance reduction schemes to improve the quality of the estimates. We conduct large-scale experiments that show a significant improvement both in training time and generalization performance compared to sampling methods.
Output (English): We develop efficient methods to train neural embedding models with a dot-product structure, by reformulating the objective function in terms of generalized Gram matrices, and maintaining estimates of those matrices.