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We study the problem of learning similarity by using nonlinear embeddingmodels (e.g., neural networks) from all possible pairs. This problem iswell-known for its difficulty of training with the extreme number of pairs. Forthe special case of using linear embeddings, many studies have addressed thisissue of handling all pairs by considering certain loss functions anddeveloping efficient optimization algorithms. This paper aims to extend resultsfor general nonlinear embeddings. First, we finish detailed derivations andprovide clean formulations for efficiently calculating some building blocks ofoptimization algorithms such as function, gradient evaluation, andHessian-vector product. The result enables the use of many optimization methodsfor extreme similarity learning with nonlinear embeddings. Second, we studysome optimization methods in detail. Due to the use of nonlinear embeddings,implementation issues different from linear cases are addressed. In the end,some methods are shown to be highly efficient for extreme similarity learningwith nonlinear embeddings.

Efficient Optimization Methods for Extreme Similarity Learning with Nonlinear Embeddings