Efficient Optimization Methods for Extreme Similarity Learning with Nonlinear Embeddings

TL;DR

This paper develops efficient optimization techniques for training nonlinear embedding models on all pairs in similarity learning, addressing computational challenges and enabling practical application of neural network-based embeddings.

Contribution

It extends efficient optimization algorithms from linear to nonlinear embeddings, providing detailed formulations and addressing implementation issues.

Findings

Methods are highly efficient for nonlinear similarity learning.

Formulations enable the use of various optimization algorithms.

Implementation issues for nonlinear embeddings are effectively addressed.

Abstract

We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special case of using linear embeddings, many studies have addressed this issue of handling all pairs by considering certain loss functions and developing efficient optimization algorithms. This paper aims to extend results for general nonlinear embeddings. First, we finish detailed derivations and provide clean formulations for efficiently calculating some building blocks of optimization algorithms such as function, gradient evaluation, and Hessian-vector product. The result enables the use of many optimization methods for extreme similarity learning with nonlinear embeddings. Second, we study some 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 learning with nonlinear embeddings.