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.

通过深度学习模型，对于所有可能的对进行非线性嵌入模型的相似度学习问题进行了研究。通过详细推导和提供干净的公式，使得可以通过许多优化方法应用于非线性嵌入的极端相似度学习，同时讨论了一些实现的问题并提出了高效的优化算法。