We parameterize our discriminator with an MLP, and alternatively optimize the mapping matrix and the discriminator with the corresponding objectives: Aligning Known Word Pairs: Given aligned bilingual word embeddings S, we aim to minimize a similarity function (f s ) which maximizes the similarity between the corresponding matched pairs of words.
the loss is defined as: Weak Orthogonality Constraint: Given an embedding space X , we define a consistency loss that maximizes a similarity function f a between x and W T W x, x 2 X .