We construct the embeddings for each document using BERT models finetuned on MLDoc. We mean-pool each document embedding to create a single vector per document. We then calculate the cosine similarity between the embeddings for the English document and its translation. In Table TABREF21 , we observe that the median cosine similarity increases dramatically with adversarial training, which suggests that the embeddings became more language-independent. 
 Question: How do they quantify alignment between the embeddings of a document and its translation?
median cosine similarity