Compute contrastive loss for pairs of embeddings. A label of 1 marks a similar pair, while 0 marks a dissimilar pair. First compute each Euclidean distance:

Then compute each pair loss:

Here, $a_i$ and $b_i$ are the two embeddings, $d_i$ is their distance, $y_i$ is the pair label, $m$ is the margin, and $\ell_i$ is the pair loss. A one-dimensional embedding represents one pair; a two-dimensional input contains one pair per row. Return the mean or sum as a Python float according to reduction.