Max-margin loss (also known as hinge loss) is a loss function used to compare the decoded score of a true pair to a negative sample. Instead of formulating the problem as a binary classification task, it compares the direct outputs of the decoders. If the score for the positive (true) pair exceeds that of the negative pair by at least a margin $\Delta$, the loss is zero. Otherwise, a loss is incurred. This can be mathematically expressed as:

$\mathcal{L} = \max(0, \Delta - (s_{\text{true}} - s_{\text{neg}}))$

where $s_{\text{true}}$ and $s_{\text{neg}}$ represent the decoded scores for the true and negative pairs, respectively.