Reading PyTorch docs BCEWithLogitsLoss:
where c is the class number (c > 1 for multi-label binary classification, c = 1 for single-label binary classification), nn is the number of the sample in the batch and p_cp c is the weight of the positive answer for the class cc .
What is the multi-label binary classification? Binary assume only two labels AFIK
Multi-label in terms of binary classification means that both the classes can be true class for a single example.
For example, in case of dog-cat classifier, for an image containing both dog and cat, it'll predict both dog and cat.
In the multi-label problem there is no constraint on how many of the classes the instance can be assigned to. Wiki