I think there is no difference between BCEWithLogitsLoss and MultiLabelSoftMarginLoss.
BCEWithLogitsLoss = One Sigmoid Layer + BCELoss (solved numerically unstable problem)
MultiLabelSoftMargin’s fomula is also same with BCEWithLogitsLoss.
One difference is BCEWithLogitsLoss has a ‘weight’ parameter, MultiLabelSoftMarginLoss no has)
BCEWithLogitsLoss  :

MultiLabelSoftMarginLoss  :

The two formula is exactly the same except for the weight value.