Multilabel classification: How to binarize scores? (How to learn thresholds?)

You could use BCEWithLogitsLoss. I’ve created a small dummy example in another thread.

Your model will output logits, which you can feed into a sigmoid layer.
The choice of the threshold depends on your use case, e.g. some classes should have a high sensitivity while others a high specificity.
Have a look at the scikit-learn explanation of multi-class ROCs.