Hi Farhad!



 farhadzadeh:

we have the following classes: [A, B, C]
…
Non-finding: [0, 0, 0, 0]
How should I formulize the BCEWithLogitsLoss?


You would label “non-finding” as [0, 0, 0], with three yes-no labels,
one for each of your three classes.



 farhadzadeh:

our instances are assigned to one or more than one of them.


To rephrase this a little more precisely:  “our instances are assigned
to zero or one or more than one of them.”
To clarify a little further:  If this were a single-label, three-class problem,
[A, B, C], but a given instance could also be “none of the above,” then
you would add a fourth class, [none, A, B, C], and perform a four-class
classification.
But for a multi-label, three-class  problem, you would just use the
three classes, [A, B, C] because, with multiple labels, [0, 0, 0]
suffices to indicate “none of the above.”
Best.
K. Frank