# Appropriate loss function for multi-hot output vectors

I have some data in which model inputs and outputs (which are the same size) belong to multiple classes concurrently. A single input or output is a vector of zeros somewhere between one and four values that are equal to 1:

[0 0 0 1 0 0 1 0 1 0 0]


These kinds of vectors are sometimes called "multi-hot embeddings".

I am looking for an appropriate loss function for outputs of this kind. Is there a published equation I should check out? Or should I implement a custom loss function? Any suggestions others can offer on this question would be greatly appreciated!