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How to track loss of multi-label MLP?

I am given binary data points of dimension 5,000. I am asked to perform machine learning predicting a binary vector of length 1k, where each position of the output is a class. The classes are not exclusive.

How to track loss of multi-class MLP?

I am given binary data points of dimension 5,000. I am asked to perform machine learning predicting a binary vector of length 1k, where each position of the output is a class. The classes are not exclusive.