What is a good loss function between a pair of two matrices that row *i* in the target matrix does not necessarily correspond to row *i* in the trained matrix? More specifically, I’m looking to minimize the sum of all errors between target and trained tensors, where row *i* in the target corresponds to row *j* in the trained tensor where the sum of all “distances” between *(i,j)* is minimal, and if *j* is already matched with *i*, then it cannot match another *k* in the target matrix as well (“without replacement”).

Is there a built-in function for this in torch?

I’ve implemented maximum mean discrepancy (MMD) distance metric, but it’s not giving me satisfactory results.