Yes but the size of the sets is going to be enormous. Would like to avoid use of one-hot encodings. That still doesn't solve the issue of solving for any injec

Yes but the size of the sets is going to be enormous. Would like to avoid use of one-hot encodings. That still doesn't solve the issue of solving for any injective mapping though - solving for a specific one can be done thru the standard loss functions - but the density of solutions is sparse in 1/n! where n is the output set size.