As neural networks are universal function approximators (Hornik, 1991), we can attempt to approximate f with a neural network, called the critic D, with weight clipping to ensure the function family is K-Lipschitz.
the objective of the critic is Conceptually, the critic D assigns scores f D to real target embeddings and fake ones generated by the generator G. When the objective (6) is trained until optimality, the difference of the scores will approximate the Wasserstein distance up to a multiplicative constant.