While the DV representation is the strong bound of mutual information shown in MINE, we are primarily interested in maximizing MI but not focusing on its precise value.
dIM proposes an alternative estimation using Jensen-Shannon divergence (JS), which can be efficiently implemented using the cross-entropy (BCE) loss: While two representations should behave similarly, considering that both act like classifiers with objectives maximizing the expected log-ratio of the joint over the product of marginals, it is found that the BCE loss empirically works better than the dV-based objective Ravanelli and Bengio, 2018;Veličković et al., 2018).