Use the paper's coarse-versus-fine neighborhood comparison as a differentiable penalty on a neural representation. For each sample, compare similarity of target or sensitive-variable embeddings among points close in context Z alone against points close in (Z,R), where R=f_theta(X) is the learned representation. Under conditional independence, adding R should not increase local similarity, so the network is penalized when the fine-neighborhood statistic differs systematically from the coarse one.
Apply a low-degree polynomial feature lift to normalized hidden representations and penalize degeneracy of the covariance in that lifted space. This can detect collapse in nonlinear combinations of features even when the raw hidden covariance appears healthy.
Add a graph-derived conditional moment penalty to a neural representation or predictor. For each nested Markov constraint represented after fixing variables in R, residualize functions of (X,Z) with respect to Z under the post-fixing distribution and penalize their weighted correlation with functions of (Y,Z). This directly targets the equality constraint and can be more informative than an unconditional decorrelation penalty.