When Marginals Match but Structure Fails: Covariance Fidelity in Generative Models

In three linesTheoretical paper on generative model evaluation. Authors show standard criteria (marginal matching) don't guarantee covariance structure preservation. They introduce D_Sigma = ||Sigma_P - Sigma_Q||_F to measure dependence fidelity, with formal proofs and validation on Fashion-MNIST VAE, RNA-seq (TCGA-BRCA, n=1111), and Alzheimer's data (n=113).

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