Latent Spectroscopy: Posterior Collapse as a Feature

We show that, in linear Gaussian VAEs, posterior collapse is a form of latent feature selection. Feature importance is set by each latent coordinate's contribution to reconstruction, itself given by the corresponding PCA eigenvalue. Varying the regularizer strength $β$ reveals a ranked spectrum of collapse events, with thresholds set by the utility/PCA spectrum. A mode-by-mode analysis identifies the scale-invariant signal fraction as an order parameter obeying Landau scaling near collapse. WorldClim experiments confirm both the utility-threshold calibration and the predicted near-collapse scaling.

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