Posterior Collapse as Automatic Spectral Pruning (opens in new tab)

We show that posterior collapse in $\beta$-VAEs implements automatic spectral pruning. A latent mode collapses if its contribution to reconstruction is below the cutoff set by $\beta$. Equilibrium solutions with different $\beta$ thus reveal a cascade of collapses as latent modes decouple from least to most useful. We derive this as a consequence of the loss via a Landau stability analysis. We define a latent-rescaling-invariant order parameter ...