Residual spectral instabilities in representation learning
The paper explores how residual spectral instabilities cause dimensionwise posterior collapse in Gaussian Variational Autoencoders (VAEs). By treating this as a fluctuation theory around collapsed states, it reveals a spectral cascade governed by residual information. The stability of the representation is determined by comparing the variance of fluctuations ($\sigma'^2$) against an upper edge of the residual spectrum ($\Lambda(A)^*$).