  In narrow asymptotic settings Gaussian VAE models of continuous data have
been shown to possess global optima aligned with ground-truth distributions.
Even so, it is well known that poor solutions whereby the latent posterior
collapses to an uninformative prior are sometimes obtained in practice.
However, contrary to conventional wisdom that largely assigns blame for this
phenomena on the undue influence of KL-divergence regularization, we will argue
that posterior collapse is, at least in part, a direct consequence of bad local
minima inherent to the loss surface of deep autoencoder networks. In
particular, we prove that even small nonlinear perturbations of affine VAE
decoder models can produce such minima, and in deeper models, analogous minima
can force the VAE to behave like an aggressive truncation operator, provably
discarding information along all latent dimensions in certain circumstances.
Regardless, the underlying message here is not meant to undercut valuable
existing explanations of posterior collapse, but rather, to refine the
discussion and elucidate alternative risk factors that may have been previously
underappreciated.
