• $$\beta$$-VAE
• $$\beta$$-VAE objective is equivalent to a standard ELBO with the alternative prior $$f_{\beta}(\mathbf{z}) \propto p(\mathbf{z})^{\beta}$$ (Mathieu et al. 2018):
• for Gaussian $$p(\mathbf{z})$$:
• $$\beta$$-VAE simply anneals the latent space by $$1/\sqrt{\beta}$$, i.e., $$f_{\beta}(\mathbf{z}) = \mathcal{N}(\mathbf{z};0,\Sigma/\beta)$$.
• $$\beta$$-VAE objective is invariant to rotations of the latent space.