tags: - colorclass/probability theory ---The Gaussian annulus theorem is a specific instance of the Concentration of Measure phenomenon that applies to Gaussian distributions in high-dimensional spaces. It states that for a high-dimensional Gaussian Distribution, most of the probability mass lies within a thin annulus (or shell) at a certain distance from the origin. This has profound implications for deep learning models like VAEs, which often use Gaussian distributions to model latent spaces. The theorem suggests that the effective volume where latent representations are likely to be found is much smaller than the entire space, impacting how these models encode and decode information.
Also suggests we should expect to find spherical geometry associated with representations learned over a multivariate guassian prior.