Better Mixing via Deep Representations

It has been hypothesized, and supported with experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related conjecture: better representations, in the sense of better disentangling, can be exploited to produce Markov chains that mix faster between modes. Consequently, mixing between modes would be more efficient at higher levels of representation. To better understand this, we propose a secondary conjecture: the higher-level samples fill more uniformly the space they occupy and the high-density manifolds tend to unfold when represented at higher levels. The paper discusses these hypotheses and tests them experimentally through visualization and measurements of mixing between modes and interpolating between samples.