For a recently introduced class of autoencoders, we prove that they orient the encoding level sets exactly with respect to the data distribution, and if the latter lies on a lower-dimensional manifold, the extra encoding dimensions carry absolutely no additional information. The former leads to a remarkable performance in cases where the data comes from a physical simulation, where the method can recover the minimum free energy path, while the latter opens up possibilities of testing for manifold dimensionality, for example.
