  In this paper, it is shown that an auto-encoder using optimal reconstruction
significantly outperforms a conventional auto-encoder. Optimal reconstruction
uses the conditional mean of the input given the features, under a maximum
entropy prior distribution. The optimal reconstruction network, which is called
deterministic projected belied network (D-PBN), resembles a standard
reconstruction network, but with special non-linearities that mist be
iteratively solved. The method, which can be seen as a generalization of
maximum entropy image reconstruction, extends to multiple layers. In
experiments, mean square reconstruction error reduced by up to a factor of two.
The performance improvement diminishes for deeper networks, or for input data
with unconstrained values (Gaussian assumption).
