  Existing Bayesian treatments of neural networks are typically characterized
by weak prior and approximate posterior distributions according to which all
the weights are drawn independently. Here, we consider a richer prior
distribution in which units in the network are represented by latent variables,
and the weights between units are drawn conditionally on the values of the
collection of those variables. This allows rich correlations between related
weights, and can be seen as realizing a function prior with a Bayesian
complexity regularizer ensuring simple solutions. We illustrate the resulting
meta-representations and representations, elucidating the power of this prior.
