Algebraic Geometry of the Restricted Boltzmann Machine

The restricted Boltzmann machine was the original building block of deep learning models.  An implicit description of the set of probability distributions it can represent is very difficult, and is unknown even in the smallest nontrivial case.  However there are aspects of the RBM's algebraic geometry which are accessible.  We discuss a series of four papers on the geometry of RBMs leading to, among other things, a proof that the RBM always has the expected dimension: in other words, it doesn't waste parameters.