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Expressive Power and Approximation Errors of Restricted Boltzmann Machines
Guido F Montufar · Johannes Rauh · Nihat Ay

Wed Dec 14 08:45 AM -- 02:59 PM (PST) @

We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model with n visible and m hidden units is bounded from above by (n-1)-log(m+1). In this way we can specify the number of hidden units that guarantees a sufficiently rich model containing different classes of distributions and respecting a given error tolerance.

Author Information

Guido F Montufar (UCLA)
Johannes Rauh (MPI for Mathematics in the Sciences)
Nihat Ay (MPI for Mathematics in the Sciences)

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