1. Representational Capacity

Is $RBM_{4,3}$ a universal approximator?
Problem 1.1.
[Guido Montufar] Does the closure of $RBM_{4,3}$ fill the simplex $\Delta_{15},$ making it a universal approximator? 
Determine the maximum divergence of $RBM_{3,1}.$
Problem 1.2.
[org.aimpl.user:tmerkh@g.ucla.edu] Determine the maximum divergence of $RBM_{3,1}.$ 
What kind of distributions can be represented by an RBM as opposed to directed models?
Problem 1.3.
What kind of distributions can be represented by an RBM as opposed to directed models? 
Characterize the limiting set of distributions for $\lim_{n\to\infty} RBM_{n,n}.$
Problem 1.4.
[Jason Morton] Consider the limit as $n \to \infty$ for $RBM_{n,n}.$ It was suggested that this limiting set of distributions can be seen as a set of measures on the unit interval. Do all possible measures belong to this set? If not, which ones do?
Cite this as: AimPL: Boltzmann Machines, available at http://aimpl.org/boltzmann.