4. Tropical RBMs

Is it true that tropical RBMs always have expected dimension?
Problem 4.1.
Is it true that tropical RBMs always have expected dimension, meaning equal to the number of parameters within the model or the dimension of the ambient probability simplex? 
What tropical objects characterize all tropical RBMs?
Problem 4.2.
What tropical objects (varieties) characterize all tropical RBMs?
Cite this as: AimPL: Boltzmann Machines, available at http://aimpl.org/boltzmann.