2. Algebraic Statistics and Tensor Characterizations

Can we characterize tensors of nonnegative rank at most 3 using the description of $RBM_{3,2}?$
Problem 2.1.
[org.aimpl.user:tmerkh@g.ucla.edu] Is it possible to use the implicit description of $RBM_{3,2}$ to determine the characterizing properties of nonnegative rank $\leq 3$ tensors?
Could this recent finding be used to determine a nonnegative rank 3 generalization of the supermodularity and flattening rank constraints known for nonnegative rank $\leq 2$ tensors? $$ $$ See $$ $$ Seigal, Anna, and Guido Montufar. "Mixtures and products in two graphical models." arXiv preprint arXiv:1709.05276 (2017).$$ $$ and $$ $$ Allman, Elizabeth S., et al. "Tensors of nonnegative rank two." Linear algebra and its applications 473 (2015): 3753. 
What are the algebraic structures relevant for studying learning algorithms for RBMs?
Problem 2.2.
[Anna Seigal] What are the algebraic structures relevant for studying learning algorithms for RBMs?
Cite this as: AimPL: Boltzmann Machines, available at http://aimpl.org/boltzmann.