Our inference algorithm passes information from the branches inwards to the trunk, and then upward along the trunk, in time O(K 4 MN).
a fully connected lattice model has tree-width = min(M, N), making inference and learning intractable (Sutton, McCallum, and Rohanimanesh 2007), partly because of the difficulty in enumerating and summing over the exponentially-many configurations y for a given x.