Heat Flow Leaves Two-Hidden-Unit Restricted Boltzmann Models

Independent bit-flip heat flow preserves binary restricted Boltzmann machines with one hidden unit, by their classical representation as mixtures of two product distributions. We give explicit evolving parameters. With two hidden units and at least four visible units, the behavior is different: for every fixed positive vector of flip rates, a generic positive parameter leaves even the algebraic closure of the model immediately. A sixteen-by-sixteen integer Jacobian determinant proves transversality in the four-visible case. A coordinate-permutation argument covers arbitrary positive rates, and conditioning extends the obstruction to every larger visible dimension. The proof distinguishes a rank witness from a pointwise smoothness certificate. For the logarithmic-mean graph transport metric, this yields a generically nonzero residual in projected entropy flow. This is a complete scoped finite-state theorem, not a solution of the broad AIM question about PDE approximation. The preprint is unrefereed and makes no absolute priority claim.