Since the binary-binary energy model is linear in the parameters ai, bj and wij, it is easy to see that the derivatives with respect to the various optimization parameters yield expressions used in the evaluation of gradients like
∂E(x,h;Θ)∂wij=−xihj,and
∂E(x,h;Θ)∂ai=−xi,and
∂E(x,h;Θ)∂bj=−hj.