Anticipating results to be derived

Since the binary-binary energy model is linear in the parameters $a_i$, $b_j$ and $w_{ij}$, it is easy to see that the derivatives with respect to the various optimization parameters yield expressions used in the evaluation of gradients like

$$\frac{\partial E(\boldsymbol{x}, \boldsymbol{h};\boldsymbol{\Theta})}{\partial w_{ij}}=-x_ih_j,$$

and

$$\frac{\partial E(\boldsymbol{x}, \boldsymbol{h};\boldsymbol{\Theta})}{\partial a_i}=-x_i,$$

and

$$\frac{\partial E(\boldsymbol{x}, \boldsymbol{h};\boldsymbol{\Theta})}{\partial b_j}=-h_j.$$

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