And the gradient
\begin{align*}
G_i = \frac{\partial \langle E_L \rangle}{\partial \alpha_i}
= 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \alpha_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \alpha_i} \rangle ),
\end{align*}
where \alpha_i = a_1,...,a_M,b_1,...,b_N,w_{11},...,w_{MN} .