Addition and multiplication nodes

Equations (20)-(24) for the addition and multiplication nodes are proven in the following section. Only the Equation (20) applies in general, the others assume that the incoming signals are independent a posteriori. That is, $q(s_1,s_2,\dots,s_n)=q(s_1)q(s_2)\dots q(s_n)$. Also the proof of the form of the cost function mostly concerns propagation through addition and multiplication nodes, so it is presented here. Finally, the formulas of propagating the gradients of the cost function w.r.t. the expectations are derived.