Here, we begin by depicting the key idea of the recurrent design technique for reaction networks following the example shown in Figure . Note that for any reaction network, the final product at the root node has two reactants in its parent nodes. We consider that at each step of SMC, denoted by t, only the two reactants of the final product are explored. In the forward cascade model Y = h • g(S|G), only the single-step reaction S 1 + S 2 → P is considered as G, and the two reactants {S 1 , S 2 } are selected from the original set B of commercial compounds and an additional set I t-1 containing all intermediate products computationally synthesized until step t -1. Let B t = B ∪ I t-1 be the expanded set of candidate reactants and let x t = {S 1 , S 2 } be the auxiliary variable at t. Then, the auxiliary distribution π t (x t ) is defined as