derivation of Eqs . 3 and 5

A.1 Derivation of Eq. (3) By expanding Eq. (2) with the definition of εli,t = xli,t µli,t, we have: Et = We note that each xli,t influences Et in two ways: (i) it occurs in Eq. (6) explicitly, but (ii) it also determines the values of µl 1k,t via Eq. Considering also the special cases of l = Land l = 0, we obtain Eq. (3). We note that θl+1i,j affects the value of the function Et of Eq. (6) by influencing µli,t via Eq. Here, we provide further details about training PCNs, useful to reproduce them. Furthermore, we have applied a decay factor of 0.9 to γ, applied each time the energy failed to decrease.