Computation nodes

The addition and multiplication nodes are used for summing and multiplying variables. These standard mathematical operations are typically used to construct linear mappings between the variables. This task is automated in the software, but in general, the nodes can be connected in other ways, too. An addition node that has $n$ inputs denoted by $s_1,s_2,\ldots,s_n$, gives the sum of its inputs as the output $\sum_{i=1}^n s_i$. Similarly, the output of a multiplication node is the product of its inputs $\prod_{i=1}^n s_i$.

A nonlinear computation node can be used for constructing nonlinear mappings between the variable nodes. The nonlinearity

$$f(s) = \exp(-s^2)$$ (9)

is chosen because the required expectations can be solved analytically for it. Another implemented nonlinearity for which the computations can be carried out analytically is the cut function $g(s)=\max(s,0)$. Other possible nonlinearities are discussed in Section 4.3.