Then, for a given path θ in A of size k: The last equation is because N (0) is the weight accumulated in all paths in the WFA, W A (Θ A (0, |Q| − 1, •)) (as we will see below), and W A (θ) is defined in a way similar to Equation (6).
note that, in Hernando, Crespi, and Cybenko (2005), Mann and McCallum (2007), and Ilic (2011), the computation of Equation (2) is studied, whereas in this article the computation of Equation (3) is studied, as in Grenander (1967).