These sums represent the total alignment score for the surrounding source words, similar to fertility in a traditional latent variable model, which is the sum over binary alignment random variables.
it is well established for latent variable translation models that the alignments improve if p(s|t) is also modelled and the inferences of both directional models are combined -evidenced by the symmetrisation heuristics used in most decoders , and also by explicit joint agreement training objectives (Liang et al., 2006;Ganchev et al., 2008).