  Given enough data, Deep Neural Networks (DNNs) are capable of learning
complex input-output relations with high accuracy. In several domains, however,
data is scarce or expensive to retrieve, while a substantial amount of expert
knowledge is available. It seems reasonable that if we can inject this
additional information in the DNN, we could ease the learning process. One such
case is that of Constraint Problems, for which declarative approaches exists
and pure ML solutions have obtained mixed success. Using a classical
constrained problem as a case study, we perform controlled experiments to probe
the impact of progressively adding domain and empirical knowledge in the DNN.
Our results are very encouraging, showing that (at least in our setup)
embedding domain knowledge at training time can have a considerable effect and
that a small amount of empirical knowledge is sufficient to obtain practically
useful results.
