  Deep learning has consistently defied state-of-the-art techniques in many
fields over the last decade. However, we are just beginning to understand the
capabilities of neural learning in symbolic domains. Deep learning
architectures that employ parameter sharing over graphs can produce models
which can be trained on complex properties of relational data. These include
highly relevant NP-Complete problems, such as SAT and TSP. In this work, we
showcase how Graph Neural Networks (GNN) can be engineered -- with a very
simple architecture -- to solve the fundamental combinatorial problem of graph
colouring. Our results show that the model, which achieves high accuracy upon
training on random instances, is able to generalise to graph distributions
different from those seen at training time. Further, it performs better than
the Neurosat, Tabucol and greedy baselines for some distributions. In addition,
we show how vertex embeddings can be clustered in multidimensional spaces to
yield constructive solutions even though our model is only trained as a binary
classifier. In summary, our results contribute to shorten the gap in our
understanding of the algorithms learned by GNNs, as well as hoarding empirical
evidence for their capability on hard combinatorial problems. Our results thus
contribute to the standing challenge of integrating robust learning and
symbolic reasoning in Deep Learning systems.
