Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems
Abstract
Deep learning has consistently defied stateoftheart 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 NPComplete 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 DOI:
 10.48550/arXiv.1903.04598
 arXiv:
 arXiv:1903.04598
 Bibcode:
 2019arXiv190304598L
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Logic in Computer Science;
 Computer Science  Neural and Evolutionary Computing;
 Statistics  Machine Learning
 EPrint:
 Under submission