  Graph neural networks (GNNs) have achieved great success for a variety of
tasks such as node classification, graph classification, and link prediction.
However, the use of GNNs (and machine learning more generally) to solve
combinatorial optimization (CO) problems is much less explored. Here, we
introduce a novel GNN architecture which leverages a complex filter bank and
localized attention mechanisms designed to solve CO problems on graphs. We show
how our method differentiates itself from prior GNN-based CO solvers and how it
can be effectively applied to the maximum clique, minimum dominating set, and
maximum cut problems in a self-supervised learning setting. In addition to
demonstrating competitive overall performance across all tasks, we establish
state-of-the-art results for the max cut problem.
