Can Hybrid Geometric Scattering Networks Help Solve the Maximal Clique Problem?

We propose a geometric scattering-based graph neural network (GNN) for approximating solutions of the NP-hard maximal clique (MC) problem. We construct a loss function with two terms, one which encourages the network to find a large set of nodes and the other which acts as a surrogate for the constraint that the nodes form a clique. We then use this loss to train a novel GNN architecture that outputs a vector representing the probability for each node to be part of the MC and apply a rule-based decoder to make our final prediction. The incorporation of the scattering transform alleviates the so-called oversmoothing problem that is often encountered in GNNs and would degrade the performance of our proposed setup. Our empirical results demonstrate that our method outperforms representative GNN baselines in terms of solution accuracy and inference speed as well as conventional solvers like GUROBI with limited time budgets.