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Poster
Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?
Yimeng Min · Frederik Wenkel · Michael Perlmutter · Guy Wolf

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #416
We propose a geometric scattering-based graph neural network (GNN) for approximating solutions of the NP-hard maximum clique (MC) problem. We construct a loss function with two terms, one which encourages the network to find highly connected 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 an efficient 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. Furthermore, our scattering model is very parameter efficient with only $\sim$ 0.1\% of the number of parameters compared to previous GNN baseline models.

Author Information

Yimeng Min (Cornell)
Frederik Wenkel (Université de Montréal, Mila)

Frederik Wenkel is a PhD candidate in Applied Mathematics at Université de Montréal and Mila (the Quebec AI institute) working on Geometric Deep Learning. In particular, he is interested in Graph Neural Networks and their applications in domains such as Social Networks, Biochemistry and Finance. He holds a bachelor’s and master’s degree in Mathematics at Technical University of Munich.

Michael Perlmutter (University of California, Los Angeles)
Guy Wolf (Université de Montréal; Mila)

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