Concretely, we prove that polynomial-sized message-passing algorithms can representthe most powerful polynomial time algorithms for Max Constraint SatisfactionProblems assuming the Unique Games Conjecture. We leverage this result toconstruct efficient graph neural network architectures, OptGNN, that obtain high quality approximate solutions on landmark combinatorial optimization problemssuch as Max-Cut, Min-Vertex-Cover, and Max-3-SAT.

Concretely, we prove that polynomial-sized message-passing algorithms can representthe most powerful polynomial time algorithms for Max Constraint SatisfactionProblems assuming the Unique Games Conjecture. We leverage this result toconstruct efficient graph neural network architectures, OptGNN, that obtain high quality approximate solutions on landmark combinatorial optimization problemssuch as Max-Cut, Min-Vertex-Cover, and Max-3-SAT. Finally, we take advantage of OptGNN'sability to capture convex relaxations to design an algorithm for producing boundson the optimal solution from the learned embeddings of OptGNN.

Recurrent graph convolutional neural networks are highly effective machine learning techniques for spatiotemporal signal processing. Newly proposed graph neural network architectures are repetitively evaluated on standard tasks such as traffic or weather forecasting. In this paper, we propose the Chickenpox Cases in Hungary dataset as a new dataset for comparing graph neural network architectures. Our time series analysis and forecasting experiments demonstrate that the Chickenpox Cases in Hungary dataset is adequate for comparing the predictive performance and forecasting capabilities of novel recurrent graph neural network architectures.

Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto benchmark for a significant body of research. Interestingly, several works have recently shown that graph neural networks do not perform much better than predefined low-pass filters followed by a linear classifier in these particular settings. However, when learning with little data in a high-dimensional space, it is not surprising that simple and heavily regularized learning methods are near-optimal. In this paper, we show empirically that in settings with fewer features and more training data, more complex graph networks significantly outperform simpler architectures, and propose a few insights towards to the proper choice of graph neural networks architectures. We finally outline the importance of using sufficiently diverse benchmarks (including lower dimensional signals as well) when designing and studying new types of graph neural networks.