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Current graph neural networks (GNNs) lack generalizability with respect toscales (graph sizes, graph diameters, edge weights, etc..) when solving manygraph analysis problems. Taking the perspective of synthesizing graph theoryprograms, we propose several extensions to address the issue. First, inspiredby the dependency of the iteration number of common graph theory algorithms ongraph size, we learn to terminate the message passing process in GNNsadaptively according to the computation progress. Second, inspired by the factthat many graph theory algorithms are homogeneous with respect to graphweights, we introduce homogeneous transformation layers that are universalhomogeneous function approximators, to convert ordinary GNNs to be homogeneous.Experimentally, we show that our GNN can be trained from small-scale graphs butgeneralize well to large-scale graphs for a number of basic graph theoryproblems. It also shows generalizability for applications of multi-bodyphysical simulation and image-based navigation problems.

Towards Scale-Invariant Graph-related Problem Solving by Iterative Homogeneous Graph Neural Networks