Towards Scale-Invariant Graph-related Problem Solving by Iterative Homogeneous Graph Neural Networks
This addresses the problem of scale invariance in GNNs for researchers and practitioners in graph machine learning, offering incremental improvements to enhance generalizability.
The paper tackles the lack of scale generalizability in graph neural networks (GNNs) for graph analysis problems by proposing adaptive termination of message passing and homogeneous transformation layers, resulting in GNNs trained on small-scale graphs that generalize well to large-scale graphs for basic graph theory problems and applications like multi-body simulation and image-based navigation.
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs, we propose several extensions to address the issue. First, inspired by the dependency of the iteration number of common graph theory algorithms on graph size, we learn to terminate the message passing process in GNNs adaptively according to the computation progress. Second, inspired by the fact that many graph theory algorithms are homogeneous with respect to graph weights, we introduce homogeneous transformation layers that are universal homogeneous function approximators, to convert ordinary GNNs to be homogeneous. Experimentally, we show that our GNN can be trained from small-scale graphs but generalize well to large-scale graphs for a number of basic graph theory problems. It also shows generalizability for applications of multi-body physical simulation and image-based navigation problems.