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

10/26/2020
by   Hao Tang, et al.
0

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.

READ FULL TEXT

page 7

page 29

10/02/2022

Gradient Gating for Deep Multi-Rate Learning on Graphs

We present Gradient Gating (G^2), a novel framework for improving the pe...
01/31/2022

GSN: A Universal Graph Neural Network Inspired by Spring Network

The design of universal Graph Neural Networks (GNNs) that operate on bot...
09/30/2022

MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initialization

Training graph neural networks (GNNs) on large graphs is complex and ext...
12/14/2020

A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks

In this paper, we derive generalization bounds for the two primary class...
07/06/2021

Non-Homogeneity Estimation and Universal Kriging on the Sphere

Kriging is a widely recognized method for making spatial predictions. On...
03/02/2020

Benchmarking Graph Neural Networks

Graph neural networks (GNNs) have become the standard toolkit for analyz...
09/08/2018

Learning to Solve NP-Complete Problems - A Graph Neural Network for the Decision TSP

Graph Neural Networks (GNN) are a promising technique for bridging diffe...