Deep learning long-range information in undirected graphs with wave networks

TL;DR

This paper introduces the wave network architecture, which efficiently propagates long-range information in undirected graphs, outperforming local aggregation methods like graph convolution on various complex tasks.

Contribution

The paper presents the wave network, a novel architecture capable of propagating information across long distances in undirected graphs, demonstrated through multiple challenging tasks.

Findings

Wave learns three graph-based tasks more efficiently and accurately.

Wave can extrapolate from small training data to larger test cases.

Wave outperforms graph convolution in long-range information propagation.

Abstract

Graph algorithms are key tools in many fields of science and technology. Some of these algorithms depend on propagating information between distant nodes in a graph. Recently, there have been a number of deep learning architectures proposed to learn on undirected graphs. However, most of these architectures aggregate information in the local neighborhood of a node, and therefore they may not be capable of efficiently propagating long-range information. To solve this problem we examine a recently proposed architecture, wave, which propagates information back and forth across an undirected graph in waves of nonlinear computation. We compare wave to graph convolution, an architecture based on local aggregation, and find that wave learns three different graph-based tasks with greater efficiency and accuracy. These three tasks include (1) labeling a path connecting two nodes in a graph, (2) solving a maze presented as an image, and (3) computing voltages in a circuit. These tasks range from trivial to very difficult, but wave can extrapolate from small training examples to much larger testing examples. These results show that wave may be able to efficiently solve a wide range of problems that require long-range information propagation across undirected graphs. An implementation of the wave network, and example code for the maze problem are included in the tflon deep learning toolkit (https://bitbucket.org/mkmatlock/tflon).