GRAPH EDIT NETWORKS

Abstract

While graph neural networks have made impressive progress in classification and regression, few approaches to date perform time series prediction on graphs, and those that do are mostly limited to edge changes. We suggest that graph edits are a more natural interface for graph-to-graph learning. In particular, graph edits are general enough to describe any graph-to-graph change, not only edge changes; they are sparse, making them easier to understand for humans and more efficient computationally; and they are local, avoiding the need for pooling layers in graph neural networks. In this paper, we propose a novel output layer -the graph edit network -which takes node embeddings as input and generates a sequence of graph edits that transform the input graph to the output graph. We prove that a mapping between the node sets of two graphs is sufficient to construct training data for a graph edit network and that an optimal mapping yields edit scripts that are almost as short as the graph edit distance between the graphs. We further provide a proof-of-concept empirical evaluation on several graph dynamical systems, which are difficult to learn for baselines from the literature.

1. INTRODUCTION

Recent advances in graph representation learning have mostly focused on tasks of classification or regression, i.e. tasks with graph-structured input but numeric output (Battaglia et al., 2018; Kipf & Welling, 2016a; Veličković et al., 2018) . By contrast, few approaches to date can transform a graph-structured input to a graph-structured output (Hajiramezanali et al., 2019; Paaßen et al., 2018; Zambon et al., 2019) . This lacuna is crucial because time series prediction on graphs requires graphstructured output, namely the next graph in a time series. Applications of time series prediction on graphs include epidemiological models (Keeling & Eames, 2005) , social (Liben-Nowell & Kleinberg, 2007; Masuda & Holme, 2019 ), telecommunications (Nanavati et al., 2006 ), traffic (Cui et al., 2019 ), citation (Shibata et al., 2012) , and financial transaction networks (Chan & Olmsted, 2017), as well as student solutions in intelligent tutoring systems (Paaßen et al., 2018) . In each of these settings, predicting the changes in graphs can deepen the understanding of the domain and provide useful knowledge for designing interventions. Currently, methods for time series prediction on graphs are limited to the dynamics of the node attributes (Yu et al., 2018) , or changes in connectivity (Goyal et al., 2020; Hajiramezanali et al., 2019) , but do not cover changes in the node set. Fortunately, there exists a rich research tradition of edit distances (e.g. Levenshtein, 1965; Zhang & Shasha, 1989; Sanfeliu & Fu, 1983) which can describe any change between two graphs. Further, edits are sparse and have a simple semantic (delete, insert, relabel), which makes them easier to interpret for human observers and makes them computationally

