STRUCTURAL LANDMARKING AND INTERACTION MODELLING: ON RESOLUTION DILEMMAS IN GRAPH CLASSIFICATION

Abstract

Graph neural networks are promising architecture for learning and inference with graph-structured data. However, generating informative graph level features has long been a challenge. Current practice of graph-pooling typically summarizes a graph by squeezing it into a single vector. However, from complex systems point of view, properties of a complex system are believed to arise largely from the interaction among its components. In this paper, we analyze the intrinsic difficulty in graph classification under the unified concept of "resolution dilemmas" and propose "SLIM", an inductive neural network model for Structural Landmarking and Interaction Modelling, to remedy the information loss in graph pooling. We show that, by projecting graphs onto end-to-end optimizable, and well-aligned substructure landmarks (representatives), the resolution dilemmas can be resolved effectively, so that explicit interacting relation between component parts of a graph can be leveraged directly in explaining its complexity and predicting its property. Empirical evaluations, in comparison with state-of-the-art, demonstrate promising results of our approach on a number of benchmark datasets for graph classification.

1. INTRODUCTION

Complex systems are ubiquitous in natural and scientific disciplines, and how the relation between component parts gives rise to global behaviour of a system is a central research topic in many areas such as system biology (Camacho et al., 2018 ), neural science (Kriegeskorte, 2015) , and drug and material discoveries (Stokes et al., 2020; Schmidt et al., 2019) . Recently, graph neural networks provide a promising architecture for representation learning on graphs -the structural abstraction of a complex system. State-of-the-art performances are observed in various graph mining tasks (Bronstein et al., 2017; Defferrard et al., 2016; Hamilton et al., 2017; Xu et al., 2019; Velickovic et al., 2017; Morris et al., 2019; Wu et al., 2020; Zhou et al., 2018; Zhang et al., 2020) . However, due to the non-Euclidean nature, important challenges still exist in graph classification. For example, in order to generate a fixed-dimensional representation for a graph of arbitrary size, graph pooling is typically adopted to summarize the information from each each node. In the pooled form, the whole graph is squeezed into a "super-node", in which the identities of the constituent sub-graphs and their interconnections are mixed together. Is this the best way to generate graph-level features? From a complex system's view, mixing all parts together might make it difficult for interpreting the prediction results, because properties of a complex system arise largely from the interactions among its components (Hartwell et al., 1999; Debarsy et al., 2017; Cilliers, 1998) . The choice of the "collapsing"-style graph pooling roots deeply in the lack of natural alignment among graphs that are not isomorphic. Therefore pooling sacrifices structural details for feature (dimension) compatibility. Recent years, substructure patterns 1 draw considerable attention in graph mining, such as motifs (Milo et al., 2002; Alon, 2007; Wernicke, 2006; Austin R. Benson, 2016) and graphlets (Shervashidze et al., 2009) . It provides an intermediate scale for structure comparison or counting, and has been applied to node embedding (Lee et al., 2019; Ahmed et al., 2018) , deep graph kernels (Yanardag & Vishwanathan, 2015) and graph convolution (Yang et al., 2018) . However, due to combinatorial nature, only substructures of very small size (4 or 5 nodes) can be considered (Yanardag 1 Informally, substructure in this paper means a connected subgraph and will be used interchargeably with it. 1

