TRANSFER LEARNING OF GRAPH NEURAL NETWORKS WITH EGO-GRAPH INFORMATION MAXIMIZATION

Abstract

Graph neural networks (GNNs) have been shown with superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards the transferability of GNNs. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of EGI (ego-graph information maximization) to analytically achieve this goal. Secondly, we specify the requirement of structurerespecting node features as the GNN input, and conduct a rigorous analysis of GNN transferability based on the difference between the local graph Laplacians of the source and target graphs. Finally, we conduct controlled synthetic experiments to directly justify our theoretical conclusions. Extensive experiments on realworld networks towards role identification show consistent results in the rigorously analyzed setting of direct-transfering (freezing parameters), while those towards large-scale relation prediction show promising results in the more generalized and practical setting of transfering with fine-tuning.

1. INTRODUCTION

Graph neural networks (GNNs) have been intensively studied recently (Kipf & Welling, 2017; Keriven & Peyré, 2019; Chen et al., 2019; Oono & Suzuki, 2020; Huang et al., 2018) , due to their established performance towards various real-world tasks (Hamilton et al., 2017; Ying et al., 2018b; Velickovic et al., 2018) , as well as close connections to spectral graph theory (Defferrard et al., 2016; Bruna et al., 2014; Hammond et al., 2011) . While most GNN architectures are not very complicated, the training of GNNs can still be costly regarding both memory and computation resources on real-world large-scale graphs (Chen et al., 2018; Ying et al., 2018a) . Moreover, it is intriguing to transfer learned structural information across different graphs and even domains in settings like few-shot learning (Vinyals et al., 2016; Finn et al., 2017; Ravi & Larochelle, 2017) . Therefore, several very recent studies have been conducted on the transferability of GNNs, which focus on the setting of pre-training plus fine-tuning (Hu et al., 2019a (Hu et al., ,b, 2020;; Wu et al., 2020) . However, it is unclear in what situations the models will excel or fail especially when the pre-training and fine-tuning tasks are different. To provide rigorous analysis and guarantee on the transferability of GNNs, we focus on the setting of direct-transfering between the source and target graphs, under an analogous setting of "domain adaptation" (Ben-David et al., 2007) . In this work, we establish a theoretically grounded framework for the transfer learning of GNNs, and leverage it to design a practically transferable GNN model. Figure 1 gives an overview of our framework. It is based on a novel view of a graph as samples from the joint distribution of its k-hop ego-graph structures and node features, which allows us to define graph information and similarity, so as to analyze GNN transferability ( §2). This view motivates us to design EGI, a novel GNN model based on ego-graph information maximization, which is effective in capturing the graph information as we define ( §2.1). Then we further specify the requirement on transferable node features and analyze the transferability of EGI that is dependent on the local graph Laplacians of source and target graphs ( §2.2).

