Towards the Universal Learning Principle for Graph Neural Networks

Abstract

Graph neural networks (GNNs) are currently highly regarded in graph representation learning tasks due to their significant performance. Although various propagation mechanisms and graph filters were proposed, few works have considered the convergence and stability of graph filters under infinite-depth scenarios. To address this problem, we elucidate the criterion for the graph filter formed by power series and further establish a scalable regularized learning principle, which can guide us on how to design infinite deep GNN. Following the framework, we develop Adaptive Power GNN (APGNN), a deep GNN that employs exponentially decaying weights to aggregate graph information of different orders so as to mine the deeper neighbor information. Different from existing GNNs, APGNN can be seamlessly extended to an infinite-depth network. Moreover, we analyze the generalization of the proposed learning framework via uniform convergence and present its upper bound in theory. Experimental results show that APGNN obtains superior performance against the state-of-the-art GNNs.