Constant Time Graph Neural Networks
Authors: Ryoma Sato, Makoto Yamada, Hisashi Kashima
Keywords: graph neural networks, constant time algorithm
TL;DR: We propose an approximation algorithm of GNNs that works in constant time with respect to the input size.
Abstract: The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs such as social network graphs and web graphs still remains a challenge. In particular, the existing methods for accelerating GNNs are either not theoretically guaranteed in terms of approximation error, or they require at least a linear time computation cost. 
In this study, we analyze the neighbor sampling technique to obtain a constant time approximation algorithm for GraphSAGE, the graph attention networks (GAT), and the graph convolutional networks (GCN). The proposed approximation algorithm can theoretically guarantee the precision of approximation. The key advantage of the proposed approximation algorithm is that the complexity is completely independent of the numbers of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability. To the best of our knowledge, this is the first constant time approximation algorithm for GNNs with a theoretical guarantee. Through experiments using synthetic and real-world datasets, we demonstrate the speed and precision of the proposed approximation algorithm and validate our theoretical results.