# Constant Time Graph Neural Networks

## TL;DR

This paper introduces a novel constant-time node sampling method for GNNs that guarantees approximation accuracy independently of graph size, enabling scalable analysis of large graphs.

## Contribution

It provides the first theoretical guarantee of approximation error for GNNs using constant-time node sampling, independent of graph size.

## Key findings

- Node sampling complexity depends only on error tolerance and confidence, not graph size.
- Experimental validation confirms speed and accuracy of the proposed method.
- The approach scales efficiently to large real-world graphs.

## 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 networks and Web graphs, remains a challenge. In particular, the existing methods for accelerating GNNs either are not theoretically guaranteed in terms of the approximation error or incur at least a linear time computation cost. In this study, we reveal the query complexity of the uniform node sampling scheme for Message Passing Neural Networks, including GraphSAGE, graph attention networks (GATs), and graph convolutional networks (GCNs). Surprisingly, our analysis reveals that the complexity of the node sampling method is completely independent of the number of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability while providing a theoretical guarantee for the approximation error. To the best of our knowledge, this is the first paper to provide a theoretical guarantee of approximation for GNNs within constant time. Through experiments with synthetic and real-world datasets, we investigated the speed and precision of the node sampling scheme and validated our theoretical results.