Joint Edge-Model Sparse Learning is Provably Efficient for Graph Neural Networks

Shuai Zhang, Meng Wang, Pin-Yu Chen, Sijia Liu, Songtao Lu, Miao Liu

Keywords: Learning theory, Graph neural networks, Generalization analysis, Graph sparisification

TL;DR: Encouraged by the empirical success of sparse learners in accelerating GNN training, this paper characterizes the impact of graph sampling and neuron pruning on the sample complexity and convergence rate for a desirable test accuracy quantitatively.

Abstract: Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include graph sparsification that samples a subgraph to reduce the amount of data aggregation and model sparsification that prunes the neural network to reduce the number of trainable weights. Despite the empirical successes in reducing the training cost while maintaining the test accuracy, the theoretical generalization analysis of sparse learning for GNNs remains elusive. To the best of our knowledge, this paper provides the first theoretical characterization of joint edge-model sparse learning from the perspective of sample complexity and convergence rate in achieving zero generalization error. It proves analytically that both sampling important nodes and pruning neurons with lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy. Although the analysis is centered on two-layer GNNs with structural constraints on data, the insights are applicable to more general setups and justified by both synthetic and practical citation datasets.

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