A Unifying Relational Perspective on Expressive Lottery Tickets

2026-08-19

AI Summary

研究通过关系视角探讨了稀疏参数对图神经网络变体表达能力的影响，证明了存在保持1-关系WL表达能力的稀疏子网络，并给出了概率下界。

Abstract

Graph neural networks (GNNs) are widely used, but how parameter sparsity affects the expressivity of relational (RGNNs) and temporal (TGNNs) variants is poorly understood. The Strong Expressive Lottery Ticket Hypothesis (SELTH) posits the existence of sparse GNNs that preserve Weisfeiler-Leman (WL) expressivity on static graphs. We generalize this existence result to a probabilistic statement for multi-relational and temporal domains via the relational WL (RWL). We prove that sufficiently parameterized RGNNs contain sparse subnetworks that maintain 1-RWL expressivity and derive a lower bound on the probability that a random pruning yields such a subnetwork. We show that common TGNNs and cross-graph message passing schemes admit RGNN reformulations such that they inherit these guarantees and, moreover, that the expressivity of a sparse RGNN is connected to its optimization behavior under common update regimes. Experiments instantiate the bound, compare it to empirical probabilities on synthetic data, and study how pre-training expressivity relates to optimization and prediction quality metrics on temporal and molecular benchmarks.

Problem

• parameter sparsity
• expressivity
• relational GNNs
• temporal GNNs
• Weisfeiler-Leman

Innovation

• Relational Weisfeiler-Leman
• Sparse Subnetworks
• Expressivity
• Temporal Graph Neural Networks
• Graph Neural Networks