关于高表达能力彩票票假设的统一关系视角
A Unifying Relational Perspective on Expressive Lottery Tickets
- Faculty of Computer Science, University of Vienna（维也纳大学计算机科学学院）
- Doctoral School Computer Science, University of Vienna（维也纳大学计算机科学博士学院）
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences（奥地利科学院CeMM分子医学研究中心）
- CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
- School of Electronic Engineering and Computer Science, Queen Mary University of London（伦敦大学玛丽女王学院电子工程与计算机科学学院）
- Research Network Data Science, University of Vienna（维也纳大学数据科学研究网络）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将强表达能力彩票票假设推广至多关系和时序领域，证明参数充足的关系型图神经网络含维持1-RWL表达能力的稀疏子网络，还通过实验验证相关概率下界并分析预训练表达能力与模型性能的关联。
AI中文摘要：
图神经网络（GNN）应用广泛，但参数稀疏性如何影响关系型图神经网络（RGNN）和时序型图神经网络（TGNN）变体的表达能力尚不明确。强表达能力彩票票假设（SELTH）提出，静态图上存在保留Weisfeiler-Leman（WL）表达能力的稀疏GNN。我们通过关系型Weisfeiler-Leman（RWL）将该存在性结果推广到多关系和时序领域的概率表述，证明参数足够的RGNN包含维持1-RWL表达能力的稀疏子网络，并推导随机剪枝得到此类子网络的概率下界。我们表明，常见TGNN和跨图消息传递方案可重构为RGNN，从而继承这些保证，且稀疏RGNN的表达能力与其在常见更新机制下的优化行为相关。实验验证了该下界，将其与合成数据上的经验概率对比，并研究预训练表达能力与时序、分子基准上的优化及预测质量指标的关系。
英文摘要：
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.
