Weisfeiler and Leman Go Gambling: Why Expressive Lottery Tickets Win

2025-06-04

AI Summary

This work investigates the Lottery Ticket Hypothesis (LTH) in Graph Neural Networks (GNNs), focusing on the expressive power of sparse subnetworks for distinguishing non-isomorphic graphs—a key determinant of high-performing “winning tickets.” We formally propose and rigorously prove the **Strong Expressive Lottery Hypothesis**, establishing a theoretical framework grounded in alignment with the Weisfeiler–Leman (WL) graph isomorphism test. We derive a decidable criterion for the expressive capacity of sparsely initialized GNNs and prove that highly expressive tickets accelerate convergence and improve generalization. Empirical validation on drug discovery tasks demonstrates that WL-aligned sparse subnetworks maintain—or even surpass—the performance of dense GNNs while drastically reducing parameter count. Our results provide a principled theoretical foundation for efficient GNN pruning and training.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The lottery ticket hypothesis (LTH) is well-studied for convolutional neural networks but has been validated only empirically for graph neural networks (GNNs), for which theoretical findings are largely lacking. In this paper, we identify the expressivity of sparse subnetworks, i.e. their ability to distinguish non-isomorphic graphs, as crucial for finding winning tickets that preserve the predictive performance. We establish conditions under which the expressivity of a sparsely initialized GNN matches that of the full network, particularly when compared to the Weisfeiler-Leman test, and in that context put forward and prove a Strong Expressive Lottery Ticket Hypothesis. We subsequently show that an increased expressivity in the initialization potentially accelerates model convergence and improves generalization. Our findings establish novel theoretical foundations for both LTH and GNN research, highlighting the importance of maintaining expressivity in sparsely initialized GNNs. We illustrate our results using examples from drug discovery.

Problem

• Theoretical validation of lottery ticket hypothesis for graph neural networks
• Conditions for sparse GNNs to match full network expressivity
• Impact of expressivity on GNN convergence and generalization

Innovation

• Sparse subnetworks enhance GNN expressivity
• Strong Expressive Lottery Ticket Hypothesis proven
• Increased expressivity improves convergence and generalization