- The paper identifies key theoretical gaps between practical GNN implementations and current combinatorial methods, emphasizing limitations in expressivity and generalization.
- The paper proposes developing fine-grained expressivity measures and robust generalization bounds to better align theory with complex real-world graph applications.
- The paper advocates for unified benchmarking platforms and practical tools that integrate theoretical insights with practical implementation in graph learning.
Introduction
The advent of machine learning on graph-structured data has seen the popularization of Graph Neural Networks (GNNs), especially Message-Passing Neural Networks (MPNNs), which have been subjected to extensive studies. Their applicability spans various fields, including social sciences, bioinformatics, and engineering, dealing with inherently graph-structured information. Despite the practical successes achieved by GNNs, a gap exists in the theoretical understanding of their foundations, leading to a misalignment between theory and practice.
Expressivity of GNNs
One of the central themes in the analysis of GNNs is their expressiveness, which relates to the capability of these networks to capture and distinguish between different graph structures. Morris et al. have shown that the separation power of MPNNs is constrained to that of the 1-dimensional Weisfeiler-Lehman (1-WL) graph isomorphism heuristic. Attempts to surpass these limitations have led to the development of architectures with greater expressiveness, often at a higher computational cost. Existing studies, however, heavily rely on combinatorial techniques and present a binary perspective, often insufficient to characterize the subtleties in graph similarities essential for complex real-world applications.
Generalization and Optimization in GNNs
While expressiveness is critical, it's equally important to understand the generalization capabilities of GNNs – their ability to perform well on unseen data. Current theoretical frameworks utilize principles such as VC dimension, resulting in bounds that can be too loose to provide practical insight. These analyses typically fail to accommodate complex characteristics of graph structures. Additionally, the optimization process through which GNNs learn, primarily stochastic gradient descent (SGD), has been understudied and simplified in existing literature, using assumptions like linear activation functions, which do not hold in practical scenarios.
Bridging Theory and Practice
The paper emphasizes the need for a balanced theory of graph machine learning, incorporating insights from wide-ranging architectural choices to training dataset characteristics. This refined theory should also consider practical implementation choices actively used in various application domains. Steps toward achieving this include the development of unified platforms for benchmarking, evaluation, and implementing state-of-the-art theoretically-principled GNN architectures.
Future Directions and Conclusion
The authors advocate for concerted efforts to address the lacunae in our theoretical understanding of GNNs, such as developing fine-grained expressivity measures, constructing robust generalization bounds, and providing a sound theoretical foundation for optimization strategies in the context of graph-learning tasks. Moreover, it is crucial to refine theory with the considerations from real-world application domains and provide efficient, accessible tools for practitioners. By tackling these challenges, the graph machine learning community can achieve a more comprehensive understanding of GNNs, contributing to the development of more effective graph-based learning systems.