Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting (2006.09252v3)

Abstract: While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the expressive power of standard GNNs is bounded by the Weisfeiler-Leman (WL) graph isomorphism test, from which they inherit proven limitations such as the inability to detect and count graph substructures. On the other hand, there is significant empirical evidence, e.g. in network science and bioinformatics, that substructures are often intimately related to downstream tasks. To this end, we propose "Graph Substructure Networks" (GSN), a topologically-aware message passing scheme based on substructure encoding. We theoretically analyse the expressive power of our architecture, showing that it is strictly more expressive than the WL test, and provide sufficient conditions for universality. Importantly, we do not attempt to adhere to the WL hierarchy; this allows us to retain multiple attractive properties of standard GNNs such as locality and linear network complexity, while being able to disambiguate even hard instances of graph isomorphism. We perform an extensive experimental evaluation on graph classification and regression tasks and obtain state-of-the-art results in diverse real-world settings including molecular graphs and social networks. The code is publicly available at https://github.com/gbouritsas/graph-substructure-networks.

• The paper presents a novel GNN architecture that encodes subgraph isomorphism counts to overcome limitations of the Weisfeiler-Leman test.
• It provides theoretical proofs and empirical evaluations demonstrating superior performance in graph classification and regression tasks.
• The method retains key GNN features such as locality and efficiency, offering practical benefits in fields like molecular chemistry and social network analysis.

Enhancing Graph Neural Network Capabilities Through Subgraph Isomorphism Counting

Graph Neural Networks (GNNs) have demonstrated substantial success in handling data with inherent graph structures across numerous scientific and engineering domains. Despite this success, prevailing concerns have arisen regarding their ability to robustly capture graph structures. Specifically, standard GNNs are commonly constrained by the Weisfeiler-Leman (WL) test, which limits their capability to differentiate graph substructures—a critical factor in various real-world applications.

This paper presents the Graph Substructure Networks (GSNs), a novel GNN architecture aimed at transcending the expressivity limitations imposed by the WL isomorphism test. The authors introduce a mechanism to encode structural information via substructure isomorphism counts, thereby enhancing the expressivity of GNNs. Crucially, GSNs maintain essential GNN features including locality and computational efficiency, setting them apart from GNN approaches that extend WL hierarchically to increase expressiveness.

The effectiveness of GSNs is backed by theoretical analysis and comprehensive empirical evaluations. Theoretically, the paper demonstrates that GSNs are strictly more expressive than the WL test, capable of distinguishing graph isomorphism in instances where standard GNNs fail. The authors articulate the sufficient conditions under which GSNs achieve universality in graph representation tasks. Notably, this universality is achievable without the strict adherence to the WL hierarchy which can impair computational efficiency.

Experimental results further solidify the promise of the proposed architecture, evidenced by state-of-the-art performance across various benchmarks, including graph classification and regression challenges. The exemplary performance is particularly noted in domains such as molecular chemistry and social networks, where the significance of subgraph structure is well-recognized. The practical usability of GSN is highlighted by its efficient implementation, where structural role encodings are integrated into the message-passing architecture without overheads typically associated with higher-order methods.

This research posits critical implications both in the theoretical understanding and practical applications of GNNs. By enhancing the expressivity via subgraph isomorphisms, complex tasks and network structures that were not easily tackled by standard GNNs become more approachable. In application domains such as drug discovery or social network analysis, where local structure holds substantial importance, GSN presents a robust tool for more precise and informative representations.

Looking ahead, the insights gained from this paper open new avenues for research into GNN architectures that strategically leverage subgraph information. It invites exploration of adaptive substructure selection, potentially leading to more generalized frameworks across diverse domains. Furthermore, speculations on unresolved theoretical questions such as the graph Reconstruction Conjecture may unveil deeper intersections between graph theory and neural network design.

The advent of GSNs continues to enrich the toolkit available to researchers and practitioners, powerfully extending the applicability of neural architectures to a broader range of structured data problems. In doing so, it marks a significant step towards more nuanced and capable network representations, bridging current gaps in expressivity and utility.