Can Graph Neural Networks Count Substructures?

Chen, Zhengdao; Chen, Lei; Villar, Soledad; Bruna, Joan

doi:10.48550/arxiv.2002.04025

Cited by 23 publications

(52 citation statements)

References 41 publications

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“…Recently, there have been several research attempts [39]- [41] basis. These methods focus on counting of isomorphic subgraphs or producing approximate matching results, which are different from the target in this paper, i.e., generating matching orders to find exact subgraph mappings.…”

Section: Related Workmentioning

confidence: 99%

Reinforcement Learning Based Query Vertex Ordering Model for Subgraph Matching

Wang¹,

Zhang²,

Lu³

et al. 2022

Preprint

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Subgraph matching is a fundamental problem in various fields that use graph structured data. Subgraph matching algorithms enumerate all isomorphic embeddings of a query graph q in a data graph G. An important branch of matching algorithms exploit the backtracking search approach which recursively extends intermediate results following a matching order of query vertices. It has been shown that the matching order plays a critical role in time efficiency of these backtracking based subgraph matching algorithms. In recent years, many advanced techniques for query vertex ordering (i.e., matching order generation) have been proposed to reduce the unpromising intermediate results according to the preset heuristic rules. In this paper, for the first time we apply the Reinforcement Learning (RL) and Graph Neural Networks (GNNs) techniques to generate the high-quality matching order for subgraph matching algorithms. Instead of using the fixed heuristics to generate the matching order, our model could capture and make full use of the graph information, and thus determine the query vertex order with the adaptive learning-based rule that could significantly reduces the number of redundant enumerations. With the help of the reinforcement learning framework, our model is able to consider the long-term benefits rather than only consider the local information at current ordering step. Extensive experiments on six real-life data graphs demonstrate that our proposed matching order generation technique could reduce up to two orders of magnitude of query processing time compared to the state-ofthe-art algorithms.

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Section: Related Workmentioning

confidence: 99%

Reinforcement Learning Based Query Vertex Ordering Model for Subgraph Matching

Wang¹,

Zhang²,

Lu³

et al. 2022

Preprint

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show abstract

“…They make predictions by learning graph representations via the message-passing mechanism, where the representation h u of each node u ∈ V is updated by aggregating messages from its neighbors, denoted as N (u). The message passing is iteratively applied to all nodes in V, so each node can collect messages from its multi-hop neighbors and produce structure-aware representations (Chen et al, 2020). Given h…”

Section: Graph Neural Networkmentioning

confidence: 99%

“…Then, they are aggregated together with v({0}) following Equation 7to form v * τ ({0}). For graph data, the surplus allocation approach has two advantages over the all-possiblecoalition aggregation used in the Shapley value: (1): the aggregated payoff in each v * τ is structure-aware like the representations learned by GNNs (Chen et al, 2020), and…”

Section: Connecting Gnns and Hn Surplus Allocation Through The Messag...mentioning

confidence: 99%

“…In light of these considerations, we propose a new Graph Structure-aware eXplanation (GStarX) method, where we construct a structure-aware node importance scoring function based on the HN value (Hamiache & Navarro, 2020) from cooperative games with communication structures. Recall that GNNs make predictions via a message passing mechanism, during which node features are updated via collecting messages from their neighbors; and message passing helps aggregate both node feature information and graph structure information, resulting in powerful and structure-aware models for graph-level predictions (Chen et al, 2020). The HN value shares a similar idea of message passing by collecting surplus payoffs generated from collaboration between neighboring players, i.e., nodes on graphs (details in Section 5.1).…”

Section: Introductionmentioning

confidence: 99%

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Explaining Graph Neural Networks with Structure-Aware Cooperative Games

Zhang¹,

Liu²,

Shah³

et al. 2022

Preprint

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Explaining predictions made by machine learning models is important and have attracted an increased interest. The Shapley value from cooperative game theory has been proposed as a prime approach to compute feature importances towards predictions, especially for images, text, tabular data, and recently graph neural networks (GNNs) on graphs. In this work, we revisit the appropriateness of the Shapley value for graph explanation, where the task is to identify the most important subgraph and constituent nodes for graph-level predictions. We purport that the Shapley value is a no-ideal choice for graph data because it is by definition not structure-aware. We propose a Graph Structure-aware eXplanation (GStarX) method to leverage the critical graph structure information to improve the explanation. Specifically, we propose a scoring function based on a new structure-aware value from the cooperative game theory called the HN value. When used to score node importance, the HN value utilizes graph structures to attribute cooperation surplus between neighbor nodes, resembling message passing in GNNs, so that node importance scores reflect not only the node feature importance, but also the structural roles. We demonstrate that GstarX produces qualitatively more intuitive explanations, and quantitatively improves over strong baselines on chemical graph property prediction and text graph sentiment classification.

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“…For example, [34,49] show that the capability of distinguishing different graphs of MPGNNs is upper-bounded by the 1-Weisfeiler-Lehman Isomorphism Test (1-WL Test), which is known unable to distinguish many common substructures (examples in [39]). In addition, [2,9] show that MPGNNs are unable to count or detect substructures with 3 or more nodes. Both theoretical results uncover crucial limitations of MPGNNs, as graph substructures are widely recognized as indicative in various complex networks.…”

Section: Introductionmentioning

confidence: 99%

Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels

Long

Jin

et al. 2021

Proceedings of the Web Conference 2021

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Graph neural networks (GNNs) have achieved tremendous success in graph mining. However, the inability of GNNs to model substructures in graphs remains a significant drawback. Specifically, message-passing GNNs (MPGNNs), as the prevailing type of GNNs, have been theoretically shown unable to distinguish, detect or count many graph substructures. While efforts have been paid to complement the inability, existing works either rely on pre-defined substructure sets, thus being less flexible, or are lacking in theoretical insights. In this paper, we propose GSKN 1 , a GNN model with a theoretically stronger ability to distinguish graph structures. Specifically, we design GSKN based on anonymous walks (AWs), flexible substructure units, and derive it upon feature mappings of graph kernels (GKs). We theoretically show that GSKN provably extends the 1-WL test, and hence the maximally powerful MPGNNs from both graph-level and node-level viewpoints. Correspondingly, various experiments are leveraged to evaluate GSKN, where GSKN outperforms a wide range of baselines, endorsing the analysis. CCS CONCEPTS• Networks → Network structure; • Information systems → Collaborative and social computing systems and tools.

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Can Graph Neural Networks Count Substructures?

Cited by 23 publications

References 41 publications

Reinforcement Learning Based Query Vertex Ordering Model for Subgraph Matching

Reinforcement Learning Based Query Vertex Ordering Model for Subgraph Matching

Explaining Graph Neural Networks with Structure-Aware Cooperative Games

Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels

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