Weisfeiler-Lehman goes Dynamic: An Analysis of the Expressive Power of Graph Neural Networks for Attributed and Dynamic Graphs

• URL: http://arxiv.org/abs/2210.03990v2
• Date: Fri, 3 May 2024 15:44:52 GMT
• Title: Weisfeiler-Lehman goes Dynamic: An Analysis of the Expressive Power of Graph Neural Networks for Attributed and Dynamic Graphs
• Authors: Silvia Beddar-Wiesing, Giuseppe Alessio D'Inverno, Caterina Graziani, Veronica Lachi, Alice Moallemy-Oureh, Franco Scarselli, Josephine Maria Thomas,
• Abstract summary: Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent studies on the expressive power of GNNs have focused on their ability to distinguish graphs. Real-life applications often involve a much larger variety of graph types.
• Score: 1.3757956340051607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.

Related papers

• Generalization Limits of Graph Neural Networks in Identity Effects Learning [12.302336258860116]
  Graph Neural Networks (GNNs) have emerged as a powerful tool for data-driven learning on various graph domains. We establish new generalization properties and fundamental limits of GNNs in the context of learning so-called identity effects. Our study is motivated by the need to understand the capabilities of GNNs when performing simple cognitive tasks.
  arXiv  Detail & Related papers  (2023-06-30T20:56:38Z)
• Equivariant Polynomials for Graph Neural Networks [38.15983687193912]
  Graph Networks (GNN) are inherently limited in their expressive power. This paper introduces an alternative power hierarchy based on the ability of GNNs to calculate equivariants of certain degree. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks.
  arXiv  Detail & Related papers  (2023-02-22T18:53:38Z)
• Two-Dimensional Weisfeiler-Lehman Graph Neural Networks for Link Prediction [61.01337335214126]
  Link prediction is one important application of graph neural networks (GNNs) Most existing GNNs for link prediction are based on one-dimensional Weisfeiler-Lehman (1-WL) test. We study a completely different approach which can directly obtain node pair (link) representations based on textittwo-dimensional Weisfeiler-Lehman (2-WL) tests.
  arXiv  Detail & Related papers  (2022-06-20T04:50:38Z)
• Representation Power of Graph Neural Networks: Improved Expressivity via Algebraic Analysis [124.97061497512804]
  We show that standard Graph Neural Networks (GNNs) produce more discriminative representations than the Weisfeiler-Lehman (WL) algorithm. We also show that simple convolutional architectures with white inputs, produce equivariant features that count the closed paths in the graph.
  arXiv  Detail & Related papers  (2022-05-19T18:40:25Z)
• Graph Neural Networks for Graphs with Heterophily: A Survey [98.45621222357397]
  We provide a comprehensive review of graph neural networks (GNNs) for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models. We discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs.
  arXiv  Detail & Related papers  (2022-02-14T23:07:47Z)
• On the approximation capability of GNNs in node classification/regression tasks [4.141514895639094]
  Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. We show that GNNs are universal approximators in probability for node classification/regression tasks.
  arXiv  Detail & Related papers  (2021-06-16T17:46:51Z)
• The Surprising Power of Graph Neural Networks with Random Node Initialization [54.4101931234922]
  Graph neural networks (GNNs) are effective models for representation learning on relational data. Standard GNNs are limited in their expressive power, as they cannot distinguish beyond the capability of the Weisfeiler-Leman graph isomorphism. In this work, we analyze the expressive power of GNNs with random node (RNI) We prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
  arXiv  Detail & Related papers  (2020-10-02T19:53:05Z)
• Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learning [63.97983530843762]
  Graph Neural Networks (GNNs) have achieved great success in graph representation learning. GNNs generate identical representations for graph substructures that may in fact be very different. More powerful GNNs, proposed recently by mimicking higher-order tests, are inefficient as they cannot sparsity of underlying graph structure. We propose Distance Depiction (DE) as a new class of graph representation learning.
  arXiv  Detail & Related papers  (2020-08-31T23:15:40Z)
• Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting [63.04999833264299]
  "Graph Substructure Networks" (GSN) is a topologically-aware message passing scheme based on substructure encoding. We show that it is strictly more expressive than the Weisfeiler-Leman (WL) graph isomorphism test. We perform an extensive evaluation on graph classification and regression tasks and obtain state-of-the-art results in diverse real-world settings.
  arXiv  Detail & Related papers  (2020-06-16T15:30:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.