March 27 – 30 , 2022, Dagstuhl Seminar 22132

Graph Embeddings: Theory meets Practice


Martin Grohe (RWTH Aachen University, DE)
Stephan Günnemann (TU München, DE)
Stefanie Jegelka (MIT – Cambridge, US)
Christopher Morris (McGill University & MILA – Montreal)

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Graph-structured data is ubiquitous across application domains ranging from chemo- and bioinformatics to image and social network analysis. To develop successful machine learning algorithms or apply standard data analysis tools in these domains, we need techniques that map the rich information inherent in the graph structure to a vectorial representation in a meaningful way—so-called graph embeddings. Designing such embeddings comes with unique challenges. The embedding has to account for the complex structure of (real-world) networks and additional high-dimensional continuous vectors attached to nodes and edges in a (permutation) invariant way while being scalable to massive graphs or sets of graphs. Moreover, when used in supervised machine learning, the model trained with such embeddings must generalize well to new or previously unseen (graph) instances. Hence, more abstractly, designing graph embeddings results in a trade-off between expressivity, scalability, and generalization.

Starting from the 1960s in chemoinformatics, different research communities have worked in the area under various guises, often leading to recurring ideas. Moreover, triggered by the resurgence of (deep) neural networks, there is an on-going trend in the machine learning community to design invariant/equivariant neural architectures that are capable of dealing with graph- and relational input, both (semi-)supervised and unsupervised, often denoted as graph neural networks.

Although successful in practical settings, most of these developments are driven by intuition and empiricism and are geared towards specific application areas. There is no clear understanding of these approaches' limitations and their trade-offs in complexity, expressivity, and generalization. Researchers recently started to leverage connections to graph theory, group theory, logic, combinatorial algorithms, and (algorithmic) learning theory, leading to new theoretical insights and triggering new research in applications. Hence, we aim to bring together leading applied and theoretical researchers in graph embeddings and adjacent areas, such as graph isomorphism, bio- and chemoinformatics, graph theory, to facilitate an increased exchange of ideas between these communities. Concretely, we aim to understand what hinders recent theoretical developments being applied in application areas and work towards a more practical theory. Further, we aim at understanding the overarching challenges across applications and challenges inherent to specific areas to stimulate directions for further practical and theoretical research.

Motivation text license
  Creative Commons BY 4.0
  Christopher Morris


  • Discrete Mathematics
  • Machine Learning
  • Neural And Evolutionary Computing


  • Machine learning for graphs
  • Graph embedding


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