Generalized Laplacian Positional Encoding for Graph Representation Learning

Maskey, Sohir; Parviz, Ali; Thiessen, Maximilian; Stärk, Hannes; Sadikaj, Ylli und Maron, Haggai : Generalized Laplacian Positional Encoding for Graph Representation Learning. Login NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representations, New Orleans, Louisiana, United States, 03.02.2022.

Abstract

Graph neural networks (GNNs) are the primary tool for processing graph-structured data. Unfortunately, the most commonly used GNNs, called Message Passing Neural Networks (MPNNs) suffer from several fundamental limitations. To overcome these limitations, recent works have adapted the idea of positional encodings to graph data. This paper draws inspiration from the recent success of Laplacian-based positional encoding and defines a novel family of positional encoding schemes for graphs. We accomplish this by generalizing the optimization problem that defines the Laplace embedding to more general dissimilarity functions rather than the 2-norm used in the original formulation. This family of positional encodings is then instantiated by considering p-norms. We discuss a method for calculating these positional encoding schemes, implement it in PyTorch and demonstrate how the resulting positional encoding captures different properties of the graph. Furthermore, we demonstrate that this novel family of positional encodings can improve the expressive power of MPNNs. Lastly, we present preliminary experimental results.

• Dokumententyp: Konferenzbeitrag (Paper)
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik