Laplacian Canonization

Laplacian canonization aims to create consistent and robust representations of graph data by addressing ambiguities in spectral embeddings, a common technique in graph neural networks (GNNs). Current research focuses on developing efficient algorithms, such as Maximal Axis Projection (MAP), to achieve sign and basis invariance in spectral embeddings, improving the performance of GNNs on various tasks. These advancements enhance the applicability of GNNs across diverse domains, including chemistry, material science, and computer vision, by improving the reliability and interpretability of graph-based models. Furthermore, extensions of Laplacian-based methods are being explored for higher-order graph structures and applications beyond traditional graph analysis, such as image processing and reinforcement learning.