Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices

1 code implementation • 24 Jun 2023 • Wei Zhao, Federico Lopez, J. Maxwell Riestenberg, Michael Strube, Diaaeldin Taha, Steve Trettel

The uniform geometry of Euclidean and hyperbolic spaces allows for representing graphs with uniform geometric and topological features, such as grids and hierarchies, with minimal distortion.

Graph Classification

Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices

1 code implementation • NeurIPS 2021 • Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

We propose the use of the vector-valued distance to compute distances and extract geometric information from the manifold of symmetric positive definite matrices (SPD), and develop gyrovector calculus, constructing analogs of vector space operations in this curved space.

Knowledge Graph Completion Question Answering

Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach

2 code implementations • 9 Jun 2021 • Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets.

Graph Reconstruction Node Classification +3

Hermitian Symmetric Spaces for Graph Embeddings

1 code implementation • 11 May 2021 • Federico López, Beatrice Pozzetti, Steve Trettel, Anna Wienhard

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications.