differential geometry · learning on graphs · deep learning · applied mathematics
Graph Neural Networks on Pseudo-Riemannian Manifolds
My bachelor’s thesis connects differential geometry and graph neural networks, studying how non-Euclidean representations change what a network learns, from foundations to advanced concepts.
- Role
- Author of the entire bachelor's thesis
- Period
- September 2023 - June 2024
- Status
- shipped
- Visibility
- public repository
Numbers
- 9.9/10Score given by the panelacademic record
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Why change the geometry?
A graph neural network learns node representations from features and connections. The geometry of the representation space shapes the relationships it can express. My bachelor’s thesis studied these networks on pseudo-Riemannian manifolds.
From mathematics to training
The work covers indefinite metrics, geodesics and pseudo-hyperboloids. Geodesic completeness and geodesic connectedness are different properties in this setting. Exponential and logarithmic maps connect the manifold and tangent space to implement the network’s operations.
My contribution
I studied the foundations, adapted the reference implementation, examined geometric operations and optimisation methods, and ran experimental comparisons with GCN and GAT. This includes training, hyperparameter search and analysis of learned representations. QGCN is the original architecture. My contribution is its study, adapted implementation and evaluation.