Easing the Injectivity Bottleneck on Lorentzian Manifolds for GNNs(Original title LGIN)

Official code of our paper accpted at ACM SIGMOD 2025 GRADES NDA Workshop. The preprint can be found here.

Click here to go to the workshop page.

Description

While graph neural networks (GNNs) operating in hyperbolic spaces have shown promise for modeling hierarchical and complex relational data, a critical limitation often overlooked is their potentially limited discriminative power compared to their Euclidean counterparts or fundamental graph isomorphism tests like the Weisfeiler-Lehman (WL) hierarchy. Ex- isting hyperbolic aggregation schemes, while curvature-aware, may not sufficiently capture the intricate structural differences required to robustly distinguish non-isomorphic graphs owing to non-injective aggregation functions. To address this expressiveness gap in hyper- bolic graph learning, we introduce the Lorentzian Graph Isomorphic Network (LGIN), a novel GNN designed to achieve enhanced discriminative capabilities within the Lorentzian model of hyperbolic space. LGIN proposes a new update rule that effectively combines local neighborhood information with a richer representation of graph structure designed to preserve the Lorentzian metric tensor. A key theoretical contribution is demonstrating that LGIN possesses discriminative power at least approximately equivalent to the 1-dimensional Weisfeiler-Lehman test. This represents a significant step towards building more expressive GNNs in non-Euclidean geometries, overcoming a common bottleneck in current hyperbolic methods. We conduct extensive evaluations across nine diverse benchmark datasets, in- cluding molecular and protein structures. LGIN consistently outperforms or matches state- of-the-art hyperbolic and Euclidean GNNs, showcasing its practical efficacy and validating its superior ability to capture complex graph structures and distinguish between different graphs. To the best of our knowledge, LGIN is the first work to successfully adapt the core principles behind powerful, highly-discriminative GNN architectures to a Riemannian manifold

Running the Scripts

• Create a Python(preferrably >3.10) virtual environment and activate it. Run the following command

pip install -r requirements.txt

• Create a .env file and set the values of all environment variables.
• Add dataset root directory paths in the .env file.
• Model configurations such as epsilon value, curvature, dropout, batch size etc can be edited in model_config.py.
• For training on graph classification, run train.py and run train_regression.py for regression.

Datasets

Mutag
Proteins
PTC
NCI1
Reddit
IMDB
DD
Enzymes
HIV
BBBP
BACE
Zinc
AQSOL

Main Dependencies

torch
python-dotenv
torch-geometric
torchmetrics
scikit-learn
numpy
scipy
python-dotenv
matplotlib
wandb
os

Bugs/Queries

If there are any bugs, you may raise an issue. If there are any technical questions regarding the project, you may email me at smudge0110@icloud.com. Contributions are welcome : )