CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

This is the official implementation of CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection accepted at ICML 2025.

📖 Abstract

Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on structural and attribute-level anomalies. To this end, we propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies.

CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability:

1. Curvature-equivariant geometry reconstruction: Focuses exclusively on reconstructing the edge curvatures using a mixed-curvature, Riemannian encoder and Gaussian kernel-based decoder
2. Curvature-invariant structure and attribute reconstruction: Decouples structural and attribute anomalies from geometric irregularities by regularizing graph curvature under discrete Ollivier-Ricci flow

By leveraging curvature, CurvGAD refines the existing anomaly classifications and identifies new curvature-driven anomalies. Extensive experimentation over 10 real-world datasets (both homophilic and heterophilic) demonstrates an improvement of up to 6.5% over state-of-the-art GAD methods.

🏗️ Repository Structure

curvgad-codebase/
├── preprocessing/              # Curvature computation modules
│   ├── compute_curvature.py   # Main curvature computation script
│   ├── ollivier_ricci_flow.py # Ollivier-Ricci flow implementation
│   └── preprocess_external_datasets.py # Dataset preprocessing
├── models/                     # Model implementations
│   ├── curvgad_detector.py    # Main CurvGAD detector
│   ├── curvgad_gnn.py         # CurvGAD GNN architecture
│   ├── detector.py            # Base detector classes
│   ├── gnn.py                 # GNN implementations
│   ├── attention.py           # Attention mechanisms
│   ├── manifold_cheb_conv.py  # Manifold Chebyshev convolution
│   └── mobius_linear.py       # Möbius linear transformations
├── datasets/                   # Dataset storage
├── curvature_data/            # Precomputed curvature matrices
├── results/                   # Experimental results
├── plots/                     # Generated plots and visualizations
├── runs/                      # Training logs and outputs
├── benchmark.py               # Main benchmarking script
├── utils.py                   # Utility functions
├── job.sh                     # SLURM job submission script
├── requirements.txt           # Python dependencies
└── README.md                  # This file

🚀 Installation

Prerequisites

• Python 3.8+
• CUDA-compatible GPU (recommended)

Setup Environment

1. Clone the repository:

git clone https://github.com/your-username/curvgad-codebase.git
cd curvgad-codebase

2. Create a virtual environment:

python -m venv curvgad_env
source curvgad_env/bin/activate  # On Windows: curvgad_env\Scripts\activate

3. Install dependencies:

pip install -r requirements.txt

Key Dependencies

• PyTorch: Deep learning framework
• DGL: Deep Graph Library for graph neural networks
• PyTorch Geometric: Graph neural network library
• Geoopt: Riemannian optimization library
• GraphRicciCurvature: Ricci curvature computation
• PyGOD: Graph outlier detection library

📊 Datasets

The repository supports multiple graph datasets including:

• Citation Networks: Cora, CiteSeer, PubMed
• Social Networks: Actor, Chameleon, Squirrel
• Web Networks: Texas, Cornell, Wisconsin
• Fraud Detection: Amazon, Yelp, Reddit
• Financial Networks: TFinance, Elliptic

Datasets are automatically downloaded and preprocessed when first used.

🔧 Usage

Step 1: Precompute Curvature

Before running the main model, you need to compute the Ollivier-Ricci curvature for your datasets:

cd preprocessing
python compute_curvature.py --datasets cora citeseer pubmed --use_accelerated --save_matrix

Arguments:

• --datasets: List of datasets to compute curvature for
• --use_accelerated: Use fast approximation method (recommended for large graphs)
• --compare_both: Compare exact vs. accelerated methods
• --save_matrix: Save curvature matrices for later use

Step 2: Run CurvGAD

Execute the main benchmarking script:

python benchmark.py --models CurvGAD --datasets cora --trials 10 --use_autoencoder --manifold_config H32S32E32 --optimizer riemannian_adam --lr 0.01 --K 7

Key Arguments:

• --models: Model to use (CurvGAD or baseline methods)
• --datasets: Datasets to evaluate on
• --trials: Number of experimental trials
• --use_autoencoder: Enable autoencoder with curvature reconstruction
• --manifold_config: Manifold configuration (e.g., H32S32E32 for 32-dim hyperbolic, spherical, and Euclidean)
• --optimizer: Optimizer type (adam or riemannian_adam)
• --lr: Learning rate
• --K: Number of Chebyshev polynomial filters

Step 3: Analyze Results

Results are automatically saved in the results/ directory as Excel files. You can analyze the performance metrics including:

• AUC-ROC scores
• Average Precision (AP)
• Training time
• Memory usage

📝 Citation

If you use this code in your research, please cite our paper:

@misc{grover2025curvgadleveragingcurvatureenhanced,
      title={CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection}, 
      author={Karish Grover and Geoffrey J. Gordon and Christos Faloutsos},
      year={2025},
      eprint={2502.08605},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2502.08605}, 
}

🤝 Contributing

We welcome contributions! Please follow these steps:

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📞 Contact

For questions or issues, please:

• Open an issue on GitHub
• Contact: karish@cs.cmu.edu

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