Deeper Exploiting Graph Structure Information by Discrete Ricci Curvature in a Graph Transformer

Area of Science:

• Graph Neural Networks
• Geometric Deep Learning
• Topological Data Analysis

Background:

• Graph-structured data is ubiquitous, yet fully exploiting its inherent structure remains challenging.
• Existing methods for graph representation learning may not capture all relevant topological information.
• Novel geometric descriptors are needed to enhance the expressiveness of graph models.

Purpose of the Study:

• To introduce a novel graph transformer model, Curvphormer, that incorporates geometric information.
• To leverage discrete Ricci curvature (DRC) as a descriptor for uncovering deeper graph structure.
• To improve the performance of graph neural networks on complex graph-level tasks.

Main Methods:

• Developed Curvphormer, a topology-aware graph transformer.
• Integrated discrete Ricci curvature (DRC) as a key feature for quantifying graph connections.
• Conducted extensive experiments on large-scale datasets (PCQM4M-LSC, ZINC, MolHIV).

Main Results:

• Achieved significant performance gains on various graph-level and fine-tuned tasks.
• Demonstrated the effectiveness of DRC in capturing essential graph structure information.
• Showcased Curvphormer's ability to extract inherent community structures in homogeneous graphs.

Conclusions:

• Curvphormer, utilizing discrete Ricci curvature, enhances graph representation learning.
• The integration of geometric descriptors offers a promising direction for future graph neural network research.
• This approach provides a more illuminating way to quantify graph connections and extract structural information.