DATA-DRIVEN LEARNING OF GEOMETRIC SCATTERING MODULES FOR GNNS.

Area of Science:

• Graph Neural Networks
• Geometric Scattering Transforms
• Machine Learning

Background:

• Graph neural networks (GNNs) often struggle to capture long-range dependencies in graph data.
• Existing GNNs commonly rely on local neighborhood information (smoothness, similarity), limiting their relational learning capabilities.
• Geometric scattering transforms offer a promising framework for feature extraction on graphs.

Purpose of the Study:

• To introduce a new GNN module, Learnable Geometric Scattering (LEGS), designed to improve the learning of long-range graph relations.
• To enable adaptive tuning of graph wavelets for enhanced feature representation.
• To develop simplified GNN architectures with reduced parameter counts.

Main Methods:

• Proposed a novel GNN module based on relaxations of geometric scattering transforms.
• Developed the Learnable Geometric Scattering (LEGS) module for adaptive wavelet tuning.
• Integrated the LEGS module into GNN architectures for enhanced graph relation learning.

Main Results:

• LEGS-based GNNs demonstrated improved learning of longer-range graph relations compared to popular GNNs.
• The wavelet priors in LEGS led to simplified architectures with significantly fewer learned parameters.
• Achieved strong predictive performance on graph classification benchmarks.

Conclusions:

• The LEGS module effectively enhances GNNs' ability to learn complex graph structures and long-range dependencies.
• LEGS offers a more parameter-efficient and simplified approach to GNN design.
• The learned features from LEGS-based networks show high descriptive quality for biochemical data exploration.