WaveGNN

WaveGNN: A Novel Graph Neural Network Framework WaveGNN: A Novel Graph Neural Network Framework Author: Gazi Pollob Hussain | Date: May 16, 2025 Abstract Graph Neural Networks (GNNs) have gained significant attention for their ability to learn from graph-structured data. In this paper, we propose WaveGNN , a novel framework inspired by wave propagation principles, which effectively captures hierarchical and multi-scale information in graphs. This document provides a detailed overview of the model architecture, methodology, and mathematical formulations. Introduction Graphs are ubiquitous in various domains such as social networks, molecular biology, and transportation systems. Traditional GNNs often suffer from limitations in capturing long-range dependencies and hierarchical structures. For instance, many existing models struggle with oversmoothi...

f(x) = \text{Re} \left( A \cdot (W x) \cdot e^{i\phi} \right) 16 Where: - 848-1A: Adjacency matrix - 848-2W: Learnable weights - 848-3e^{i\phi}: Quantum phase factor 26 2. **Federated Learning Integration**: 972-1Client nodes compute local updates on their respective subgraphs. 972-2Updates are encrypted using QKD-derived keys before transmission to a central server, which aggregates the encrypted updates securely. 33 3. **Quantum Key Distribution (QKD)**: 1218-1The BB84 protocol generates symmetric encryption keys between client and server, ensuring key confidentiality based on quantum mechanics and preventing interception. 37 4. **Quantum-Safe Gradient Encryption**: 1427-1Encrypted gradients utilize XOR operations: 41 \[ g_{\text{encrypted}} = g \oplus K_{\text{secure}} 43 5. **Secure Aggregation**: 1584-1Gradients are decrypted post-aggregation using the same key: 47 \[ g_{\text{decrypted}} = g_{\text{...