f(x) = \text{Re} \left( A \cdot (W x) \cdot e^{i\phi} \right)
16
Where:
- 848-1A: Adjacency matrix
- 848-2W: Learnable weights
- 848-3e^{i\phi}: Quantum phase factor 26
2. **Federated Learning Integration**: 972-1Client nodes compute local updates on their respective subgraphs. 972-2Updates are encrypted using QKD-derived keys before transmission to a central server, which aggregates the encrypted updates securely. 33
3. **Quantum Key Distribution (QKD)**: 1218-1The 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**: 1427-1Encrypted gradients utilize XOR operations: 41
\[
g_{\text{encrypted}} = g \oplus K_{\text{secure}}
43
5. **Secure Aggregation**: 1584-1Gradients are decrypted post-aggregation using the same key: 47
\[
g_{\text{decrypted}} = g_{\text{encrypted}} \oplus K_{\text{secure}}
49
### 🧠 Claims of the Invention
1. **WaveGNN Integration**: 1763-2A novel GNN architecture utilizing quantum phase modulation for wave-inspired graph propagation. 53
2. **QKD Encryption**: 1923-1Application of QKD-derived keys for secure federated learning gradient exchange. 57
3. **Secure Aggregation**: 2031-1Quantum-safe aggregation mechanism ensuring parameter confidentiality. 61
4. **Scalability**: 2133-1Compatibility with decentralized and large-scale federated networks. 65
5. **Inventor**: 2226-1Gazi Pollob Hussain as the sole innovator of this quantum-enhanced federated learning framework. 69
### 🧩 Summary of Innovation
2344-1This architecture introduces a quantum-enhanced federated learning system that secures data exchange through QKD-derived encryption. 2344-2It leverages the WaveGNN for wave-based propagation and quantum-phase modulation to enhance representational power in graph learning tasks. 2344-3The integration of QKD ensures that the system remains impervious to classical and quantum attacks, making it a groundbreaking framework for secure distributed learning. 79
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...
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