Advanced Graph Neural Networks: Architectures and Implementation
Chapter 1: Revisiting Graph Neural Network Foundations
Graph Representations for Machine Learning
The Message Passing Framework Revisited
Spectral Graph Theory Fundamentals for GNNs
Graph Signal Processing Concepts
Expressive Power and the WL Test
Chapter 2: Advanced Graph Neural Network Architectures
Graph Convolutional Networks (GCN)
Graph Attention Networks (GAT)
Implementing Multi-Head Attention in GATs
Graph Transformers
Advanced Spectral GNNs (ChebNet, CayleyNets)
Advanced Spatial GNNs (GraphSAGE Variants, PNA)
Comparing Architectural Choices and Trade-offs
Hands-on Practical: Implementing GAT Layers
Chapter 3: Addressing Training Complexities in GNNs
The Oversmoothing Problem
Techniques to Mitigate Oversmoothing
The Oversquashing Problem
Handling Large Graphs: Scalability Challenges
Neighborhood Sampling Techniques (GraphSAGE)
Graph Sampling Techniques (GraphSAINT, ShaDow-GNN)
Subgraph and Clustering Methods (Cluster-GCN)
Optimization Strategies for GNNs
Practice: Applying Scalable GNN Training
Chapter 4: Advanced GNN Tasks and Techniques
Handling Heterogeneous Graphs (RGCN, HAN)
Modeling Dynamic and Temporal Graphs
Knowledge Graph Embeddings with GNNs
Graph Generative Models
Self-Supervised Learning on Graphs
Graph Pooling and Readout Functions
Hands-on Practical: Heterogeneous Graph Node Classification
Chapter 5: GNN Implementation, Tooling, and Optimization
Deep Graph Library (DGL) Advanced Features
PyTorch Geometric (PyG) Advanced Features
Efficient Sparse Matrix Operations for GNNs
GPU Acceleration and Memory Management
Debugging and Visualizing GNNs
Benchmarking and Performance Tuning
Integrating GNNs into Production Systems
Hands-on Practical: Optimizing a GNN Implementation
Spectral Graph Theory Fundamentals for GNNs
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- Spectral Graph Theory, Fan R. K. Chung, 1997 (American Mathematical Society) - This seminal textbook establishes the mathematical foundations of spectral graph theory, providing essential background on the Graph Laplacian and its eigen-decomposition.
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains, David I. Shuman, S. K. Narang, Pascal Frossard, Antonio Ortega, Pierre Vandergheynst, 2012 IEEE Signal Processing Magazine, Vol. 30 (IEEE) DOI: 10.1109/MSP.2012.2235192 - This influential review article introduces Graph Signal Processing, formally defining the Graph Fourier Transform and spectral graph convolutions.
- A Comprehensive Survey on Graph Neural Networks, Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and S. Yu Philip, 2020 IEEE Transactions on Neural Networks and Learning Systems, Vol. 32 (IEEE) DOI: 10.1109/TNNLS.2020.2978070 - A comprehensive survey that reviews various Graph Neural Network architectures, including a dedicated discussion on spectral-based GNNs and their evolution.