Introduction to Graph Neural Networks
Chapter 1: Foundations of Graph-Based Learning
What is Graph Data?
Limitations of Standard Neural Networks on Graphs
Common Graph Machine Learning Tasks
Representing Graphs: Adjacency and Feature Matrices
Graph Properties and Measurements
Introduction to the NetworkX Library
Hands-on: Loading and Inspecting a Graph Dataset
Chapter 2: The Message Passing Mechanism
The Neighborhood Aggregation Idea
A General GNN Layer: Aggregate and Update
Common Aggregation Functions
Update Functions and Non-Linearities
Permutation Invariance and Equivariance
Stacking Layers to Form a Deep GNN
Practice: A Simple GNN Layer with NumPy
Chapter 3: Foundational GNN Architectures
Graph Convolutional Networks (GCN)
A Spatial Interpretation of Graph Convolutions
GraphSAGE: Sampling and Aggregating Neighborhoods
Inductive Learning with GraphSAGE
Graph Attention Networks (GAT)
The Attention Mechanism in GATs
Comparing GCN, GraphSAGE, and GAT
Hands-on: Implementing a GCN from Scratch
Chapter 4: Training GNN Models
Setting up a GNN for Node Classification
Loss Functions for Graph Tasks
The Training Loop for GNNs
Data Splitting in Graphs: Transductive vs. Inductive
Evaluation Metrics for Node Classification
Overfitting and Regularization in GNNs
Practice: Training and Evaluating your GCN
Chapter 5: GNN Implementation with PyTorch Geometric
Introduction to PyTorch Geometric (PyG)
The PyG Data Object
Working with PyG Datasets
Building Models with PyG GNN Layers
Mini-Batching for Large Graphs
A Complete Training Script in PyG
Hands-on: Node Classification on the Cora Dataset with PyG
Permutation Invariance and Equivariance
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- Neural Message Passing for Quantum Chemistry, Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, George E. Dahl, 2017 Proceedings of the 34th International Conference on Machine Learning (ICML), Vol. Volume 70 (Proceedings of Machine Learning Research (PMLR)) DOI: 10.5555/3305891.3305943 - This paper introduces the Neural Message Passing framework, formalizing how GNNs aggregate information and implicitly achieving permutation invariance and equivariance.
- Geometric Deep Learning: Grids, Graphs, Groups, Geodesics, and Gauges, Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković, 2021 (Cambridge University Press) - This foundational book provides a unified mathematical framework for deep learning on geometric data, offering a rigorous treatment of symmetry, invariance, and equivariance as fundamental principles for GNNs.
- Graph Representation Learning, William L. Hamilton, 2020 Synthesis Lectures on Artificial Intelligence and Machine Learning, Vol. 14 (Morgan & Claypool Publishers) DOI: 10.2200/S00996ED1V01Y202002AIM003 - This textbook provides a comprehensive introduction to graph representation learning, including a detailed explanation of message passing and its permutation invariance and equivariance properties.
- Semi-Supervised Classification with Graph Convolutional Networks, Thomas N. Kipf and Max Welling, 2017 International Conference on Learning Representations (ICLR) DOI: 10.48550/arXiv.1609.02907 - This seminal paper introduced Graph Convolutional Networks (GCNs), a widely adopted GNN model that exemplifies the message passing paradigm and its inherent permutation invariance and equivariance.