Graph Neural Networks

  1. Foundational GNN Architectures
    1. Spectral-based Methods
      1. Graph Signal Processing
        1. Graph Signals Definition
          1. Signal Processing on Graphs
            1. Filtering Operations
            2. Spectral Graph Theory
              1. Graph Fourier Transform
                1. Frequency Domain Analysis
                  1. Spectral Filtering
                  2. Spectral Convolution Networks
                    1. Spectral CNN
                      1. Convolution in Spectral Domain
                        1. Computational Complexity
                        2. ChebNet
                          1. Chebyshev Polynomial Approximation
                            1. Localized Filters
                              1. K-hop Neighborhoods
                            2. Limitations of Spectral Approaches
                              1. Graph Structure Dependency
                                1. Computational Overhead
                                  1. Non-inductive Nature
                                    1. Fixed Graph Size Requirements
                                  2. Spatial-based Methods
                                    1. Graph Convolutional Networks (GCN)
                                      1. Motivation from Spectral Methods
                                        1. First-order Approximation
                                          1. Symmetric Normalization
                                            1. Layer-wise Propagation Rule
                                              1. Renormalization Trick
                                                1. Multi-layer Architecture
                                                  1. Limitations and Challenges
                                                  2. GraphSAGE
                                                    1. Inductive Learning Paradigm
                                                      1. Neighborhood Sampling Strategy
                                                        1. Fixed-size Sampling
                                                          1. Uniform Random Sampling
                                                            1. Importance Sampling
                                                            2. Aggregator Functions
                                                              1. Mean Aggregator
                                                                1. LSTM Aggregator
                                                                  1. Pooling Aggregator
                                                                    1. GCN Aggregator
                                                                    2. Feature Concatenation
                                                                      1. Unsupervised Training
                                                                      2. Graph Attention Networks (GAT)
                                                                        1. Attention Mechanism Fundamentals
                                                                          1. Self-attention on Graphs
                                                                            1. Attention Coefficient Computation
                                                                              1. Additive Attention
                                                                                1. Dot-product Attention
                                                                                2. Multi-head Attention
                                                                                  1. Parallel Attention Heads
                                                                                    1. Head Concatenation vs Averaging
                                                                                    2. Masked Attention
                                                                                      1. Residual Connections
                                                                                      2. Graph Isomorphism Networks (GIN)
                                                                                        1. Theoretical Motivation
                                                                                          1. Weisfeiler-Leman Test Connection
                                                                                            1. Injective Aggregation Functions
                                                                                              1. MLP as Universal Approximator
                                                                                                1. Epsilon Parameter Learning
                                                                                                  1. Theoretical Guarantees
                                                                                                2. Specialized Architectures
                                                                                                  1. Message Passing Neural Networks (MPNN)
                                                                                                    1. General Framework
                                                                                                      1. Customizable Message Functions
                                                                                                        1. Edge Feature Integration
                                                                                                          1. Flexible Aggregation
                                                                                                          2. Gated Graph Neural Networks (GGNN)
                                                                                                            1. Gated Recurrent Units for Graphs
                                                                                                              1. Sequential Processing
                                                                                                                1. Memory Mechanisms
                                                                                                                2. Relational Graph Convolutional Networks (R-GCN)
                                                                                                                  1. Multi-relational Graphs
                                                                                                                    1. Relation-specific Transformations
                                                                                                                      1. Parameter Sharing Strategies
                                                                                                                        1. Basis Decomposition
                                                                                                                          1. Block Diagonal Decomposition
                                                                                                                          2. Graph Transformer Networks
                                                                                                                            1. Transformer Architecture for Graphs
                                                                                                                              1. Positional Encodings for Graphs
                                                                                                                                1. Global Attention Mechanisms

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                                                                                                                            2. Core Concepts of Graph Neural Networks

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                                                                                                                            4. Advanced GNN Architectures