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Intermediate•Machine Learning
Graph Neural Networks (GNNs)
Message passing paradigms, Graph Convolutional Networks (GCN), GraphSAGE, and non-Euclidean graph representations.
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Research-Level Deep Dive & Equations
Standard convolutional neural networks (CNNs) operate on regular 2D/3D grids (images/voxels) with defined spatial ordering. **Graph Neural Networks (GNNs)** operate on non-Euclidean graph topologies defined by node features and an adjacency matrix .
•Graph Representation:
- Node Feature Matrix where is the number of nodes.
- Adjacency Matrix where if edge and otherwise.
- Degree Matrix diagonal matrix where .
•Permutation Equivariance Requirement: Because node indices are arbitrarily assigned, graph operators must produce identical predictions regardless of node ordering. For any permutation matrix :
Key Equations
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