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Learn the mathematical foundations and machine learning applications of graphons in this comprehensive bootcamp lecture that bridges graph theory with modern neural network architectures. Explore graphons as both limit objects for dense graph sequences and generative models for random graphs, starting with core mathematical concepts including homomorphism densities, cut distance, sampling techniques, dense graph convergence, and spectral convergence properties. Discover how graphons formalize the convergence behavior of convolutional architectures on convergent graph sequences and understand their implications for transferability of Graph Neural Networks (GNNs) when trained on subsampled graph data. Examine recent advances in graphon-based machine learning approaches while critically analyzing the practical limitations of graphon models in contemporary ML applications. Investigate alternative methodologies for capturing structural patterns in sparse large-scale graphs, providing a thorough foundation for researchers working at the intersection of theoretical computer science and graph learning.
