Hyperbolic Graph Convolutional Networks | Geometric ML Paper Explained

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In this video we dig deep into the hyperbolic graph convolutional networks paper introducing a class of GCNs operating in the hyperbolic space.

Hyperbolic GCNs give exceptional results for the class of scale-free/hierarchical/tree-like graphs. I dive deep into differential geometry theory and explain how the method works.

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✅ Paper: https://arxiv.org/abs/1910.12933
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⌚️ Timetable:
00:00 Intro - why the hyperbolic space?
04:00 Graph Convolutional Networks recap
08:50 Hyperbolic space and curvature theory
15:25 Geodesics, exp, and log maps
23:00 Mapping from Euclidean to hyperbolic space
26:35 Feature transform in hyperbolic space
32:47 Aggregregation on the hyperboloid manifold
35:25 Non-linear activation with different curvatures
36:30 Holistic overview of the method
38:20 Results, Ablations, and curvature analysis
41:00 Why does curvature help?
42:05 Outro

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#graphs #graphconvolutionalnetwork #hyperbolicspace