Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs
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In this video I cover βNeural Sheaf Diffusion:
A Topological Perspective on Heterophily and Oversmoothing in GNNsβ paper. The paper takes ideas from the sheaf theory - a branch of algebraic topology - and combines them with GNNs, enriching them with a rich geometric structure (sheaves) achieving provably more expressive diffusion-based graph neural networks!
It took a lot of time to prepare this video and read everything that was necessary as a background reading - check out the resource section below for how to get started!
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Paper:
Truly gentle introduction to sheaves:
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A Very Elementary Introduction to Sheaves:
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Opinion dynamics on discourse sheaves:
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Sheaf Neural Networks:
Blogs:
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Blog accompanying the paper:
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Differential geometry and algebraic topology papers overview:
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Beginner intro to topology:
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βοΈ Timetable:
00:00:00 Gentle intro to sheaf theory and algebraic topology
00:12:00 Making it less abstract: examples from sheaf theory
00:23:50 Formal terminology
00:27:40 Sheaf Laplacian dissected
00:40:00 The separation power of sheaf diffusion
00:53:00 Dirichlet energy and converging to harmonic space
01:01:05 Neural Sheaf Diffusion GNN
01:06:00 Results and outro (feedback appreciated)
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#sheaftheory #algebraictopology #oversmoothing #heterophily
2 years ago 01:08:06 1
