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STATISTICAL MECHANICS OF GRAPH NEURAL NETWORKS
04/10
2023
Seminar
- Title STATISTICAL MECHANICS OF GRAPH NEURAL NETWORKS
- Speaker Cheng Shi (University of Basel)
- Date 15:00 Apr. 10, 2023
- Venue 6620, South Building
Abstract
Graph convolution networks are excellent models for relational data but their success is not well understood. I will show how ideas from statistical physics and random matrix theory allow us to precisely characterize GCN generalization on the contextual stochastic block model—a community-structured graph model with features. The resulting curves are rich: they predict double descent thus far unseen in graph learning and explain the qualitative distinction between learning on homophilic graphs (such as friendship networks) and heterophilic graphs (such as protein interaction networks). Earlier approaches based on VC-dimension or Rademacher complexity are too blunt to yield similar mechanistic insight. Our findings pleasingly translate to real “production-scale” networks and datasets and suggest simple redesigns which improve performance of state-of-the-art networks on heterophilic datasets. They further suggest intriguing connections with spectral graph theory, signal processing, and iterative methods for the Helmholtz equation. Joint work with Liming Pan, Hong Hu and Ivan Dokmani？.
Invitor: Pan Zhang