Event Date
Speaker: Arash A. Amini (Associate Professor, Dept. of Statistics and Data science, University of California Los Angeles)
Title: "Lessons from Poly-GNNs: Depth, Noise, and Limits on Large Graphs"
Abstract: Polynomial graph neural networks (poly-GNNs)—obtained by repeatedly applying the standard GNN aggregation—provide a clean lens on depth in semi-supervised node classification. Working in a contextual stochastic block model, we ask whether adding layers improves class separation. Using random-matrix tools and graph-walk combinatorics, we show that in the large-graph limit the separation rate is independent of depth: the extra “signal” from wider neighborhoods is exactly canceled by graph noise.
The same analysis yields a central limit theorem for poly-GNN embeddings: after rescaling, representations converge to a Gaussian mixture whose effective dimension collapses toward one as the depth k grows, again exposing the limits of deeper aggregation. I will close with open questions and possible directions.
Bios: Arash A. Amini is an Associate Professor of Statistics and Data Science at the University of California, Los Angeles. He received his Ph.D. in electrical engineering from the University of California, Berkeley in 2011, and completed a postdoctoral fellowship at the University of Michigan. His research spans high-dimensional statistics, functional and nonparametric estimation, network data analysis, optimization, and graphical models, with recent work shedding light on the performance limits of graph neural networks. At UCLA, he teaches courses from introductory machine learning to advanced theoretical statistics, mentoring the next generation of statisticians and data scientists.
Faculty website (links to UCLA): http://www.stat.ucla.edu/~arashamini/