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SUMMARY:Spectral Graph Neural Network: Polynomial Approximation and Optimi
 zation - Keke Huang\, National University of Singapore
DTSTART:20231018T163000Z
DTEND:20231018T173000Z
UID:TALK207505@talks.cam.ac.uk
CONTACT:Pietro Lio
DESCRIPTION:Graph Neural Networks (GNNs)\, functioning as spectral graph f
 ilters\, have found extensive applications in practical scenarios. However
 \, deriving optimal graph filters through eigendecomposition of the Laplac
 ian matrix is computationally prohibitive. To address this challenge\, pol
 ynomial graph filters have been proposed as an approximation method. These
  filters leverage diverse polynomial bases for training\, yet a unified ex
 ploration of these filters for optimization is lacking in existing studies
 .\n\nIn this presentation\, we systematically examine existing polynomial 
 filters within a unified framework. Specifically\, we investigate polynomi
 al graph filters of identical degrees within the Krylov subspace of the sa
 me order\, thus providing equivalent theoretical expressive power. Subsequ
 ently\, we delve into the asymptotic convergence behavior of polynomials w
 ithin this unified Krylov subspace. Our analysis reveals the limited adapt
 ability of these polynomials in graphs with varying degrees of heterophily
 . Inspired by these insights\, we introduce a novel adaptive Krylov subspa
 ce approach. This method optimizes polynomial bases with control over the 
 graph spectrum\, allowing adaptation to diverse graphs with different hete
 rophily degrees. Based on this approach\, we propose AdaptKry\, an optimiz
 ed polynomial graph filter that uses the adaptive Krylov basis. Moreover\,
  considering the complex nature of graphs\, we extend AdaptKry by incorpor
 ating multiple adaptive Krylov bases without additional training costs. Th
 is extended version captures the intricate characteristics of graphs\, pro
 viding valuable insights into their complexity.\n\n\n\nKeke Huang is a Res
 earch Fellow at the National University of Singapore. He received his Ph.D
 . degree from Nanyang Technological University in Singapore. His research 
 primarily focuses on graph algorithm design and analysis\, approximation a
 lgorithms in social networks\, and graph neural networks.
LOCATION:Lecture Theatre 2\, Computer Laboratory\, William Gates Building
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