The Geometric Scattering Transform for High-dimensional Data Analysis - (Slides) In this talk (from the IPAM Workshop on the Mathematics of Cancer: Open Mathematical Problems in February 2026): 1) An overview of the Scattering Transform 2) A discussion of Message-Passing vs Spectral Graph Neural Networks (GNNs) 3) The Geometric Scattering Transform on graphs and manifolds 4) Extensions to vector-valued data 5) Statistical Consistency of Scattering Transforms/GNNs under the manifold hypothesis 6) Extensions to higher-order networks (hypergraphs and simplicial complexes). When possible, all algorithms were motivated by biomedical applications. Talk features several off-the-cuff remarks about the validity of the manifold hypothesis; this was inspired by a very excellent talk earlier in the week from Andrew Blumberg (part 1 , part 2) discussing (among other things) the validity of this assumption.
Group Invariant Scattering on Graphs, Manifolds, and Other Measure Spaces - CodEx Seminar - (Slides) In this talk: 1) An overview of the Scattering Transform 2) The Scattering Transform on Graphs and Manifolds 3) Extensions to General Measure Spaces 4) Applications to Combinatorial Optimization, Drug Discovery, and Single Cell Data 5) Convergence of the Manifold Scattering Transform from Finitely Many Samples
The Scattering Transform for Data with Geometric Structure - BIRS workshop on Deep Exploration of non-Euclidean Data - (Slides) In this talk: 1) An overview of the Scattering Transform 2) The Scattering Transform on Graphs and Manifolds 3) Incorporating Learning into the Geometric Scattering Transform
Convolutional Networks on Graphs - CodEx Seminar - (Slides) In this talk: 1) Common machine learning tasks for Graph-Structured Data 2) The Graph Laplacian and Graph Neural Networks 3) The Oversmoothing Problem and the Graph Scattering Transform 4) The Magnetic Laplacian and Directed Graphs
Geometric Scattering and Applications - ICERM Workshop on Geometric and Topological Methods in Data Science - (Slides) In this talk: 1) An overview of the Scattering Transform 2) The Scattering Transform on Graphs and Manifolds 3) Applications to Drug Discovery