Curvature for Graph Learning

Abstract: Curvature bridges geometry and topology, using local information to derive global statements. While well-known in a differential topology context, it was recently extended to the domain of graphs. In fact, graphs give rise to various notions of curvature, which differ in expressive power and purpose. We will give a brief overview of curvature in graphs, define some relevant concepts, and show their utility for data science and machine learning applications. In particular, we shall discuss two applications: first, the use of curvature to distinguish between different models for synthesising new graphs from some unknown distribution; second, a novel framework for defining curvature for hypergraphs, whose structural properties require a more generic setting. We will also describe new applications that are specifically geared towards a treatment by curvature, thus underlining the utility of this concept for data science.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html