Mathematical Connections of Some Local-to-Global Expressivity Results Over Geometric Graphs and Geometric Rigidity

Explore the mathematical foundations connecting expressivity results in geometric machine learning with classical geometric rigidity theory in this conference talk. Delve into recent findings on expressivity for geometric Message Passing Graph Neural Networks (MPGNNs) applied to Euclidean point clouds, and discover how the search for simple expressions of complete invariants of geometric objects relates to established mathematical studies of geometric rigidity. Learn about milestone results in rigidity theory, examine current open questions in the field, and uncover lesser-known theoretical developments that bridge classical mathematics with modern geometric deep learning approaches. Gain insights into how understanding these mathematical connections can illuminate new research directions and methodologies in the intersection of graph learning and theoretical computer science.