Topological Message Passing: From Graph Neural Networks to Simplicial Complexes on CW Networks

Explore an advanced technical video that delves into the evolution from Message Passing Graph Neural Networks (MPGNN) to Topological Message Passing on CW Networks. Learn how lifting a graph to higher topological spaces enables complex high-dimensional interactions beyond traditional two-dimensional constraints. Understand the implications for computational Graph Neural Networks, particularly in fields like chemistry, pharmaceutical research, and molecular design where n-body interactions are crucial. Drawing from seminal works by Michael Bronstein, Petar Veličković, and other leading researchers, examine the theoretical foundations of geometric deep learning, including concepts like grids, groups, graphs, geodesics, and gauges. Discover how Weisfeiler-Lehman algorithms extend to topological frameworks and explore the implementation of Graph Attention Networks in modern deep learning architectures. Building upon previous content, this 25-minute presentation synthesizes cutting-edge research in topological approaches to neural networks and their practical applications in complex system modeling.