Beyond Message Passing: Learning Representations from Dynamics on Graphs

This talk introduces two complementary frameworks that harness geometric and topological structure in dynamics on graphs for representation learning. I will first introduce Neurospectrum, a modular architecture that models brain activity as graph signals and learns latent neural trajectories shaped by multiscale spatial and temporal structure. By extracting geometric and topological invariants of these naturally occurring dynamics, such as curvature, path signatures, persistent homology, and recurrent dynamics, Neurospectrum reveals interpretable patterns in brain function, offering insights into neural synchrony, coordination, sensory processing, and aberrant dynamics associated with psychiatric disorders like OCD. Building on the idea of using dynamical behavior to reveal structure, I will next introduce DYMAG, a novel graph neural network that replaces traditional message passing with solutions to heat, wave, and chaotic partial differential equations defined over graphs. By treating graphs as continuous dynamical systems, DYMAG captures intrinsic geometric and topological features of the graph, enabling richer node and graph-level representations that improve performance on various benchmarks.