STORM: Simplicial Topological Recurrent Models

Many dynamical systems, from traffic networks to water infrastructure, involve signals and interactions across nodes, edges, and higher-order groups. Existing temporal models often ignore this structure or use it only as preprocessing, while graph-based approaches remain limited to pairwise relations. We introduce Simplicial Topological Recurrent Models (STORM), recurrent architectures on simplicial complexes that embed simplicial operators into memory gates, allowing topology to shape hidden-state dynamics over time. We prove permutation equivariance, finite-horizon stability to bounded admissible topology perturbations, and a Rademacher-complexity generalization bound with explicit temporal dependence. On traffic and hydraulic datasets, STORM improves over the best baselines in our evaluation by up to 50% at long horizons. For node-only forecasting, STORM and LightSTORM are highly competitive with strong graph models, with LightSTORM using up to roughly two orders of magnitude fewer parameters.