Higher Order

Higher-order research focuses on modeling and leveraging complex, non-pairwise relationships within data, moving beyond traditional pairwise interactions in networks and other structures. Current research emphasizes developing novel architectures like higher-order graph neural networks, simplicial complexes, and state-space models to capture these intricate relationships, often incorporating techniques from topological data analysis and active learning to improve efficiency and accuracy. This field is significant because it enables more accurate and nuanced modeling of complex systems in diverse domains, from scientific discovery (e.g., solving high-order differential equations) to artificial intelligence (e.g., enhancing large language model reasoning capabilities).