Mathematical Structure

Mathematical structure is being investigated across diverse fields to understand and model complex systems, from human cognition and language to machine learning algorithms and robotic control. Current research focuses on applying and developing mathematical frameworks like posets, Hopf algebras, and metric structures to represent and analyze data, particularly within neural networks and optimization processes. This work aims to improve the efficiency and generalizability of machine learning models, enhance our understanding of information processing in the brain, and provide quantitative tools for comparing and evaluating complex dynamic systems. The resulting insights have implications for various applications, including automated grading, office automation, and the design of more intelligent robots.