This project is being funded through the Learning & Intelligent Systems Initiative, and is supported in part by the NSF Office of Multidisciplinary Activities in the Directorate for Mathematical & Physical Sciences. Learning in many cognitive domains, including language and vision, involves recognition of complex hierarchical structure that is hidden or only indirectly reflected in the input data. In this project a multi-disciplinary group of applied mathematicians, cognitive scientists, computer scientists, linguists, and neuroscientists will study the learning of compositional structure in language, vision, and planning, and will also probe the neural mechanisms for identifying and exploiting such structure. The research involves three interacting lines of work. The first refines and extends statistical learning models; the second applies these models to language, vision, and planning; and the third develops and applies new experimental and analysis techniques for probing the neural mechanisms that learn and exploit compositional structure. The results of the project should significantly increase our understanding of complex learning, and should have implications for a wide range of topics in education (e.g., learning of complex knowledge structures in science and math) and technology (e.g., automated speech recognition, computer vision, robotics).