New Categorical and Topological Foundations for AI and Machine Learning
The Project
The project explores novel neural network architectures based on more bespoke mathematical representation spaces and structures, including sheaf theory and category theory. These novel architectures may be able to incorporate key structural symmetries and properties of mathematical objects, and thereby enable the creation of new tools that assist in proof construction, and offer practical advantages beyond the current AI Copilot paradigm. Exploring the possibility of models that can represent and manipulate proof state in rich type theories may show us how to bridge the gap between machine learning and traditional mathematical fields.
The Team
Pietro Lio is a Professor of Computational Biology in the Department of Computer Science at the University of Cambridge, where he joined as a member of faculty in 2004. He originally studied in Firenze and Pavia, focusing on genetics and complex systems, followed by research positions in Southampton and Cambridge. His work focuses on artificial intelligence and computational biology to understand disease processes.
Jamie Vicary is Professor of Future Computation in the Department of Computer Science at the University of Cambridge. After first degrees in physics and mathematics, he worked as a researcher in Computer Science for 10 years at the University of Oxford, joining the University of Birmingham as a Senior Lecturer in 2018, and moving to Cambridge in 2020. He has broad research interests across quantum computing, theoretical computer science, and machine learning.