Connected Intelligence

Foundational mathematics for understanding computation and intelligence.

How one thinks about a subject, including the language they use, impacts their ability to reason, work with, and be creative within that domain. For example, humanity has long used numbers for counting. But if we are constrained to using ancient systems of notation, such as Roman numerals, a huge amount of what we do with numbers is impossible: imagine doing finance, e.g. compound interest, or modern science and technology using Roman numerals! By bringing the brilliant Arabic notation to the West in around 1200, Fibonacci single-handedly paved the way for the Renaissance, including the discoveries of Copernicus, Galileo, and Newton.

In this theme we create new, fundamental mathematical languages for computation and intelligence.

For example, our current model of computation is based on the Turing machine. Just as Roman numerals do indeed specify numbers, Turing machines do specify computations. However, the model is clunky and ad hoc, and it does not take into account anything other than a single disk and a single processor: no keyboard, monitor, or printer, no user, no internet. But like Arabic numerals, there's a mathematical formalism called polynomial functors that is much more versatile. In particular, it allows for machines (multiple disks, processors, keyboards, monitors, even routine mental procedures) to connect or disconnect, to send information to each other, and to thereby organize to solve larger problems. 

The same mathematical system can be used to talk about arbitrary dynamical systems, such as the brain, and how it connects to other systems such as the fingers, which connect to the keyboard for typing and then disconnect when desired. This mathematical system can even be used to model the bonding of atoms into molecules. In other words, the same mathematical structure, instead of just being about computers, is a general theory of interconnected machines, from chemicals to neurons to bodies, from machines to the internet of things. 

By replacing an impoverished language of computation with a fully compositional and general one, it becomes possible to ask the big questions. How do we ensure a safe national airspace, where airplanes can come in and out of range of each other, but should never get too close? How do we ensure AI systems interact with us in mutually beneficial ways? How can we understand the way that human brains guide the bodies they inhabit to predict the necessary actions for staying alive? Can we connect these ideas to deep learning systems and share insights between the two fields?

As part of this theme, we work with AI safety experts, predictive processing experts, and robotics engineers to see how this new mathematics can formalize the aspects of those fields that historically resisted formalization. We also build a design environment whereby users can try out their theories and prove results or simulate interactions in a precise and modular way.