I use machine learning and mathematics to understand computational principles in biological neural networks, and draw inspiration from biology to build machine learning systems.
One of the most important problems that biological systems solve is modeling the symmetries and geometric structure of the natural world. Across sensory and motor regions in the brain, a striking property of neural circuits is that they tend to mirror the structure of systems they represent—either in the topological layout of their connections, or in the implicit vector space generated by their activity. This can be described as a equivariant functor from the world to the neural substrate. I study the properties of such symmetry-preserving representations, in both biological and artificial neural systems.