When
Bruno Olshausen
Professor
Helen Wills Neuroscience Institute
School of Optometry, UC Berkeley
Director, Redwood Center for Theoretical Neuroscience
Neural computations for geometric reasoning
Abstract: In order to survive in complex, three-dimensional environments, animals must possess the ability to represent geometric structure and to perform computations on it. Here I propose an approach that is rooted in observations of animal behavior and informed by both neurobiological mechanisms (recurrence, dendritic nonlinearities, phase coding) and mathematical principles (group theory, residue numbers). What emerges from this approach is a neural circuit for factorization that can learn about shapes and their transformations from image data, and a model of the grid-cell system based on high-dimensional encodings of residue numbers. These models provide efficient solutions to long-studied problems that are well-suited for implementation in neuromorphic hardware or as a basis for forming hypotheses about visual cortex and entorhinal cortex.