Invariance and equivariance in brains and machines

Bruno Olshausen, UC Berkeley

Abstract: The goal of building machines that can perceive and act in the world as humans and other animals do has been a focus of AI research efforts for over half a century. Over this same period, neuroscience has sought to achieve a mechanistic understanding of the brain processes underlying perception and action. It stands to reason that these parallel efforts could inform one another. However recent advances in deep learning and transformers have, for the most part, not translated into new neuroscientific insights; and other than deriving loose inspiration from neuroscience, AI has mostly pursued its own course which now deviates strongly from the brain. Here I propose an approach to building both invariant and equivariant representations in vision 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.

Bio: Professor Bruno Olshausen is a Professor in the Helen Wills Neuroscience Institute, the School of Optometry, and has a below-the-line affiliated appointment in EECS. He holds B.S. and M.S. degrees in Electrical Engineering from Stanford University, and a Ph.D. in Computation and Neural Systems from the California Institute of Technology. He did his postdoctoral work in the Department of Psychology at Cornell University and at the Center for Biological and Computational Learning at the Massachusetts Institute of Technology. From 1996-2005 he was on the faculty in the Center for Neuroscience at UC Davis, and in 2005 he moved to UC Berkeley. He also directs the Redwood Center for Theoretical Neuroscience, a multidisciplinary research group focusing on building mathematical and computational models of brain function (see http://redwood.berkeley.edu).

Olshausen's research focuses on understanding the information processing strategies employed by the visual system for tasks such as object recognition and scene analysis. Computer scientists have long sought to emulate the abilities of the visual system in digital computers, but achieving performance anywhere close to that exhibited by biological vision systems has proven elusive. Dr. Olshausen's approach is based on studying the response properties of neurons in the brain and attempting to construct mathematical models that can describe what neurons are doing in terms of a functional theory of vision. The aim of this work is not only to advance our understanding of the brain but also to devise new algorithms for image analysis and recognition based on how brains work.

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