An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience. The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning. We will give several vignettes in this direction, including: (1) determining the best optimization problem to solve in order to perform regression in high dimensions; (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) derving the detailed structure of the primate retina by analyzing optimal convolutional auto-encoders of natural movies; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) understanding the geometry and dynamics of high dimensional optimization in the classical limit of dissipative many-body quantum optimizers.

References:

M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.

M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.

A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.

H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.

S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.

B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.

Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.

Y. Yamamoto, T. Leleu, S. Ganguli and H. Mabuchi, Coherent Ising Machines: quantum optics and neural network perspectives, Applied Physics Letters 2020.

B.P. Marsh, Y, Guo, R.M. Kroeze, S. Gopalakrishnan, S. Ganguli, J. Keeling, B.L. Lev

Enhancing associative memory recall and storage capacity using confocal cavity QED, https://arxiv.org/abs/2009.01227.

Bio: Surya Ganguli triple majored in physics, mathematics, and EECS at MIT, completed a PhD in string theory at Berkeley, and a postdoc in theoretical neuroscience at UCSF. He is now an associate professor of Applied physics at Stanford where he leads the Neural Dynamics and Computation Lab. His research spans the fields of neuroscience, machine learning and physics, focusing on understanding and improving how both biological and artificial neural networks learn striking emergent computations. He has been awarded a Swartz-Fellowship in computational neuroscience, a Burroughs-Wellcome Career Award, a Terman Award, a NeurIPS Outstanding Paper Award, a Sloan fellowship, a James S. McDonnell Foundation scholar award in human cognition, a McKnight Scholar award in Neuroscience, a Simons Investigator Award in the mathematical modeling of living systems, and an NSF career award.