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AM Seminar: Mean-field dynamics in shallow (and some deep) neural networks: Implications for generalization and computation

Speaker Name: 
Grant Rotskoff
Speaker Title: 
Assistant Professor
Speaker Organization: 
Stanford University
Start Time: 
Monday, February 22, 2021 - 4:00pm
End Time: 
Monday, February 22, 2021 - 5:00pm
via Zoom
Abhishek Halder


The surprising flexibility and undeniable empirical success of machine learning algorithms has inspired many theoretical explanations for the efficacy of neural networks. Here, I will briefly introduce one perspective that provides not only asymptotic guarantees of trainability and accuracy in high-dimensional learning problems, but also provides some prescriptions and design principles for learning. Bolstered by the favorable scaling of these algorithms in high dimensional problems, I will turn to a central problem in computational physics: that of computing transitions pathways between metastable states. From the perspective of an applied mathematician, these problems typically appear hopeless; they are not only high-dimensional, but also dominated by rare events. However, with neural networks in the toolkit, at least the dimensionality can be made somewhat less intimidating. I will describe an algorithm that combines stochastic gradient descent with importance sampling to optimize a function representation of the transition probabilities for an arbitrary system. Finally, I will provide numerical evidence of the power and limitations of this approach.


Grant Rotskoff is an Assistant Professor of Chemistry at Stanford. He studies the nonequilibrium dynamics of living matter with a particular focus on self-organization from the molecular to the cellular scale. His work involves developing theoretical and computational tools that can probe and predict the properties of physical systems driven away from equilibrium. Recently, he has focused on characterizing and designing physically robust machine learning techniques for applications in rare events simulation. Prior to his current position, Grant was a James S. McDonnell Fellow at the Courant Institute of Mathematical Sciences at New York University. He completed his Ph.D. at the University of California, Berkeley in the Biophysics graduate group supported by an NSF Graduate Research Fellowship. His thesis, which was advised by Phillip Geissler and Gavin Crooks, introduced theoretical tools for understanding nonequilibrium control of small, fluctuating systems, such as those encountered in molecular biophysics. He also works on coarse-grained models of mesoscale biophysical self-assembly. Grant became interested in biophysics as an undergraduate at the University of Chicago, where he received an S.B. in Mathematics, while working on free energy methods for large scale molecular dynamics simulations.

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