Mathematics Colloquium

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Analysis of algorithms in high-dimensions: When proofs inspire physics.

Speaker: Lenka Zdeborova, EPFL

Location: 60 Fifth Avenue Auditorium Hall 150

Date: Thursday, April 13, 2023, 2 p.m.

Synopsis:

I will overview the development around message passing algorithms, their analysis, and examples of applications. On the way, I will show cases where rigorous results inspired a new understanding of physics. I will discuss how widely used and studied algorithms such as Monte Carlo sampling, gradient descent of Langevin algorithm compare to message passing in some prototypical problems of high-dimensional problems. I will end up with some examples from my recent works where message passing algorithms give access to quantities that are hard to access otherwise, e.g. variances of the posterior, optimal spectral methods or estimators relying on priors coming from generative neural networks.