Probability Seminar
Thursday, October 7, 2021, 3:15pm, Virtual
Ahmed El Alaoui (Cornell University, Statistics and Data Science)
Finding ground states of spin glasses

Abstract:

We consider the question of efficiently finding a near-ground state configuration of an Ising mixed p-spin Hamiltonian H_N. I will present an algorithm which exploits the ultrametric structure of the superlevel sets of H_N in order to achieve an energy E_* characterized via an extended Parisi variational principle. This energy is maximal when the model satisfies a `no overlap gap condition’. At the heart of this algorithm is a stochastic control problem, whose dual turns out to be the Parisi formula, thereby shedding new light on the nature of the latter. Time permitting I will discuss a similar treatment for the negative spherical perceptron. This is joint work with Andrea Montanari and Mark Sellke.

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