Mean Field Models for Spin Glasses

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Fundamental limits of detection in the spiked Wigner model (2018, background): “See Talagrand (2011a), Lemma 1.6.3, for the details of a similar computation.”
On the energy landscape of deep networks (2015, background): “An effective way of modifying this landscape is to perturb the Hamiltonian by a random magnetic field (Fyodorov, 2013) or another uncorrelated Hamiltonian (Talagrand, 2010).”
Debiasing the lasso: Optimal sample size for Gaussian designs (2015, methodology): “Our proof is based on a leave-one out technique, and is partially inspired from ideas in mathematical spin glass theory [Tal10].”
The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference (2018, background): “1 Introduction A very interesting development in probability theory in recent years has been the progress on a coherent mathematical theory [1, 2, 3, 4] of the predictions of the replica and cavity methods [5] in statistical physics of spin glasses.”
The LASSO Risk for Gaussian Matrices (2010, background): “Unfortunately the methods of [28] require (among the other assumptions) a strongly convex cost function, which is not the case in the present problem.”