Related papers: Sampling from Spherical Spin Glasses in Total Vari…
Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
An approximate numerical approach to spin models is proposed, in which the original lattice is transformed into a tree. This method is applied to the Edwards-Anderson spin glass model in two and three dimensions. It captures the…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
We consider critical points of the spherical pure $p$-spin spin glass model with Hamiltonian…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G.…
We prove that the two cornerstones of mean-field spin glass theory -- the Parisi variational formula and the ultrametric organization of pure states -- break down under heavy-tailed disorder. For the mixed spherical $p$-spin model whose…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
While change point detection in time series data has been extensively studied, little attention has been given to its generalisation to data observed on spheres or other manifolds, where changes may occur within spatially complex regions…
We construct the first complete exact numerical solution of a mean field quantum spin glass model, the transverse field Sherrington-Kirkpatrick model, by implementing a continuous-time quantum Monte Carlo method in the presence of full…
We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate…
In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive…
We study a quantum extension of the spherical $p$-spin-glass model using the imaginary-time replica formalism. We solve the model numerically and we discuss two analytical approximation schemes that capture most of the features of the…
A p-spin interaction Ashkin-Teller spin glass, with three independent Gaussian probability distributions for the exchange interactions, is studied by means of the replica method. A simple phase diagram is obtained within the…