Universality of approximate message passing algorithms and tensor networks
T Wang, X Zhong, Z Fan - The Annals of Applied Probability, 2024 - projecteuclid.org
The supplementary appendix contains additional details about AMP algorithms for
rectangular matrices and the rectangular generalized invariant universality class of …
rectangular matrices and the rectangular generalized invariant universality class of …
The high-dimensional asymptotics of first order methods with random data
We study a class of deterministic flows in ${\mathbb R}^{d\times k} $, parametrized by a
random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d} $ with iid centered subgaussian …
random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d} $ with iid centered subgaussian …
Algorithmic threshold for multi-species spherical spin glasses
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses.
Our results characterize the maximum value attained by algorithms that are suitably …
Our results characterize the maximum value attained by algorithms that are suitably …
The threshold energy of low temperature Langevin dynamics for pure spherical spin glasses
M Sellke - Communications on Pure and Applied Mathematics, 2023 - Wiley Online Library
We study the Langevin dynamics for spherical pp‐spin models, focusing on the short time
regime described by the Cugliandolo–Kurchan equations. Confirming a prediction of …
regime described by the Cugliandolo–Kurchan equations. Confirming a prediction of …
High-dimensional asymptotics of Langevin dynamics in spiked matrix models
We study Langevin dynamics for recovering the planted signal in the spiked matrix model.
We provide a" path-wise" characterization of the overlap between the output of the Langevin …
We provide a" path-wise" characterization of the overlap between the output of the Langevin …
Metastability in Glauber dynamics for heavy-tailed spin glasses
R Gheissari, C Grant - arXiv preprint arXiv:2407.11874, 2024 - arxiv.org
We study the Glauber dynamics for heavy-tailed spin glasses, in which the couplings are in
the domain of attraction of an $\alpha $ stable law for $\alpha\in (0, 1) $. We show a sharp …
the domain of attraction of an $\alpha $ stable law for $\alpha\in (0, 1) $. We show a sharp …
Multi-marginal Gromov–Wasserstein transport and barycentres
Gromov–Wasserstein (GW) distances are combinations of Gromov–Hausdorff and
Wasserstein distances that allow the comparison of two different metric measure spaces …
Wasserstein distances that allow the comparison of two different metric measure spaces …
Population Level Activity in Large Random Neural Networks
J MacLaurin, M Silverstein, P Vilanova - arXiv preprint arXiv:2401.15272, 2024 - arxiv.org
We determine limiting equations for large asymmetricspin glass' networks. The initial
conditions are not assumed to be independent of the disordered connectivity: one of the …
conditions are not assumed to be independent of the disordered connectivity: one of the …
Diagram Analysis of Iterative Algorithms
C Jones, L Pesenti - arXiv preprint arXiv:2404.07881, 2024 - arxiv.org
We study a general class of first-order iterative algorithms which includes power iteration,
belief propagation and Approximate Message Passing (AMP), and many forms of gradient …
belief propagation and Approximate Message Passing (AMP), and many forms of gradient …
Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors
T Yu - arXiv preprint arXiv:2401.03668, 2024 - arxiv.org
We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into
the asymptotic energy limit. Our approach involves integro-differential equations …
the asymptotic energy limit. Our approach involves integro-differential equations …