Saved in:
Bibliographic Details
Main Author: Ros, Valentina
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.14084
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms: low-rank matrix estimation (Case 1) and low-rank tensor estimation (Case 2). We show how to map the inference problem onto the optimization problem of a high-dimensional landscape, which exhibits distinct geometrical properties in the two cases. We discuss methods for characterizing typical realizations of these landscapes and their optimization through local dynamics. We conclude by highlighting connections between the landscape problem and Large Deviation Theory.