Perspectives on Stochastic Localization
It aims to broaden accessibility and ease future use of stochastic localization across communities like probability theory, theoretical computer science, information theory, and machine learning, but is incremental as a survey.
This paper surveys different perspectives on Eldan's stochastic localization process, providing a self-contained presentation of all known alternative constructions with an emphasis on connections between them.
We survey different perspectives on the stochastic localization process of [Eld13], a powerful construction that has had many exciting recent applications in high-dimensional probability and algorithm design. Unlike prior surveys on this topic, our focus is on giving a self-contained presentation of all known alternative constructions of Eldan's stochastic localization, with an emphasis on connections between different constructions. Our hope is that by collecting these perspectives, some of which had primarily arisen within a particular community (e.g., probability theory, theoretical computer science, information theory, or machine learning), we can broaden the accessibility of stochastic localization, and ease its future use.