Effective Theory Building and Manifold Learning

TL;DR

This paper proposes that manifold learning, effective model building, and effective field theory are interconnected, sharing a common principle of exploiting redundancies and regularities in high-dimensional data for scientific modeling.

Contribution

It introduces a unified perspective showing that effective model building and manifold learning are special cases of the same underlying process, emphasizing the role of algorithmic compressibility.

Findings

Effective model building relies on exploiting data regularities.

Manifold learning and effective theories can be viewed as algorithmic compression techniques.

The approach sheds light on the common principles underlying different modeling methods.

Abstract

Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another model. Nonetheless, I argue that certain kinds of high-dimensional effective model building, and effective field theory construction in quantum field theory, can be viewed as special cases of manifold learning. I argue that this helps to shed light on all of these techniques. First, it suggests that the effective model building procedure depends upon a certain kind of algorithmic compressibility requirement. All three approaches assume that real-world systems exhibit certain redundancies, due to regularities. The use of these regularities to build simplified models is essential for scientific progress in many different domains.