Work

Bliss of dimensionality: How an unsupervised criterion identifies optimal low-resolution representations of high-dimensional datasets

Year: 2026

Type: article

Abstract: Selecting the optimal resolution for discretizing high-dimensional data is a central problem in physics and data analysis, particularly in unsupervised settings where the underlying distribution is unknown. The resolution-relevance (Res-Rel) framework addresses this issue through an information-theoretic trade-off between descriptive detail and statistical reliability. Here, we provide a systematic validation of this approach by comparing its characteristic optima—maximum relevance and the − 1 slope point—with the discretization that minimizes the Kullback-Leibler (KL) divergence from a known or physically motivated ground truth distribution. Across unstructured and structured synthetic datasets, Gaussian clones of MNIST, and molecular dynamics simulations of the alanine dipeptide, we find that as the dimensionality or informative content increases the KL-optimal discretization consistently lies within the Res-Rel optimality region. Furthermore, in high-dimensional regimes the − 1 slope criterion closely matches the KL divergence minimum. These results establish the quantitative consistency of unsupervised information-theoretic selection with distribution-based optimality.

Source: Physical Review Research

DOI: 10.1103/3jcr-qy3d

Authors: Margherita Mele, Daniel Campos, Raffaello Potestio

Institutions: Istituto Nazionale di Fisica Nucleare, University of Trento, Istituto Nazionale di Fisica Nucleare, Trento Institute for Fundamental Physics And Applications, Universitat Autònoma de Barcelona

Language: English

Topic: Statistical Mechanics and Entropy

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funders: European Commission, Research Executive Agency, NextGenerationEU