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  • Letter
  • Open Access

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

Margherita Mele1,2, Daniel Campos3, and Raffaello Potestio1,2,*

  • 1Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy
  • 2INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
  • 3Grup de Física Estadística, Departament de Física, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

  • *Contact author: raffaello.potestio@unitn.it
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Phys. Rev. Research 8, L042011 – Published 26 October, 2026

DOI: https://doi.org/10.1103/3jcr-qy3d

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.

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Outline

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Phys. Rev. Research 8, L042011– Published 26 October, 2026
  • Received 6 March 2026
  • Accepted 29 September 2026
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