Intrinsic Dimensionality

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Overview

Intrinsic dimensionality studies how many degrees of freedom are needed to describe data, even when observations have many coordinates. It matters because low-dimensional structure can reduce the data and computation needed for learning, support compression, and help explain how models represent information. Researchers estimate it using nearest-neighbor distances, local geometry, spectral or Hessian methods, and theoretical analyses of learning on manifolds and other structured distributions. Theory increasingly shows benefits over ambient-dimension bounds, but estimates remain sensitive to noise, scale, anisotropy, and the representation or task being measured, so no single estimator or definition works reliably in every setting.

Latest papers

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56 papers4 papers in the last four weeks, down 33% on the four weeks before. 0.0% of all new papers.

  1. Emergent Sparsity: How Many Effective Variables Survive Coarse-Graining in AlphaEarth Embeddings?

    Oct 18, 2026Johannes HirnDimensionality ReductionIntrinsic Dimensionality

    Image Processing Laboratory (IPL), Universitat de València, 46980 Paterna, Valencia, Spain · Universidad Cardenal Herrera-CEU, 46115 Alfara del Patriarca, Valencia, Spain

  2. Quantifying the Value of Constructive Induction, Knowledge, and Noise Filtering on Inductive Learning

    Oct 2, 2026Carl M. KadieIntrinsic DimensionalityStatistical Learning Theory

  3. Interpretable intrinsic dimension estimation through componentwise calibration of distance and angle

    Sep 29, 2026Chih-Hsuan Huang, Chih-Wei Chen, Szu-Chi ChungIntrinsic DimensionalityNeural Representation Geometry

    Department of Applied Mathematics, National Sun Yat-sen University, No. 70, Lienhai Rd., Kaohsiung, 80424, Taiwan

  4. Measuring trainable degrees of freedom in materials graph neural networks: a random-subspace intrinsic dimension analysis

    Sep 28, 2026Shehroz Ahmad Shoaib, Kangming LiIntrinsic DimensionalityGraph Neural Networks

    Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia. · Department of Electrical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

  5. Geometry-Adaptive Mechanisms for Private Synthetic Data

    Sep 27, 2026Raoof Zare Moayedi, Amir R. Asadi, Mohammad Hossein Yassaee +1Intrinsic DimensionalityDifferentially Private Synthetic Data Generation

    Sharif University of Technology · University of Birmingham · The Alan Turing Institute

  6. Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction

    Sep 27, 2026Lu Wei, Yufeng Wang, Chenfeng Cao +1Variational Monte CarloIntrinsic Dimensionality

    Data Science Department, Stony Brook University · Department of Computer Science, Stony Brook University · Dahlem Center for Complex Quantum Systems, Freie Universität Berlin +1

  7. It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification

    Sep 24, 2026Xiao Fan, Jingyuan Li, Yubo Han +6Intrinsic DimensionalityFunctional Connectivity

  8. Symmetry without a manifold: intrinsic dimension on orbits

    Sep 15, 2026Chon-Fai Kam, Miloud Bessafi, Frédéric CadetIntrinsic DimensionalityModular Addition

    Dipartimento di Fisica e Chimica, Universit`a degli Studi di Palermo, via Archirafi 36, I-90123 Palermo, Italy · EnergyLab, Universit´e de La R´eunion, F-97715 Saint-Denis, France · Universit´e Paris Cit´e and Universit´e de La R´eunion, BIGR, INSERM UMR S1134, F-75014 Paris, France +1

  9. Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimension

    Sep 4, 2026Jaehee Seo, Wontae Jeong, Jisu KimIntrinsic DimensionalityMinimax Estimation

    Department of Statistics, Seoul National University

  10. Fractal dimension predicts quantum kernel collapse in angle-encoded data

    Aug 31, 2026Ana Paula AppelQuantum Feature MapsIntrinsic Dimensionality

  11. A Hub of Short Rows Inflates Intrinsic Dimension Estimation of Token Embeddings

    Aug 30, 2026Alexandre QuemyIntrinsic DimensionalityNeural Representation Geometry

    Hother Labs

  12. Representation Measurements Under Function-Preserving Reparameterizations

    Aug 27, 2026Abdullah KarasanIntrinsic DimensionalityRepresentation Identifiability

    University of Maryland, Baltimore County 1000 Hilltop Circle, Baltimore, MD 21250, USA

  13. The Changing Geometry of Grammar: Dimensionality and Neighborhood Reorganization across Transformer Layers

    Aug 25, 2026Samuele Vallisa, Federico Ravenda, Claudio Palominos +5Representation Geometry in Language ModelsTransformer

    Grammar and Cognition Lab, Department of Translation & Language Sciences, Universitat Pompeu Fabra, Barcelona, Spain. · Euler Institute, Università della Svizzera italiana, Lugano, Switzerland. · Department of Adult Psychiatry and Psychotherapy, University Hospital of Psychiatry Zurich, University of Zurich, Zurich, Switzerland. +2

  14. A Comparative Study of Label-free Representation Quality Metrics in Deep Learning

    Aug 24, 2026Daniel Richards Arputharaj, Daniel Jönsson, Gabriel EilertsenReference-Free EvaluationVisual Representation Learning

    Department of Science and Technology Linköping University

  15. Diffusion Models for High-Dimensional Clustered Data: Intrinsic-Dimension Adaptivity via Bayesian Classification

    Aug 19, 2026Yuga Iguchi, Paul FearnheadDiffusion ModelsIntrinsic Dimensionality

    School of Mathematical Sciences, Lancaster University, Lancaster, UK

  16. Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems

    Aug 19, 2026Mark Kozdoba, Shie MannorDimensionality ReductionKoopman Operator Learning

    Technion, IIT · Technion, IIT and NVIDIA

  17. Local and Global Regimes of Geometric Complexity in Language Model Representations

    Aug 14, 2026Arwa Osman, Marco Baroni, Iuri MacoccoIntrinsic DimensionalityRepresentation Geometry in Language Models

    Universitat Pompeu Fabra (UPF) · ICREA

  18. Function Lives Where Variance Doesn't: Task-Weighted Charts of a Language Model's Computation

    Aug 12, 2026Alexandre QuemyRepresentation Geometry in Language ModelsIntrinsic Dimensionality

    Hother, Krak´ow, Poland

  19. FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data

    Aug 11, 2026Viktoria Schuster, Sana Tonekaboni, Caroline UhlerIntrinsic DimensionalityRepresentation Learning

    Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA · Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard, Cambridge, MA, USA · Technical University of Denmark, Lyngby, Denmark +1

  20. ββ-VAEs as Effective Theories: Tolerance-Dependent Dimension

    Aug 11, 2026Johannes HirnVariational AutoencodersIntrinsic Dimensionality

    Image Processing Laboratory (IPL), Universitat de València, Paterna, València 46980, Spain

  21. Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension

    Aug 11, 2026Tingan Jin, Shuhang Dong, Haosong Li +1Intrinsic DimensionalityNeural Representation Geometry

    UCLA · Independent Researcher · Cal Poly Pomona

  22. ERank in Latent Space as an Image-Complexity and Richness Measure

    Jul 21, 2026Maksim Smirnov, Grigory Kononov, Anastasiia Linich +2Intrinsic DimensionalityImage Quality Assessment

  23. GLID: Gated Local Intrinsic Dimension Repairs the Blind Spots of Face-Forgery Detectors

    Jul 21, 2026Guang Yang, Fengchen LiuIntrinsic DimensionalityDeepfake Detection

    University of California, Los Angeles · University of California, Berkeley

  24. Physics-Informed Neural Embeddings of PDE Solution Families

    Jul 7, 2026Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3Intrinsic DimensionalityPDE Solving

    Institute of Cosmos Sciences (ICC), University of Barcelona, Martí i Franquès 1, ES-08028, Barcelona, Spain. · Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092, Zürich, Switzerland. · Institute for Applied Computational Science, Harvard University, Cambridge, MA, USA. +1

  25. Transformer Geometry Observatory TGO-II: Representational Similarity Observatory

    Jul 2, 2026Kaustubh Kapil, Kishor P. UplaIntrinsic DimensionalityRepresentational Similarity Analysis

    Department of Electronics Engineering Sardar Vallabhai National Institute of Technology (SVNIT), Surat, India

  26. Function-Counting Theory for Low-Dimensional Data Structures

    Jul 1, 2026Konstantin Häberle, Helmut BölcskeiIntrinsic DimensionalityBinary Classification

    ETH Zurich

  27. I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory

    Jun 29, 2026Igor HalperinIntrinsic DimensionalityRandom Matrix Theory

  28. Effective Dimension Governs Generalization in Quantum Kernel Vision Models

    Jun 18, 2026Jian Xu, Delu Zeng, John Paisley +1Quantum Feature MapsIntrinsic Dimensionality

    RIKEN iTHEMS · RIKEN AIP · South China University of Technology +1

  29. Transformer Geometry Observatory TGO-I: Spectral Geometry Observatory

    Jun 17, 2026Kaustubh Kapil, Kishor P. UplaIntrinsic DimensionalityNeural Representation Geometry

    Department of Electronics Engineering Sardar Vallabhai National Institute of Technology (SVNIT), Surat, India

  30. The Data Manifold under the Microscope

    Jun 14, 2026Marios Koulakis, Constantin SeiboldIntrinsic DimensionalitySynthetic Benchmark Generation

    Independent Researcher, Germany · Diagnostic and Interventional Radiology, University Clinic Heidelberg, Heidelberg, Germany.