Intrinsic Dimensionality

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4 papers in the last four weeks, down 20% on the four weeks before. 0.0% of all new papers.

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Measuring trainable degrees of freedom in materials graph neural networks: a random-subspace intrinsic dimension analysis
Sep 28, 2026Shehroz Ahmad Shoaib, Kangming LiIntrinsic Dimensionality Graph 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.
Geometry-Adaptive Mechanisms for Private Synthetic Data
Sep 27, 2026Raoof Zare Moayedi, Amir R. Asadi, Mohammad Hossein Yassaee +1Intrinsic Dimensionality Synthetic Data Generation
Sharif University of Technology · University of Birmingham · The Alan Turing Institute
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 Dimensionality Functional Connectivity
Symmetry without a manifold: intrinsic dimension on orbits
Sep 15, 2026Chon-Fai Kam, Miloud Bessafi, Frédéric CadetIntrinsic Dimensionality Neural Scaling Laws
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
Fractal dimension predicts quantum kernel collapse in angle-encoded data
Aug 31, 2026Ana Paula AppelQuantum Feature Maps Intrinsic Dimensionality
A Hub of Short Rows Inflates Intrinsic Dimension Estimation of Token Embeddings
Aug 30, 2026Alexandre QuemyIntrinsic Dimensionality Neural Representation Geometry
Hother Labs
FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data
Aug 11, 2026Viktoria Schuster, Sana Tonekaboni, Caroline UhlerIntrinsic Dimensionality Representation 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
$β$ -VAEs as Effective Theories: Tolerance-Dependent Dimension
Aug 11, 2026Johannes HirnVariational Autoencoders Intrinsic Dimensionality
Image Processing Laboratory (IPL), Universitat de València, Paterna, València 46980, Spain
Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension
Aug 11, 2026Tingan Jin, Shuhang Dong, Haosong Li +1Intrinsic Dimensionality Neural Representation Geometry
UCLA · Independent Researcher · Cal Poly Pomona
ERank in Latent Space as an Image-Complexity and Richness Measure
Jul 21, 2026Maksim Smirnov, Grigory Kononov, Anastasiia Linich +2Intrinsic Dimensionality Image Quality Assessment
GLID: Gated Local Intrinsic Dimension Repairs the Blind Spots of Face-Forgery Detectors
Jul 21, 2026Guang Yang, Fengchen LiuIntrinsic Dimensionality Deepfake Detection
University of California, Los Angeles · University of California, Berkeley
Physics-Informed Neural Embeddings of PDE Solution Families
Jul 7, 2026Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3Intrinsic Dimensionality PDE 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
Transformer Geometry Observatory TGO-II: Representational Similarity Observatory
Jul 2, 2026Kaustubh Kapil, Kishor P. UplaIntrinsic Dimensionality Representational Similarity Analysis
Department of Electronics Engineering Sardar Vallabhai National Institute of Technology (SVNIT), Surat, India
Function-Counting Theory for Low-Dimensional Data Structures
Jul 1, 2026Konstantin Häberle, Helmut BölcskeiIntrinsic Dimensionality Binary Classification
ETH Zurich
I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory
Jun 29, 2026Igor HalperinIntrinsic Dimensionality Random Matrix Theory
Effective Dimension Governs Generalization in Quantum Kernel Vision Models
Jun 18, 2026Jian Xu, Delu Zeng, John Paisley +1Quantum Feature Maps Intrinsic Dimensionality
RIKEN iTHEMS · RIKEN AIP · South China University of Technology +1
Transformer Geometry Observatory TGO-I: Spectral Geometry Observatory
Jun 17, 2026Kaustubh Kapil, Kishor P. UplaIntrinsic Dimensionality Neural Representation Geometry
Department of Electronics Engineering Sardar Vallabhai National Institute of Technology (SVNIT), Surat, India
The Data Manifold under the Microscope
Jun 14, 2026Marios Koulakis, Constantin SeiboldIntrinsic Dimensionality Synthetic Benchmark Generation
Independent Researcher, Germany · Diagnostic and Interventional Radiology, University Clinic Heidelberg, Heidelberg, Germany.
Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA
Jun 6, 2026Andreas SchlapbachIntrinsic Dimensionality Principal Component Analysis
Swiss Federal Railways (SBB), Switzerland
Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
Jun 4, 2026Cornelius Otchere, Michael ShieldsIntrinsic Dimensionality Physics-Informed ML
Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, Maryland, USA
IdEst: Assessing Self-Supervised Learning Representations via Intrinsic Dimension
Jun 2, 2026Julie Mordacq, Vicky Kalogeiton, Steve OudotIntrinsic Dimensionality Self-Supervised Learning
Inria Saclay 2LIX, CNRS, École Polytechnique, IP Paris
Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension
May 22, 2026Hong Qian, Xiang Shu, Xiang Xia +5Intrinsic Dimensionality Bayesian Optimization
Shanghai Institute of AI for Education, and School of Computer Science and Technology, East China Normal University, Shanghai 200062, China · Ant Group, Hangzhou 310013, China · Nanjing University, Nanjing 210023, China
Representation Gap: Explaining the Unreasonable Effectiveness of Neural Networks from a Geometric Perspective
May 20, 2026David Perera, Victor Moura, Lais Isabelle Alves dos Santos +2Intrinsic Dimensionality Neural Network Generalization
Universidade Federal de Minas Gerais · Queen Mary University of London
Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds
May 15, 2026Guoji Fu, Taiji Suzuki, Wee Sun Lee +1Intrinsic Dimensionality Generative Modeling
National University of Singapore · The University of Tokyo · RIKEN Center for Advanced Intelligence Project +2
Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models
May 11, 2026Nikolaos Nakis, Panagiotis Promponas, Konstantinos Tsirkas +4Representation Geometry Intrinsic Dimensionality
Human Nature Lab, Yale University · Department of Electrical and Computer Engineering, Yale University · Department of Statistics and Data Science, Yale University +1
Local Intrinsic Dimension Unveils Hallucinations in Diffusion Models
May 6, 2026Bartlomiej Sobieski, Matthew Tivnan, Dawid Płudowski +4Intrinsic Dimensionality Hallucination Mitigation
Centre for Credible AI, Warsaw University of Technology · University of Warsaw · Massachusetts General Hospital +1
Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch
May 5, 2026Dionysis Arvanitakis, Vaggos Chatziafratis, Yiyuan LuoIntrinsic Dimensionality Contrastive Learning
Northwestern University, IL, USA · University of California
Dimensionality-Aware Anomaly Detection in Learned Representations of Self-Supervised Speech Models
May 4, 2026Sandra Arcos-Holzinger, Sarah M. Erfani, James Bailey +1Intrinsic Dimensionality Unsupervised Anomaly Detection
University of Melbourne, School of Computing and Information Systems, Australia · Monash University, Department of Data Science and Artificial Intelligence, Australia · Johns Hopkins University, Center for Language and Speech Processing, USA
Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
May 2, 2026Genki OsadaIntrinsic Dimensionality Spectral Methods
LY Corporation.
When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry
Apr 30, 2026Kathrin Korte, Joachim Winter Pedersen, Eleni Nisioti +1Intrinsic Dimensionality Continual Learning
IT University of Copenhagen, Denmark

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

Shehroz Ahmad Shoaib, Kangming Li

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.

Intrinsic Dimensionality Graph Neural Networks Materials Property Prediction

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Final predictive accuracy is the standard basis for comparing graph neural networks (GNNs) in materials-property prediction, but it does not show how strongly performance depends on access to trainable parameter-space directions. Here, we introduce trainable-degree dependence as a complementary characterization of materials GNN learning. Using random-subspace intrinsic-dimension analysis, we train CGCNN, ALIGNN, and DimeNet++ in randomly oriented parameter subspaces across six prediction tasks and measure how performance recovers as independent trainable degrees of freedom are restored. The resulting recovery curves separate endpoint accuracy from the trainable-dimensional demand required to recover it. They reveal distinctions that final errors alone miss: metallic classification and log-bulk-modulus regression recover near-reference performance from small fractional subspaces, formation-energy and band-gap prediction show stronger architecture dependence, and phonon prediction is most sensitive to dimensional restriction. Dataset-size sweeps show that band-gap models require larger fractional subspaces as training data grows, whereas formation-energy and bulk-modulus responses are more stable. A width sweep shows that fractional thresholds can remain stable while absolute threshold dimensions increase with model size. Random-subspace analysis therefore provides a targeted stress test for how materials GNNs use their optimization space.

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