Representation Geometry

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Representation geometry asks how a model arranges information in its internal feature spaces, including whether concepts form clusters, lie on low-dimensional manifolds, or are distorted by anisotropy and collapse. Researchers use tools such as probing, covariance and spectrum analysis, intrinsic-dimension estimates, layerwise comparisons, and geometric alignment to study representations in language, vision, audio, and multimodal models. These analyses help explain what models encode and can guide transfer, robustness, pruning, and the choice of layers or spaces for downstream tasks. A central open tension is that no single geometric measure reliably predicts useful behavior across models and tasks, so geometry must be interpreted in context and checked against task performance.

Latest papers

33 papers1 paper in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Shared Geometry As A Rosetta Stone: Cross-Modal Alignment Without Paired Data
Oct 7, 2026Dominik Schnaus, Thomas Dagès, Daniel Cremers +2Cross-Modal Alignment Cross-Modal Representation Transfer
TU Munich · MCML · Ulm University +2
LAYERSCOPE: A Layerwise Characterization of Video and Multimodal Learned Representations
Sep 23, 2026Sandra Arcos-Holzinger, Debashish Chakraborty, Rohita Mocharla +7Representation Geometry Representation Learning
Johns Hopkins University · University of Melbourne · Human Language Technology Center of Excellence +2
Arbitrary-Order Hermite Interpolation of Rigid-Motion Jets via Hyper-Multidual Quaternions
Aug 27, 2026Daniel ConduracheLie Group Methods Representation Geometry
Technical University of Iasi, D. Mangeron Street no. 59, 700050 Iasi, Romania · Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 14, 400114 Cluj-Napoca, Romania
On the Representational Geometry of Dynamic Programs
Aug 25, 2026Richard F. M. Lim, Ruriko YoshidaDynamic Programming Representation Geometry
Departments of Mathematics and Computer Science, Bowdoin College, Brunswick, Maine · Department of Operations Research, Naval Postgraduate School, Monterey, California · Department of Mathematical Sciences, Aalborg University, Denmark
Convergent Evolution in Neural Representation Space: Emergent Order in Deep Belief Networks
Aug 6, 2026Patrick Krauss, Achim Schilling, Andreas Maier +2Representation Geometry Hierarchical Representation Learning
Cognitive Computational Neuroscience Group, Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Germany · Neuromodulation and Neuroprosthetics, University Hospital Mannheim, University Heidelberg, Germany · Neuroscience Lab, University Hospital Erlangen, Germany +1
Understanding Submodular Information Measure Based Objectives for Representation Learning: A Variance and Separation Perspective
Jul 30, 2026Rishabh Iyer, Truong Pham, Anay MajeeRepresentation Geometry Submodular Optimization
The University of Texas at Dallas, Richardson, TX, USA · Adobe, San Jose, CA, USA
On the Geometry of Learned Representations in Event-Based Multi-Modal Egomotion Estimation
Jul 17, 2026Stefano Silvestrini, Michele CeresoliRepresentation Geometry Event-Based Vision
Politecnico di Milano, Via Giuseppe La Masa, 34, 20156, Milan, Italy
Muse: Representation Geometry of Muon Beyond Normalized Momentum
Jul 16, 2026Da Chang, Qiankun Shi, Lvgang Zhang +4Representation Geometry Momentum Methods
1Pengcheng Laboratory · 2Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences +3
InsideSSL: Understanding Self-Supervised Speech Representations using a Model-Centric Perspective
Jul 7, 2026Samir Sadok, Xavier Alameda-PinedaRepresentation Geometry Self-Supervised Speech Representation Learning
Inria, Universit´e Grenoble Alpes CNRS, LJK, France
Probing Geospatial SSL Representations with Environmental Signals
Jul 6, 2026Rohita Mocharla, Vishal M. PatelRepresentation Geometry Geospatial Representation Learning
Johns Hopkins Applied Physics Laboratory · Johns Hopkins University · Laurel, MD +1
Platonic Projection Structures: Operator-Induced Observability in Representation Learning
Jul 6, 2026Kazuo Ishii, Bishnu Prasad Gautam, Jieling Wu +1Representation Geometry Representation Learning
Department of Applied Information Engineering, Faculty of Engineering, Suwa University of Science, Chino 391-0292, Nagano, Japan · Department of Information Engineering, Kanazawa Gakuin University, Kanazawa 920-1392, Ishikawa, Japan
Probing Low-Level Acoustic Attribute Encoding in CLAP Audio Embeddings
Jul 4, 2026Héctor Martel, Joe Hennessy-Priest, Taemin ChoRepresentation Geometry Audio Representation Learning
BandLab Technologies, Singapore
Optimization Dynamics Imprint Semantic Specificity in Contrastive Embedding Norms
Jun 29, 2026Ziwei Su, Junyu Ren, Victor VeitchRepresentation Geometry Contrastive Learning
University of Chicago
The Hidden Cost of Pairwise Verification in Synthetic Speech Source Tracing
Jun 10, 2026Anton Firc, Zbyněk Lička, Vojtěch Staněk +1Representation Geometry Speaker Verification
Structure and Scale in Simplicial Sequence Modelling
May 31, 2026Matthew Farrugia-RobertsRepresentation Geometry Transformer
Department of Computer Science, University of Oxford
MLLM-Microscope: Unlocking Hidden Structure Within Multimodal Large Language Models
May 30, 2026Ravil Mussabayev, Rustam MussabayevRepresentation Geometry Multimodal Large Language Models
Satbayev University
The Geometry of Activity Cliffs: Representation Dependence and Multi-Scale Characterization of Activity Landscapes
May 29, 2026Pawel Dabrowski-Tumanski, Bartosz Topolski, Dariusz Plewczynski +1Representation Geometry Molecular Representation Learning
†Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw 00-662, Poland · ¶Ingenix.AI · §Centre of New Technologies, University of Warsaw, Warsaw 02-097, Poland
NITP: Next Implicit Token Prediction for LLM Pre-training
May 24, 2026Xiangdong Zhang, Debing Zhang, Shaofeng Zhang +3Language Model Pretraining Representation Geometry
School of AI, Shanghai Jiao Tong University · Dots Studio, Xiaohongshu Inc. · University of Science and Technology of China +1
RADAR: Relative Angular Divergence Across Representations
May 21, 2026Xavier Cadet, Mateusz Nowak, Peter ChinRepresentation Geometry Task Transferability Estimation
Dartmouth College
LLM Pretraining Shapes a Generalizable Manifold: Insights into Cross-Modal Transfer to Time Series
May 19, 2026Alexis Roger, Prateek Humane, Zhenghan Tai +4Cross-Modal Learning Language Model Pretraining
Université de Montréal Mila - Quebec AI Institute
Your CLIP has 164 dimensions of noise: Exploring the embeddings covariance eigenspectrum of contrastively pretrained vision-language transformers
May 14, 2026Jakub Grzywaczewski, Dawid Płudowski, Przemysław BiecekRepresentation Geometry Representation Learning
Warsaw University of Technology · Centre for Credible Artificial Intelligence · University of Warsaw
TAPIOCA: Why Task- Aware Pruning Improves OOD model Capability
May 14, 2026Krish Sharma, Omar Naim, Soumadeep Saha +3Representation Geometry LLM Pruning
ANITI, France · Meta · Apple, USA
Where Should Diffusion Enter a Language Model? Geometry-Guided Hidden-State Replacement
May 14, 2026Injin Kong, Hyoungjoon Lee, Yohan JoRepresentation Geometry Diffusion Language Models
Graduate School of Data Science, Seoul National University · Department of Biosystems & Biomaterials Science and Engineering, Seoul National University
Uncovering Symmetry Transfer in Large Language Models via Layer-Peeled Optimization
May 12, 2026Zhehang Du, Hangfeng He, Weijie SuRepresentation Geometry LLM Training
The Wharton School, University of Pennsylvania · University of Rochester
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
HEART: Hyperspherical Embedding Alignment via Kent-Representation Traversal in Diffusion Models
May 8, 2026Arani Roy, Shristi Das Biswas, Kaushik RoyRepresentation Geometry Diffusion-Based Image Editing
Purdue University
Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability
May 4, 2026Yucheng DuRepresentation Geometry LLM Reliability
University of Southern California
Lost in State Space: Probing Frozen Mamba Representations
Apr 30, 2026Bhagyashree Wagh, Akash SinghRepresentation Geometry Representation Collapse
University of Washington · University of Florida
Closed Form Relations and Higher-Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)
Apr 24, 2026Andreas MuellerRepresentation Geometry Lie Group Methods
Institute of Robotics, Johannes Kepler University Linz, Austria
Supervised Learning Has a Necessary Geometric Blind Spot: Theory, Consequences, and Minimal Repair
Apr 23, 2026Vishal RajputAdversarial Training Representation Geometry
1KU Leuven, Belgium.

Oct 7, 2026J/K move · Enter open · S save

Shared Geometry As A Rosetta Stone: Cross-Modal Alignment Without Paired Data

Dominik Schnaus, Thomas Dagès, Daniel Cremers, Xi Wang+1

TU Munich · MCML · Ulm University+2

Cross-Modal Alignment Cross-Modal Representation Transfer Representation Geometry Orthogonal Procrustes Alignment

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Multimodal representations enable zero-shot classification and retrieval, but aligning independently trained models usually requires large amounts of paired data. Yet, the Platonic Representation Hypothesis suggests that models trained on different modalities may converge spontaneously toward a shared representation geometry. But then, do we even need paired examples for cross-modal alignment? Remarkably, we show that paired examples are unnecessary for coarse cross-modal alignment. Our simple Wasserstein Procrustes method with a coarse geometric initialization aligns two disjoint embedding sets by estimating a single orthogonal map without seeing any pairs. Across datasets, modalities, and unimodal models, we show that we can consistently align independently trained representations without pairs, and standard geometric alignment metrics accurately predict when this is possible. Nevertheless, we can naturally benefit from paired examples. In the very few-pair regime, our method substantially outperforms existing ones, while staying competitive with pair-based methods with more added examples. Finally, we demonstrate that the resulting alignments can enable text-to-image generation without paired examples. These results show that independently trained models often share enough geometry to establish cross-modal correspondence with little or no paired data.