Latent Space Geometry

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29 papers8 papers in the last four weeks, up 60% on the four weeks before. 0.0% of all new papers.

Stable Dimensionality Reduction via Isometric Centroid-Encoder
Oct 24, 2026Tomojit Ghosh, Siva Rama Krishna Prasad Changala, Prathyusha Kanakamalla +1Dimensionality Reduction Latent Space Geometry
Colonel Glenn Hwy, Dayton, OH 45435-0001, USA Department of Computer Science and Engineering Wright State University
When Do Gaussian Priors Fail? A Latent Geometry Investigation of RL Fine-Tuning
Oct 20, 2026Wang RuLatent Space Geometry Diffusion Model Fine-Tuning
Department of Chemical Engineering, Tsinghua University
Learning to Be Guided: Shaping Latent Geometry for Classifier-Free Guidance
Oct 16, 2026Haoming Liu, Junhao Zhu, Shaoyi Zheng +4Latent Space Geometry Diffusion-Based Image Generation
New York University · New York University Shanghai · Georgia Institute of Technology
Native Geometry vs. Linear Recoverability: How Alignment Changes Platonic Scaling
Oct 15, 2026Angus Hoy, Austin Lutterbach, Jasper Chong +2Neural Representation Geometry Latent Space Geometry
EleutherAI SOAR · UniverseTBD · University of Queensland +4
Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models
Oct 13, 2026Junlin Wu, Wen Fan, Dandan ZhangLatent Space Geometry Latent-Space Planning
Imperial College London, London, United Kingdom
Do Neural Networks Learn Structure-Preserving Maps? A Case Study in Latent-to-Hilbert Embeddings
Oct 4, 2026Muhammad Adnan ShahzadRepresentation Learning Latent Space Alignment
Department of Computer Science and Software Engineering (CSSE) Montreal, QC, Canada
GeoLatent: Geometry-Guided Latent Structuring with Routed Optimization for 3D Reasoning
Oct 1, 2026Yakun Zhu, Yi Bin, Yujuan Ding +53D Spatial Reasoning Geometric Representation Learning
Tongji University · The Hong Kong Polytechnic University
Group-Invariant Statistics Determine Embedding Geometry: Harmonic Analysis of Representations from Bach to the Night Sky
Sep 30, 2026Liam Storan, Andreas Tolias, Nina MiolaneWord Embeddings Representation Geometry in Language Models
Stanford University · University of California, Santa Barbara
Latent Space Is Not Flat: Rethinking Latent Structure for 3D Medical Image Synthesis
Sep 26, 2026Haowen Xue, Hao Chen, Hexuan Hu +6Latent Space Geometry Medical Image Synthesis
Hohai University · University of Cambridge · National University of Defense Technology
Beyond Gaussian Worlds: Latent Geometry Matters for JEPAs
Sep 18, 2026Léo Nicollier, Enric Meinhardt-Llopis, Marc Pic +2Joint-Embedding Predictive Architecture Latent Space Geometry
CB, ATT · Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centre Borelli, France · Advanced Track and Trace +5
Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory
Sep 16, 2026Michael W. Trosset, Carey E. PriebeSemi-Supervised Learning Decision-Making under Uncertainty
Department of Statistics, Indiana University. · Department of Applied Mathematics & Statistics, Johns Hopkins University.
$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition
Sep 14, 2026Xingrun Li, Yusuke Mukuta, Xin Yang +2Finsler Geometry Graph Representation Learning
The University of Tokyo · Stanford University
Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces
Aug 31, 2026Jing Wang, Shuaiqiang Liu, Cornelis VuikConstrained Generative Modeling Neural Representation Geometry
Delft Institute of Applied Mathematics, Delft University of Technology
Unsupervised Latent Space Alignment with Hyperspherical Geodesic Matching
Aug 28, 2026Cameron Ryan, Vivek Sivaraman Narayanaswamy, Kowshik Thopalli +1Latent Space Alignment Latent Space Geometry
Northeastern University, Boston, MA 02115. Work performed during a summer internship at Lawrence Livermore National Laboratory · Lawrence Livermore National Laboratory, Livermore, CA 94551-0808.
Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off
Aug 25, 2026Peter Flo, Luca GrossmannLatent Space Geometry Neural Representation Geometry
Harvard University, Cambridge, MA, USA.
Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
Aug 25, 2026Sohini Gupta, Michael Gao, Bahareh TolooshamsDisentangled Representation Learning Latent Space Geometry
University of Alberta Alberta Machine Intelligence Institute (Amii) · University of Alberta Alberta Machine Intelligence Institute (Amii) Canada CIFAR AI Chair
On the Geometry of Music Bandwidth Extension in Latent Spaces of Audio Codecs
Aug 4, 2026Hendrik Vincent Koops, Hao Hao Tan, Elio QuintonNeural Audio Codecs Neural Representation Geometry
Music & Audio Machine Learning Lab · Universal Music Group, London, U.K.
I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory
Jun 29, 2026Igor HalperinIntrinsic Dimensionality Random Matrix Theory
Constructing VAE Latent Spaces with Prescribed Topology
Jun 5, 2026Jilles S. van Hulst, Jakub M. Tomczak, W. P. M. H. Heemels +1Variational Autoencoders Manifold Learning
Control Systems Technology Section, Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. · The research is carried out as part of the ITEA4 20216 ASIMOV project.
SPHERE-JEPA: Spherical Prediction with Homogeneous Embeddings
May 26, 2026L{é}o Nicollier, Max Dunitz, Marc Pic +3Self-Supervised Learning Joint-Embedding Predictive Architecture
CB,ATT · ATT · CB,IFUMI +1
Structure Retention in Embedding Spaces as a Predictor of Benchmark Performance
May 21, 2026Amanda Myntti, Jenna Kanerva, Veronika Laippala +1Text Embedding Evaluation Text Embedding Models
TurkuNLP, University of Turku, Finland · ELLIS Institute Finland
Scale Determines Whether Language Models Organize Representation Geometry for Prediction
May 16, 2026Weilun XuLanguage Model Pretraining Neural Representation Geometry
School of Computer and Communication Sciences ´Ecole Polytechnique F´ed´erale de Lausanne
Aligning Latent Geometry for Spherical Flow Matching in Image Generation
May 14, 2026Tuna Han Salih Meral, Kaan Oktay, Hidir Yesiltepe +2Flow Matching Neural Representation Geometry
Virginia Tech · fal
Geometric Decoupling: Diagnosing the Structural Instability of Latent
Apr 20, 2026Yuanbang Liang, Zhengwen Chen, Yu-Kun LaiNeural Representation Geometry Latent Diffusion Models
School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom
Understanding Latent Diffusability via Fisher Geometry
Apr 3, 2026Jing Gu, Morteza Mardani, Wonjun Lee +2Information Geometry Neural Representation Geometry
School of Mathematics, University of Minnesota · NVIDIA · Department of Mathematics, The Ohio State University +1
Denoising distances beyond the volumetric barrier
Apr 1, 2026Han Huang, Pakawut Jiradilok, Elchanan MosselManifold Learning Latent Space Geometry
Manifold-Matching Autoencoders
Mar 17, 2026Laurent Cheret, Vincent Létourneau, Isar Nejadgholi +3Multidimensional Scaling Autoencoders
Department of Computer Science, University of Ottawa, Ottawa, Canada · MILA, Montréal, Canada · National Research Council of Canada, Ottawa, Canada
Symmetry in language statistics shapes the geometry of model representations
Feb 16, 2026Dhruva Karkada, Daniel J. Korchinski, Andres Nava +2Representation Learning Neural Representation Geometry
1UC Berkeley · 2EPFL · 3Johns Hopkins +1
Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
Nov 4, 2025Ronald KatendeIntrinsic Dimensionality Information Bottleneck
Department of Mathematics, Kabale University, Katuna Road, Kikungiri Hill, Kabale, 317, Uganda

Oct 24, 2026J/K move · Enter open · S save

Stable Dimensionality Reduction via Isometric Centroid-Encoder

Tomojit Ghosh, Siva Rama Krishna Prasad Changala, Prathyusha Kanakamalla, Harigovind Harikumar

Colonel Glenn Hwy, Dayton, OH 45435-0001, USA Department of Computer Science and Engineering Wright State University

Dimensionality Reduction Latent Space Geometry

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Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geometry, leading to variability in the relative arrangement of classes across independent runs. Such variability limits the reproducibility and interpretability of low-dimensional embeddings. We propose the Isometric Centroid-Encoder (ICE), a supervised dimensionality reduction framework in which class centroids are learned directly in the latent space while preserving a prescribed pairwise class-centroid geometry. Unlike existing centroid- or prototype-based methods that primarily encourage intra-class compactness, ICE explicitly regularizes the relative arrangement of latent class centroids. Unlike multidimensional scaling and many metric-learning approaches that preserve sample-level relationships, ICE operates on class centroids, preserving inter-class geometry without requiring large numbers of sample-pair or triplet constraints. We further show that the intrinsic dimensionality required to represent the centroid-distance configuration of

M

classes is at most

M-1

, explaining the observed saturation of distance-preservation measures as the latent dimensionality increases. To quantify embedding reproducibility, we introduce the Centroid Neighborhood Stability (CNS) metric, which measures the consistency of class-level neighborhood topology across independent runs and complements existing embedding quality measures. Experiments on image and biological datasets demonstrate that ICE produces stable embeddings with improved preservation of class-centroid geometry while remaining computationally efficient. Additional analyses of optimization dynamics, sensitivity, and preprocessing further provide practical insights into latent dimensionality and explicit geometry modeling for supervised dimensionality reduction.