Riemannian Geometry

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Optimization over covariance matrices with a parameterized metric
Sep 15, 2026Yibang Li, Bamdev Mishra, Pratik Jawanpuria +1Riemannian Optimization Second-Order Optimization
Nanyang Technological University, Singapore · Microsoft India · Indian Institute of Technology Bombay, India
Information-Induced Training Geometry: Exact Reduction, Canonical Completion, and Structured Expressivity
Sep 14, 2026Zavier LiInformation Geometry Riemannian Optimization
Xidian University Xi’an, China
The Field Knows: Cross-Dimensional Geometry from Navigation to Black Holes
Aug 3, 2026Chenghao XuGeometric Representation Learning Riemannian Geometry
School of Artificial Intelligence and Robotics and National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, Changsha, Hunan, China
Sphere Retraction Normalizations
Aug 2, 2026Jie Zhang, Cheng-Fang Su, Yi-Jui Huang +1Residual Learning Riemannian Geometry
Department of Computer Science and Information Engineering, National Central University, Taiwan · Department of Applied Mathematics, National Yang Ming Chiao Tung University, Taiwan · Department of Mathematics, National Central University, Taiwan
Landmark shape spaces with induced metrics
Jul 30, 2026Sarang Joshi, Peter W. Michor, Stefan SommerNon-Rigid Shape Correspondence Riemannian Geometry
A Riemannian View on Active Subspaces
Jul 28, 2026Zachary GreyDimensionality Reduction Riemannian Geometry
Riemannian Geometry for Pre-trained Language Model Embeddings
Jul 8, 2026Szczepan Konior, Alexandre Quemy, Przemysław Klocek +2Sentence Embeddings Geometric Representation Learning
IBM Automation and AI, Krakow, Poland · Hother, Krakow, Poland · University of Warsaw +1
On the convergence of graph Laplacians with a symmetric divergence
Jul 7, 2026Liane XuManifold Learning Riemannian Geometry
Program in Applied and Computational Mathematics, Princeton University
Fisher Width: A Geometric Measure of Complexity on Statistical Manifolds
Jun 16, 2026Vu Khac KyInformation Geometry Riemannian Geometry
Department of Mathematics, FPT University, Vietnam
Riemannian Metric Matching for Scalable Geometric Modeling of Distributions
Jun 12, 2026Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst +2Geometric Representation Learning Metric Learning
Department of Computer Science, University of Oxford, Oxford, UK · Institute of Artificial Intelligence, Medical University of Vienna, Vienna, Austria · EPFL, Lausanne, Switzerland +1
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
Jun 11, 2026Srinivas NambirajanMarkov Random Fields Riemannian Geometry
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Jun 6, 2026Kisung YouRiemannian Geometry Optimal Transport
Department of Mathematics Baruch College
Geodesic Flow Matching on a Riemannian Degradation Manifold for Blind Image Restoration
Jun 4, 2026Akshay Janardan Bankar, Ankita Chatterjee, Sayan Banerjee +3Flow Matching Riemannian Flow Matching
Samsung Research Institute, Bangalore, India
Knowledge Manifold: A Riemannian Geometric Framework for Semantic Mapping and Geodesic Analysis of Scientific Literature
Jun 4, 2026Tomonaga Okabe, Kazuhiko KomatsuKnowledge Representation Manifold Learning
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan · Research Center for Green X-Tech, Tohoku University, 6-6-11, Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan
Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
Jun 2, 2026Li Sun, Zhenhao Huang, Yiding Wang +3GNN Expressivity Geometric Representation Learning
Beijing University of Posts and Telecommunications, Beijing, China · North China Electric Power University, Beijing, China · University of Cambridge, Cambridge, UK +1
Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds
Jun 1, 2026Phone Thiha Kyaw, Jonathan KellyMotion Planning Riemannian Geometry
Space and Terrestrial Autonomous Robotic Systems (STARS) Laboratory, University of Toronto Institute for Aerospace Studies (UTIAS), Toronto, Ontario M3H 5T6, Canada
Riemannian Gradient Descent for Low-Rank Architectures
Jun 1, 2026Nicholas KnightRiemannian Optimization Low-Rank Approximation
NVIDIA
Riemannian Optimization for Hadamard Products of Low-Rank Matrices
May 31, 2026Pratik Jawanpuria, Ankish Chandresh, Bamdev MishraRiemannian Optimization Low-Rank Approximation
Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay, India · Microsoft India
Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering
May 24, 2026Narmeen Oozeer, Shivam Raval, Philip Quirke +4Language Model Steering Representation Steering
Martian · Harvard University · Thoughtworks +1
Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
May 22, 2026Willem Diepeveen, Deanna NeedellManifold Learning Dimensionality Reduction
Department of Mathematics University of California, Los Angeles Los Angeles, CA 90095, USA
Disentanglement Beyond Generative Models with Riemannian ICA
May 21, 2026Edmond CunninghamDisentangled Representation Learning Independent Component Analysis
University of Massachusetts Amherst
Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces
May 21, 2026Mario Severino, Manuela Moretto, Robert A. McCutcheon +1Functional Connectivity Neuroimaging
Department of Information Engineering, University of Padova, Padova, Italy · Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience (IoPPN), King’s College London, London, United Kingdom · Department of Psychiatry, University of Oxford, Warneford Hospital, Warneford Ln, Headington, Oxford OX3 7JX, United Kingdom +2
Riemannian Networks over Full-Rank Correlation Matrices
May 18, 2026Ziheng Chen, Xiaojun Wu, Bernhard Schölkopf +1Geometric Representation Learning Manifold Learning
Department of Information Engineering and Computer Science, University of Trento, Trento, Italy · Max Planck Institute for Intelligent Systems, Tübingen, Germany · School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China
Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learning
May 6, 2026Tushar Das, Subrata Dutta, Sarmistha Neogy +1Geometric Representation Learning Metric Learning
National Institute of Technology Jamshedpur · Jadavpur University · Machine Vision and Intelligence Lab National Institute of Technology Jamshedpur
Entropic Riemannian Neural Optimal Transport
May 5, 2026Alessandro Micheli, Silvia Sapora, Anthea Monod +1Riemannian Geometry Optimal Transport
Imperial College London London, UK · University of Oxford Oxford, UK · Statens Serum Institut Copenhagen, Denmark +1
Flow Matching on Symmetric Spaces
May 5, 2026Francesco Ruscelli, Ferdinando Zanchetta, Rita FioresiFlow Matching Riemannian Flow Matching
Institute for Mathematics University of Heidelberg 69120 Heidelberg, Germany · Department of Pharmacy and Biotechnologies University of Bologna Bologna, Italy
Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
May 4, 2026Benyamin GhojoghRiemannian Optimization Riemannian Geometry
Waterloo, Ontario, Canada
MOC-3D: Manifold-Order Consistency for Text-to-3D Generation
May 3, 2026Chenyang Fan, Junshi Cheng, Wen Yang +5Multi-View Consistency Text-to-3D Generation
Chongqing Normal University Chongqing, China
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
Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoders
Feb 10, 2026Amandeep Kumar, Vishal M. PatelFlow Matching Diffusion Transformer
Johns Hopkins University

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Optimization over covariance matrices with a parameterized metric

Yibang Li, Bamdev Mishra, Pratik Jawanpuria, Cyrus Mostajeran

Nanyang Technological University, Singapore · Microsoft India · Indian Institute of Technology Bombay, India

Riemannian Optimization Second-Order Optimization Matrix Optimization Riemannian Geometry

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The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by

X^{p}LX^{q}+X^{q}LX^{p}=U

, solved for

L

at each tangent vector

U

, that contains all three as exact members, at

(0,0)

(1,0)

and

(1,1)

, and extends past them. We treat the choice of member as a particular way of preconditioning for a given problem. To this end, we analyze the conditioning of the Riemannian Hessian at the solution. We show that it obeys a lower bound that depends on

(p,q)

only through the exponent

r=p+q

. When the Euclidean Hessian is a pure power that mixes no eigendirections, the member

p=q=r/2

attains that bound, and a closed-form criterion identifies the other members that do. We discuss ways to tune

r

for a given problem. Experiments on real covariance data confirm the predicted conditioning and the benefit of tuning

r

. A task covariance example shows a further gain from tuning the shape.

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