Riemannian Optimization

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Period ending 2026-09-14

1 new paper

A weekly snapshot of new work published in Riemannian Optimization.

Period ending 2026-09-07

2 new papers

A weekly snapshot of new work published in Riemannian Optimization.

31 papers

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Optimization over covariance matrices with a parameterized metric
Sep 15, 2026Yibang Li, Bamdev Mishra, Pratik Jawanpuria +1Riemannian Optimization Covariance Estimation
Riemannian Optimization for Multi-Player Quantum Games on Product Unitary Manifolds
Sep 7, 2026Alireza Habibi, Setareh MaghsudiNash Equilibria Riemannian Optimization
Stochastic Optimization of Tree Tensor Networks
Sep 1, 2026Marius Willner, Maximilian Scharf, André Uschmajew +2Tensor Networks Neural Network Optimization
Controlling Refusal Behavior of LLMs via Stiefel-Constrained Rotation Steering
Aug 31, 2026Kirill Bunin, Dmitry Bylinkin, Vladimir Aletov +3Steering Refusals
Retraction-Free Optimization over the Stiefel Manifold for the LoRA Fine-Tuning
Jul 28, 2026Yuan Zhang, Jiang Hu, Zhijian Lai +2Riemannian Optimization Manifolds
Sparse Gaussian-Mixture-Model Q-Functions via Hadamard Overparametrization for Online Reinforcement Learning
Jul 26, 2026Minh Vu, Konstantinos SlavakisRiemannian Optimization Over-Parameterized Neural Networks
Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers
Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural Partial Differential Equation Solvers Riemannian Optimization
Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions
Jul 22, 2026Zhanyuan Cai, Emre Sahinoglu, Shahin ShahrampourRiemannian Optimization Convex Optimization
Beyond Euclidean Clipping: Overcoming Exploration Collapse in LLM RL via Riemannian Isometric Policy Optimization
Jul 11, 2026Zhicheng Cai, Xinyuan Guo, Hanlin Wu +4Gradient Clipping Riemannian Optimization
Learning Adaptive Solvers for Distributed Factor Graph Optimization on Matrix Lie Groups
Jul 9, 2026Jaeho Shin, Maani Ghaffari, Yulun TianRiemannian Optimization Lie Group
Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
Jul 8, 2026Jianing Liu, Dong H. ZhangRiemannian Optimization Least Squares
Bridging the Manifold Gap: Riemannian Residual Line Search for One-Step Image Editing
Jun 23, 2026Hongzhu Yi, Zhongtian Luo, Tong Li +2Diffusion Editing Image Editing
Decentralized Pose Graph Riemannian Optimization for Object-based Multi-Robot SLAM
Jun 23, 2026Yixian Zhao, Yan Huang, Yang Xu +2Simultaneous Localization And Mapping Multi-Robot Motion Planning
A Riemannian Approach to Low-Rank Optimal Transport
Jun 10, 2026Pratik Jawanpuria, Bamdev MishraOptimal Transport Low-Rank Factorization
Generalized-CVO: Fast and Correspondence-Free Local Point Cloud Registration with Second Order Riemannian Optimization
Jun 8, 2026Ray Zhang, Marcus Greiff, Thomas Lew +1Point Cloud Registration Point Clouds
Riemannian Gradient Descent for Low-Rank Architectures
Jun 1, 2026Nicholas KnightLow-Rank Factorization Riemannian Optimization
Riemannian Optimization for Hadamard Products of Low-Rank Matrices
May 31, 2026Pratik Jawanpuria, Ankish Chandresh, Bamdev MishraRiemannian Optimization Low-Rank Factorization
Riemannian Stochastic Optimization for Sufficient Dimension Reduction
May 29, 2026Thibault Pautrel, François PortierDimensionality Reduction Riemannian Optimization
Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling
May 29, 2026Dmitrii Feoktistov, Timofey Belinsky, Andrey Veprikov +2Adaptive Optimizers Stochastic Gradient Descent
Dynamic Elliptical Graph Factor Models via Riemannian Optimization with Geodesic Temporal Regularization
May 18, 2026Chuansen Peng, Xiaojing ShenRiemannian Manifolds Factor Graphs
Distributed Pose Graph Optimization via Continuous Riemannian Dynamics
May 11, 2026Jaeho Shin, Maani Ghaffari, Yulun TianRiemannian Optimization Robust Pose Estimation
Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
May 10, 2026Yibang Li, Bihari Lal Pandey, Ravi Sah +4Muon Spectral Norm
Demystifying Manifold Constraints in LLM Pre-training
May 6, 2026Kang An, Jiaxiang Li, Donald Goldfarb +1Large Language Model Post-Training Riemannian Optimization
Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
May 4, 2026Benyamin GhojoghRiemannian Optimization Riemannian Manifolds
Model Compression with Exact Budget Constraints via Riemannian Manifolds
May 1, 2026Michael Helcig, Dan AlistarhRiemannian Optimization Large Language Model Compression
BOOOM: Loss-Function-Agnostic Black-Box Optimization over Orthonormal Manifolds for Machine Learning and Statistical Inference
Apr 23, 2026Beomchang Kim, Subhrajyoty Roy, Priyam DasRiemannian Optimization Black-Box Optimization
Safety-Critical Contextual Control via Online Riemannian Optimization with World Models
Apr 21, 2026Tongxin LiModel Predictive Control Safety Constraints
Fisher Decorator: Refining Flow Policy via a Local Transport Map
Apr 20, 2026Xiaoyuan Cheng, Haoyu Wang, Wenxuan Yuan +4Offline Safe Reinforcement Learning Kullback-Leibler Regularization
Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization
Apr 16, 2026Mathias DusPolicy Optimization Riemannian Optimization
Smooth Quasar-Convex Optimization with Constraints
Oct 2, 2025David Martínez-RubioNonconvex Convex Optimization
Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates
Mar 31, 2025Flavia Esposito, Andersen AngRiemannian Optimization Low-Rank Factorization

Sep 15, 2026 · math.OCJ/K move · Enter open · S save

Optimization over covariance matrices with a parameterized metric

Yibang Li, Bamdev Mishra, Pratik Jawanpuria, Cyrus Mostajeran

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.

Riemannian Optimization Covariance Estimation

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