Riemannian Manifolds

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18 papers in the last four weeks, with none the four weeks before. 0.2% of all new papers.

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Pointwise Generalization in Deep Neural Networks
May 18, 2026Shaojie Li, Yunbei XuDeep Network Generalization Bounds
National University of Singapore
Dynamic Elliptical Graph Factor Models via Riemannian Optimization with Geodesic Temporal Regularization
May 18, 2026Chuansen Peng, Xiaojing ShenRiemannian Manifolds Factor Graphs
School of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China
The Geometry of Projection Heads: Conditioning, Invariance, and Collapse
May 16, 2026Faris ChaudhryProjection Heads Self-Supervised Learning
Department of Computing, Imperial College London, United Kingdom.
Don't Stop Me Yet: Sampling Loss Minima via Dissipative Riemannian Mechanics
May 14, 2026Albert Kjøller Jacobsen, Leo Uhre Jakobsen, Johanna Marie Gegenfurtner +1Reparameterization Flat Minima
Section for Cognitive Systems, Technical University of Denmark · Center for Quantum Information Physics, New York University
Topology-Preserving Neural Operator Learning via Hodge Decomposition
May 13, 2026Dongzhe Zheng, Tao Zhong, Christine Allen-BlanchetteNeural Operators Graph Laplacians
Princeton University
Distributed Pose Graph Optimization via Continuous Riemannian Dynamics
May 11, 2026Jaeho Shin, Maani Ghaffari, Yulun TianCategory-Level Object Pose Estimation Multi-Robot Systems
University of Michigan Ann Arbor, MI 48109, USA
Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions
May 7, 2026James Rowbottom, Nick Huang, Carola-Bibiane Schönlieb +1Optimal Sensor Placement Posterior Sampling
Department of Mathematics Simon Fraser University Canada
Optimal Transport Audio Distance with Learned Riemannian Ground Metrics
May 7, 2026Wonwoo JeongNeural Audio Distance
Sogang University
Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes
May 5, 2026Aaron Havens, Brian Karrer, Neta ShaulDiffusion Sampling Riemannian Manifolds
FAIR at Meta · Weizmann Institute of Science
Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
May 5, 2026Hanfei Zhou, Lei ShiLogarithmic Sobolev Inequalities Neural Approximations
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China · Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
Flow Matching on Symmetric Spaces
May 5, 2026Francesco Ruscelli, Ferdinando Zanchetta, Rita FioresiRiemannian Flow Matching Riemannian Manifolds
Institute for Mathematics University of Heidelberg 69120 Heidelberg, Germany · Department of Pharmacy and Biotechnologies University of Bologna Bologna, Italy
A second-order method landing on the Stiefel manifold via Newton $\unicode{x2013}$ Schulz iteration
May 4, 2026Xinhui Xiong, Bin Gao, P. -A. AbsilNewton Riemannian Manifolds
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China · ICTEAM Institute, UCLouvain, Belgium
Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
May 4, 2026Benyamin GhojoghRiemannian Optimization Riemannian Manifolds
Waterloo, Ontario, Canada
Model Compression with Exact Budget Constraints via Riemannian Manifolds
May 1, 2026Michael Helcig, Dan AlistarhRiemannian Optimization Token Budget Allocation
ETH Zürich · IST Austria
Decoding High-Dimensional Finger Motion from EMG Using Riemannian Features and RNNs
Apr 24, 2026Martin Colot, Cédric Simar, Guy Cheron +2Surface Electromyography Robotic Hands
Machine Learning Group, ULB, Bruxelles, Belgium · § These authors contributed equally to this work and share ﬁrst authorship. · Neuromove, ULB Neuroscience Institute, ULB, Brussels, Belgium +1
Geometric Decoupling: Diagnosing the Structural Instability of Latent
Apr 20, 2026Yuanbang Liang, Zhengwen Chen, Yu-Kun LaiDiscriminative Congruence Transform Instability
School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom
Complex normalizing flows can almost be information Kähler-Ricci flows
Apr 20, 2026Andrew GracykNormalizing Flows Riemannian Flow Matching
Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States
Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization
Apr 16, 2026Mathias DusRiemannian Optimization Wasserstein Distance
IRMA
Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why
Mar 30, 2026Tushar Sial, Abhishek HalderBregman Divergences Symmetry
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
Coordinate-Independent Robot Model Identification
Mar 15, 2026Yanhao Yang, Ross L. HattonInverse Dynamics System Identification
Collaborative Robotics and Intelligent Systems (CoRIS) Institute at Oregon State University, Corvallis, OR USA
Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery
Nov 24, 2025Sanjeev Manivannan, Chandra Shekar LakshminarayanElectroencephalography Decoding Electroencephalography
Department of Biotechnology · Department of Data Science and Artificial Intelligence
Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
Oct 2, 2025Dhruv Kohli, Sawyer J. Robertson, Gal Mishne +1Tangent Space Data Manifold

May 18, 2026, cs.LGJ/K move · Enter open · S save

Pointwise Generalization in Deep Neural Networks

Shaojie Li, Yunbei Xu

National University of Singapore

Deep Network Generalization Bounds Riemannian Manifolds

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We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear feature-learning regime and builds a new statistical foundation for representation learning. For each trained model, we characterize the hypothesis via a pointwise Riemannian Dimension, derived from the eigenvalues of the learned feature representations across layers. This establishes a principled framework for deriving hypothesis-dependent, representation-aware generalization bounds. These bounds offer a systematic upgrade over approaches based on model size, products of norms, and infinite-width linearizations, yielding guarantees that are orders of magnitude tighter in both theory and experiment. Analytically, we identify the structural properties and mathematical principles that explain the tractability of deep networks. Empirically, the pointwise Riemannian Dimension exhibits substantial feature compression, decreases with increased over-parameterization, and captures the implicit bias of optimizers. Taken together, our results indicate that deep networks are mathematically tractable in practical regimes and that their generalization is sharply explained by pointwise, feature-spectrum-aware complexity.

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