Manifolds

Follow this field Ask about this field

Recent momentum

emerging

0 papers in the last 28 days · 0.0% of indexed attention

Twelve weeks of publication activity for this topic as it is defined today.

Weekly history

Recent digests

What was published in this field, kept on the site without email delivery.

Period ending 2026-09-21

8 new papers

A weekly snapshot of new work published in Manifolds.

Inside this field

Focused directions

Focused topic

Manifolds

Within Manifolds

120 papersExplore

Focused topic

Statistical Manifold

Within Manifolds

35 papersExplore

Focused topic

Manifold Learning Method

Within Manifolds

33 papersExplore

175 papers

Latest in Manifolds

Browse all topics →

When Riemann flows with Wasserstein: Generative Modeling of Probability Distributions on Manifolds
Sep 22, 2026Doron Haviv, Edward De Brouwer, Rishabh Anand +4Statistical Manifold
Special Lagrangian cones in Deep Learning
Sep 17, 2026Tejas Kotwal, Govind MenonManifolds Lagrangian Methods
Stiefel Attention: When the Geometry of Transformer Projection Matrices Dominates Optimizer Choice---and When It Does Not
Sep 16, 2026Rubén Darío GuerreroRiemannian Optimization Adam
Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory
Sep 16, 2026Michael W. Trosset, Carey E. PriebeManifold Learning Method Low-Dimensional Structure
Learning Array Signal Topologies as Conditional Neural Manifolds
Sep 16, 2026Julian P. Merkofer, Vincent van de Schaft, Ruud J. G. van SlounManifolds Super-Resolution Framework
Approximating High Dimensional Self-Motion Manifolds via Deep Generative Models
Sep 16, 2026Haitao Gao, Yang Song, Liao WuRobotic Arms Motion Planners
Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds
Sep 15, 2026Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov +3Generative Models Score-Based Diffusion Model
Bracketing Uncertainty in Clustering Under the Manifold Hypothesis
Sep 15, 2026Savik Kinger, Luciano Dyballa, Steven W. ZuckerManifold Learning Method Input Uncertainties
Low-Dimensional Embeddings for Gaussian Kernels on Manifolds
Sep 14, 2026Soumik Dutta, Kunal DuttaKernel Method Manifolds
Solving Few-Shot Multiobjective Multitask Optimization via Iterative Sequential Transfer
Sep 12, 2026Tingyang Wei, Haofeng Wu, Ananda Phan Iman +3Multi-Objective Optimization Transfer Learning
Global Divergence, Local Convergence: Representation Geometry in SSMs and Transformers
Sep 8, 2026Amit Ben-Artzy, Roy SchwartzTransformer Architectures Representational Capacity
Geometry-Aware Bayesian Parameter-Efficient Fine-Tuning on the Stiefel Manifold via Stein Variational Gradient Descent
Sep 8, 2026Quang-Duy Tran, Trung Le, Bao Duong +2Manifolds Parameter-Efficient Fine-Tuning
From Explicit References to Scene Manifolds: Distributional Fidelity and Realism for Radiance Field Quality Assessment
Sep 7, 2026Saeed Mahmoudpour, Gi-Mun Um, Hyon-Gon Choo +1Novel View Synthesis Perceptual Quality
Multi-step Proximal Policy Improvement in Offline Reinforcement Learning
Sep 3, 2026Soohyun Choi, Seonvin Cho, Songnam HongOffline Reinforcement Learning Proximal Policy Optimization
Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control
Sep 3, 2026Ecem Bozkurt, Antonio OrtegaKernel Method Manifold Learning Method
Aggregating Neighbor Embedding Projection and Rank-Based Manifold Learning for Image Retrieval
Sep 2, 2026Vinicius Atsushi Sato Kawai, Gustavo Rosseto Leticio, Lucas Pascotti Valem +1Composed Image Retrieval Manifold Learning Method
Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation
Sep 1, 2026Sebastien Tchitchek, Julien TiernyWasserstein Distance Persistent Homology
DK-GBMKKM: Dynamic Kernel-Space Granular-Ball Multiple Kernel $k$ -Means Clustering
Sep 1, 2026Xiaoyu Lian, Yuchao Zhang, Shuyin Xia +2Granular-Ball Computing K-Means
Proximity3D: Shape from Capacitive Proximity on Sensing Manifold
Aug 31, 2026Hao Chen, Chenming Wu, Chun Ping Lam +6Geometric Reconstruction Sensors
Off-Manifold Refinement: Guiding Video Generators with a Frozen World Model
Aug 30, 2026Hai Nguyen-Truong, Tuan-Anh Vu, Dang HuynhLong Video Generation World Models
Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction
Aug 30, 2026Louen Pottier, Louis Lesueur, Anders ThorinMasked Autoencoders Dimensionality Reduction
Kähler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold
Aug 20, 2026Andrew GracykLoss Landscape Manifolds
Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms
Aug 11, 2026Florian Beier, Stephan EcksteinGromov--Wasserstein K-Means
Spectral Embeddings of Degree- $α$ Laplacians in Random Dot Product Graphs
Aug 11, 2026John Park, Ning HaoGraph Laplacians Image Clustering
Beyond Decision Boundaries: Relational Geometry Attacks on Contrastive Embedding Manifolds
Aug 10, 2026Fei Zhao, Peiyuan Zhang, Xi Li +2Adversarial Examples Contrastive
HoloAegis: Frozen Representation, Topological Inference --- Minimally Parametric Safety Manifolds and Their Capability Boundaries for LLM Guardrails
Aug 9, 2026Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee +3Large Language Model Safety Large Language Model Hallucination
Stochastic gradient descent with discontinuity across a manifold
Aug 7, 2026Vivek S. BorkarStochastic Gradient Descent Manifolds
Muon on the Stiefel Manifold Admits an Exact Closed-Form Update
Aug 6, 2026Mikhail Solonko, Molozhavenko Alexander, Maxim RakhubaMuon Optimizer Riemannian Optimization
Flow-Map Distillation on Relation Manifolds for Image Restoration
Aug 6, 2026Zihao He, Songhua LiuImage Restoration Self-Supervised Reconstruction Method
Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifolds
Aug 5, 2026Yizhu Wang, Mu Niu, Xiaochen YangIdentity-Conditioned Latent Diffusion Models Latent Diffusion Model
Physics-informed reduced-order modelling with equivariant spectral submanifolds
Aug 4, 2026Georg MaierhoferReduced-Order Models Manifolds
Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory
Aug 3, 2026Zhaotian Gu, Jie Su, Weiwei Wang +3Recurrent Neural Networks Synaptic Plasticity
Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matching
Aug 1, 2026Hongjie Wu, Yiping Xie, Jiancheng LvIll-Posed Inverse Problem Inverse Problem
Manifold-GS: Certified Hybrid Assets via Varifold-Conservative Gaussian Splatting
Jul 31, 2026Boyang Li3D Gaussian Splats Gaussian Splatting
Retraction-Free Optimization over the Stiefel Manifold for the LoRA Fine-Tuning
Jul 28, 2026Yuan Zhang, Jiang Hu, Zhijian Lai +2Low-Rank Adaptation Riemannian Optimization
Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning
Jul 28, 2026Jintian Ji, Xingsu Li, Songhe FengManifold Learning Method Multi-View
Why does Greedy Search produce Optimal Clustering Outcomes? A Fixed-Core Assignment Theory
Jul 27, 2026Kaifeng Zhang, Kai Ming Ting, Sanjay ChawlaImage Clustering Manifold Learning Method
Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian
Jul 25, 2026Alvaro Almeida Gomez, Jorge Duque FrancoGraph Laplacians Statistical Manifold
Queryable Self-Organizing Maps: A Database Abstraction for Topology-Driven Data Exploration
Jul 24, 2026Denis Mayr Lima Martins, Gottfried VossenData Mining Manifold Learning Method
Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers
Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural Partial Differential Equation Solvers Riemannian Optimization
Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications
Jul 23, 2026Zhuan Liang, Zheng ZhaiManifold Learning Method Regularization Techniques
Fisher Widths: Local Learning Geometry and Anisotropic Recovery
Jul 22, 2026Vu Khac KyFisher Information Sparse Recovery
A Bayesian Framework for Built-in Input Dimension Reduction for Gaussian Process Modeling
Jul 21, 2026Eric Herrison Gyamfi, Emily L. Kang, Bledar A. Konomi +1Gaussian Process Dimensionality Reduction
Riemannian Deep Learning: Modules, Networks, and Geometries
Jul 21, 2026Ziheng ChenStatistical Manifold Manifolds
NSMA: Neuro-Symbolic Manifold Alignment for Generalizable Adaptive Bitrate Streaming under Texture Shift
Jul 21, 2026Zhiqiang He, Zhi LiuNeuro-Symbolic Framework Manifolds
Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds
Jul 12, 2026Swagatam Das, Vaclav SnaselGeneralized U-Statistics Concentration Inequalities
Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima
Jul 9, 2026Lachlan Ewen MacDonald, René VidalGradient Descent Condition Number
AutoAnchor: Stable Diffusion Unlearning Using Cross-Attention as a Manifold Surrogate
Jul 9, 2026Siyuan Wen, Jiahao Zeng, Ningning DingText-To-Image Diffusion Models Exact Unlearning
Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware
Jul 8, 2026Oskar von Seeler, Christian Tetzlaff, Andrew LehrNeuromorphic Hardware Neural Control
Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE
Jul 8, 2026Alexandre QuemyIntrinsic Dimensionality Manifolds
Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Jul 7, 2026Kisung YouImportance Sampling Wasserstein Distance
EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning
Jul 7, 2026Przemysław RolaManifold Learning Method Geodesic
On the convergence of graph Laplacians with a symmetric divergence
Jul 7, 2026Liane XuGraph Laplacians Riemannian Manifolds
FlatManifold: Robust Continual Learning under Severe Label Noise and Domain Shifts via Intrinsic Manifold Flattening
Jul 6, 2026Rai Hisada, Kanji TanakaEfficient Continual Learning Noisy Labels
RSLoRA: Training-free Rank Allocation for LoRA via Representational Sensitivity Probing
Jul 5, 2026Jiaqi Liu, Haidong Kang, Qihui Zhao +1Gradient-Free Rank Allocator Low-Rank Adaptation
MANCE: Manifold Aware Concept Erasure
Jul 4, 2026Matan Avitan, Yoav Goldberg, Yanai ElazarConcept Erasure Manifolds
Missing Data Imputation under Manifold Hypothesis
Jul 3, 2026Zelong Bi, Amuchechukwu Ibenegbu, Sarat MokaMultivariate Time Series Imputation Imputation
CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification
Jul 3, 2026Alexandre L. M. LevadaStatistical Manifold Adaptive Sampling
Diffeomorphic Optimization
Jul 1, 2026Ludwig Winkler, Andrew Leaver-Fay, Joseph Kleinhenz +1Protein Design Manifolds
Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifold
Jul 1, 2026Yunsung Lee, Hyeongmin LeeReward-Guided Diffusion Training-Free

Sep 22, 2026 · cs.LGJ/K move · Enter open · S save

When Riemann flows with Wasserstein: Generative Modeling of Probability Distributions on Manifolds

Doron Haviv, Edward De Brouwer, Rishabh Anand, Rex Ying+3

Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: distributions over probability measures on non-Euclidean domains. Existing generative methods largely assume Euclidean geometry and fail to capture this structure. We introduce Riemannian Wasserstein Entropic Flow Matching (RWEFM), a generative framework on the Wasserstein space

\mathcal{P}_2(\mathcal{M})

of a Riemannian manifold

(\mathcal{M},g)

. RWEFM is trained by regressing a neural vector field onto Riemannian optimal transport velocities, using McCann displacement interpolations as conditional paths. We confirm theoretically that this construction leads to a valid flow matching approach on

\mathcal{P}_2(\mathcal{M})

and introduce the Riemannian Entropic Map, a GPU-efficient approximation of the optimal transport map on manifolds. Our experiments show that by respecting the intrinsic geometry of the data, RWEFM can generate whole single-cell samples in hyperspherical latent spaces and protein conformational ensembles on the torus. As RWEFM requires only a geodesic distance and a projection operator, it is not restricted to manifolds with closed-form geometry, which we demonstrate by generating distributions on a general triangulated mesh.

Statistical Manifold

Open paper Ask about it PDF