Optimal Transport

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Optimal transport studies how probability mass can be moved between distributions at minimum cost, giving a geometric way to compare data even when samples do not correspond one-to-one. Wasserstein distances and transport maps describe this geometry, while Gromov–Wasserstein methods compare relational structure when data live in different spaces. Practical approaches include entropic regularization with Sinkhorn algorithms, sliced and low-rank approximations, and neural transport maps used in generative modeling, domain adaptation, and trajectory inference. A central challenge is balancing computational and statistical scalability with faithful transport, especially when choosing regularization or relaxing exact mass constraints.

Latest papers

289 papers48 papers in the last four weeks, up 17% on the four weeks before. 0.3% of all new papers.

Optimal Transport for LLM Reward Modeling from Noisy Preference
May 7, 2026Licheng Pan, Haochen Yang, Haoxuan Li +8Reward Modeling Noisy-Label Learning
Zhejiang University · Xiaohongshu Inc · National University of Singapore +2
Stability of the Monge Map in Semi-Dual Optimal Transport
May 7, 2026Anton Selitskiy, David MillardOptimal Transport
Dept. of Electrical and Computer Engineering Stony Brook University Stony Brook, NY 11790, USA · Dept. of Electrical and Computer Engineering University of Rochester Rochester, NY 14627, USA
Locality-aware Private Class Identification for Domain Adaptation with Extreme Label Shift
May 7, 2026Chuan-Xian Ren, Cheng-Jun Guo, Hong YanLabel Shift Unsupervised Domain Adaptation
School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China · Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China
Optimal Transport Audio Distance with Learned Riemannian Ground Metrics
May 7, 2026Wonwoo JeongSpeech Generation Evaluation Metric Learning
Sogang University
Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport
May 6, 2026Philip Naumann, Jacob Kauffmann, Klaus-Robert Müller +1Distribution Shift Optimal Transport
BIFOLD – Berlin Institute for the Foundations of Learning and Data, 10587 Berlin, Germany · Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany · Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul 02841, Korea +2
UniVer: A Unified Perspective for Multi-step and Multi-draft Speculative Decoding
May 6, 2026Yepeng Weng, Qiao Hu, Takehisa YairiSpeculative Decoding LLM Inference Acceleration
The University of Tokyo · 2Lenovo AI Technology Center · National Center for Mathematics and Interdisciplinary Sciences (NCMIS), AMSS, CAS
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
Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions
May 5, 2026Haruto Nakashima, Siddhartha Ganguly, Kenji KashimaSemidefinite Programming Stochastic Optimal Control
The Applied Mathematics and Physics Department, Graduate School of Informatics, Kyoto University, Kyoto, Japan · Daniel Guggenheim School of Aerospace, Georgia Institute of Technology, Atlanta, USA
A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport
May 5, 2026Ling Liang, Lei YangGradient Descent Nonconvex Optimization
Department of Mathematics The University of Tennessee Knoxville, TN 37916, USA · School of Computer Science and Engineering Guangdong Province Key Laboratory of Computational Science Sun Yat-sen University Guangzhou, Guangdong 510275, China
Sampling-Based Control via Entropy-Regularized Optimal Transport
May 4, 2026Vincent Pacelli, Akash Ratheesh, Evangelos A. TheodorouRobotic Control Nonlinear MPC
Autonomous Control and Decision Systems Laboratory Georgia Institute of Technology
Analytic Bridge Diffusions for Controlled Path Generation
May 3, 2026Michael ChertkovStochastic Optimal Control Schrödinger Bridges
Program in Applied Mathematics & Department of Mathematics University of Arizona, AZ 85721, USA
Data-Driven, Geometry-Aware Optimal-Transport Calibration of Flavor Tagger
May 2, 2026Yeonjoon Kim, Un-ki YangModel Calibration Optimal Transport
Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
Apr 29, 2026Shayan Hundrieser, Insung Kong, Johannes Schmidt-HieberInput Convex Neural Networks Neural Network Approximation Theory
*Department of Applied Mathematics, University of Twente, Enschede, The Netherlands
Block-Wise Differentiable Sinkhorn Attention: Tail-Refinement Gradients with a Gap-Aware Dustbin Bridge
Apr 28, 2026Dylan FordeAutomatic Differentiation Transformer Attention
Independent Researcher
Sliced-Regularized Optimal Transport
Apr 27, 2026Khai NguyenOptimal Transport
The University of Texas at Austin
Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering
Apr 26, 2026Rafael Pereira Eufrazio, Eduardo Fernandes Montesuma, Charles Casimiro CavalcanteRepresentation Learning Multidimensional Scaling
Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Canindé, Ceará, Brazil · Federal University of Ceara, Fortaleza, Ceará, Brazil · Sigma Nova, Paris, France
Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
Apr 22, 2026Gabriel Melo, Leonardo Santiago, Peter Y. LuNeural Surrogate Modeling Chaotic Dynamical Systems
LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau · Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC · University of Campinas +1
OT on the Map: Quantifying Domain Shifts in Geographic Space
Apr 17, 2026Haoran Zhang, Livia Betti, Konstantin Klemmer +2Distribution Shift Geospatial Representation Learning
Harvard University · University of Colorado Boulder · LGND AI, Inc. +3
One-Shot Generative Flows: Existence and Obstructions
Apr 16, 2026Panos Tsimpos, Daniel Sharp, Youssef MarzoukFlow Matching One-Step Generative Modeling
Operations Research Center · Massachusetts Institute of Technology · Cambridge, MA 02139 +2
Amortized Optimal Transport from Sliced Potentials
Apr 16, 2026Minh-Phuc Truong, Khai NguyenOptimal Transport
Hanoi University of Science and Technology · The University of Texas at Austin
Enhancing time-frequency resolution with optimal transport and barycentric fusion of multiple spectrogram
Apr 16, 2026David Valdivia, Elsa Cazelles, Cédric FévotteOptimal Transport
IRIT, University of Toulouse, CNRS, France
Sliced Wasserstein Steering between Gaussian Measures
Apr 14, 2026Kaito Ito, Anqi DongOptimal Transport Optimal Control
Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8654, Japan · Department of Decision and Control Systems and Department of Mathematics, KTH Royal Institute of Technology, Stockholm 114 28, Sweden
Generative optimal transport via forward-backward HJB matching
Apr 9, 2026Haiqian Yang, Vishaal Krishnan, Sumit Sinha +1HJB Equations Stochastic Optimal Control
Department of Mechanical Engineering, MIT, Cambridge, MA 02139 · SEAS, Harvard University, Cambridge, MA 02138 · SEAS, Physics and OEB, Harvard University, Cambridge, MA 02138
Region-Graph Optimal Transport Routing for Mixture-of-Experts Whole-Slide Image Classification
Apr 8, 2026Xin Tian, Jiuliu Lu, Ephraim Tsalik +3Histopathology Image Classification Whole-Slide Image Analysis
Centre for Human Genetics, University of Oxford, Oxford, UK · Beckman Coulter Diagnostics, Brea, CA, USA · Danaher Corporation, Washington, DC, USA
SCOT: Multi-Source Cross-City Transfer with Optimal-Transport Soft-Correspondence Objective
Apr 8, 2026Yuyao Wang, Min Yang, Meng Chen +3Transfer Learning Multi-Source Domain Adaptation
Department of Mathematics and Statistics, Boston University, Boston, MA, USA · School of Software, Shandong University, Jinan, China · School of Geography, University of Leeds, Leeds, UK
A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge
Apr 8, 2026Asmaa Eldesoukey, Yongxin Chen, Abhishek HalderSchrödinger Bridges Optimal Transport
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA · School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
Apr 7, 2026Li Kunpeng, Wan Chenguang, Qu Zhisong +5Flow-Based Generative Modeling Flow Matching
Muon Dynamics as a Spectral Wasserstein Flow
Apr 6, 2026Gabriel PeyréNeural Network Training Dynamics Wasserstein Distance
CNRS and ENS, PSL Université
On the Efficiency of Sinkhorn-Knopp for Entropically Regularized Optimal Transport
Apr 4, 2026Kun HeOptimal Transport Entropy Regularization
Renmin University of China
Fast Log-Domain Sinkhorn Optimal Transport with Warp-Level GPU Reductions
Apr 4, 2026Hao XiaoOptimal Transport GPU Acceleration
ATLAS AI Lab

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Optimal Transport for LLM Reward Modeling from Noisy Preference

Licheng Pan, Haochen Yang, Haoxuan Li, Yunsheng Lu+7

Zhejiang University · Xiaohongshu Inc · National University of Singapore+2

Reward Modeling Noisy-Label Learning Optimal Transport RL from Human Feedback

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Reward models are fundamental to Reinforcement Learning from Human Feedback (RLHF), yet real-world datasets are inevitably corrupted by noisy preference. Conventional training objectives tend to overfit these errors, while existing denoising approaches often rely on homogeneous noise assumptions that fail to capture the complexity of linguistic preferences. To handle these challenges, we propose SelectiveRM, a framework grounded in optimal transport. We first devise a Joint Consistency Discrepancy to align the distribution of model predictions with preference data. Furthermore, to address the limitation of strict mass conservation which compels the model to fit outliers, we incorporate a Mass Relaxation mechanism via partial transport. This enables the autonomous exclusion of samples with noisy preference that contradict semantic consistency. Theoretically, we demonstrate that SelectiveRM optimizes a tighter upper bound on the unobserved clean risk. Extensive experiments validate that our approach significantly outperforms state-of-the-art baselines across diverse benchmarks.