Related papers: Using Optimal Transport Aligned Latent Embeddings …
Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of…
The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to the Lebesgue measure.…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…
We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…
We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the…
Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…
We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one fiber to another. For simplicity, we illustrate our construction in the Euclidean case…
This paper introduces a distributed operational solution for coordinating integrated transmission-distribution (ITD) systems regarding data privacy. To tackle the nonconvex challenges of AC optimal power flow (OPF) problems, our research…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…
Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…
Real-time and accurate prediction of aerodynamic flow fields around airfoils is crucial for flow control and aerodynamic optimization. However, achieving this remains challenging due to the high computational costs and the non-linear nature…
Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and…