Related papers: Expected Batch Optimal Transport Plans and Consequ…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
This paper describes a novel paradigm that formalizes automatic piano transcription (APT) as an optimal transport (OT) problem, not as a frame-level multi-label binary classification problem. Our method learns to minimize the cost of…
While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…
High-dimensional integration with respect to complex target measures remains a fundamental challenge in computational science. While Flow Matching (FM) offers a powerful paradigm for constructing continuous-time transport maps, its…
The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…
In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where $N$ robots are tasked to navigate to…
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…
Neural language models are often trained with maximum likelihood estimation (MLE), where the next word is generated conditioned on the ground-truth word tokens. During testing, however, the model is instead conditioned on previously…
Freight consolidation has significant potential to reduce transportation costs and mitigate congestion and pollution. An effective load consolidation plan relies on carefully chosen consolidation points to ensure alignment with existing…
Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…
The mismatch capacity characterizes the highest information rate of the channel under a prescribed decoding metric and serves as a critical performance indicator in numerous practical communication scenarios. Compared to the commonly used…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…
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,…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…