Related papers: Minibatch Optimal Transport and Perplexity Bound E…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their…
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
Flow matching has emerged as a powerful framework for generative modeling through continuous normalizing flows. We investigate a potential topological constraint: when the prior distribution and target distribution have mismatched topology…
For intelligent transportation systems and autonomous vehicles to operate safely and efficiently, they must reliably predict the future motion and trajectory of surrounding agents within complex traffic environments. At the same time, the…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
Flux-corrected transport (FCT) is one of the flux limiter methods. Unlike the total variation diminishing methods, obtaining the known FCT formulas for computing flux limiters is not quite transparent, and their transformation is not…
Dataset distillation seeks to synthesize a highly compact dataset that achieves performance comparable to the original dataset on downstream tasks. For the classification task that use pre-trained self-supervised models as backbones,…
Flow-matching models provide a powerful framework for various applications, offering efficient sampling and flexible probability path modeling. These models are characterized by flows with low curvature in learned generative trajectories,…
Recently, the rectified flow (RF) has emerged as the new state-of-the-art among flow-based diffusion models due to its high efficiency advantage in straight path sampling, especially with the amazing images generated by a series of RF…
Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…