Related papers: Wasserstein Gradient Flows for Optimizing Gaussian…
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…
This paper proposes a hybrid learning and optimization framework for mobile manipulators for complex and physically interactive tasks. The framework exploits an admittance-type physical interface to obtain intuitive and simplified human…
Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued…
Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Multi-robot systems are essential for environmental monitoring, particularly for tracking spatial phenomena like pollution, soil minerals, and water salinity, and more. This study addresses the challenge of deploying a multi-robot team for…
The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…
RMPflow is a recently proposed policy-fusion framework based on differential geometry. While RMPflow has demonstrated promising performance, it requires the user to provide sensible subtask policies as Riemannian motion policies (RMPs: a…
Evolutionary algorithms (EAs) are promising approaches for non-differentiable or strongly multimodal topology optimization problems, but they often suffer from the curse of dimensionality, generally leading to low-resolution optimized…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…
Modern trajectory optimization based approaches to motion planning are fast, easy to implement, and effective on a wide range of robotics tasks. However, trajectory optimization algorithms have parameters that are typically set in advance…
With the increasing pace of automation, modern robotic systems need to act in stochastic, non-stationary, partially observable environments. A range of algorithms for finding parameterized policies that optimize for long-term average…