Related papers: Sinkhorn Flow: A Continuous-Time Framework for Und…
Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a…
The Sinkhorn algorithm is a widely used method for solving the optimal transport problem, and the Greenkhorn algorithm is one of its variants. While there are modified versions of these two algorithms whose computational complexities are…
Estimating continuous optical flow is a fundamental yet challenging problem in dynamic visual perception. Event-based cameras, with microsecond latency and high dynamic range, capture brightness changes asynchronously, offering a unique…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert…
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
It is of increasing importance to develop learning methods for ranking. In contrast to many learning objectives, however, the ranking problem presents difficulties due to the fact that the space of permutations is not smooth. In this paper,…
The field of artificial neural network (ANN) training has garnered significant attention in recent years, with researchers exploring various mathematical techniques for optimizing the training process. In particular, this paper focuses on…
How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…