Related papers: From Baselines to Transport Geodesics: Axiomatic A…

Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper…

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…

We propose a \textbf{uni}fied \textbf{f}ramework for \textbf{i}mplicit \textbf{ge}nerative \textbf{m}odeling (UnifiGem) with theoretical guarantees by integrating approaches from optimal transport, numerical ODE, density-ratio…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

Main path analysis has long been used to trace knowledge trajectories in citation networks, yet it lacks solid theoretical foundations. To understand when and why this approach succeeds, we analyse directed acyclic graphs created from two…

Many problems in dynamic data driven modeling deals with distributed rather than lumped observations. In this paper, we show that the Monge-Kantorovich optimal transport theory provides a unifying framework to tackle such problems in the…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…

Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…

Deep learning has become the standard approach for most machine learning tasks. While its impact is undeniable, interpreting the predictions of deep learning models from a human perspective remains a challenge. In contrast to model…

Graphs are ubiquitous in many applications, such as social networks, knowledge graphs, smart grids, etc.. Graph neural networks (GNN) are the current state-of-the-art for these applications, and yet remain obscure to humans. Explaining the…

Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). Unlike diffusion-based generative models, which require costly numerical integration of a…

Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that…

A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…

Day-to-day traffic dynamics are widely used to model flow evolution due to travelers' learning and adjustment behavior, yet empirical analysis of these models often relies on descriptive calibration with limited inferential content. This…

Integrated Gradients (IG), a widely used axiomatic path-based attribution method, assigns importance scores to input features by integrating model gradients along a straight path from a baseline to the input. While effective in some cases,…

To study gap acceptance behaviour one needs the distribution (or probability density function) of gaps in the opposing stream. Further, in these times of widespread availability of large computing powers, traffic simulation has emerged as a…

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…

In this work, we develop a distributed source routing algorithm for topology discovery suitable for ISP transport networks, that is however inspired by opportunistic algorithms used in ad hoc wireless networks. We propose a plug-and-play…