相关论文: Tails of Lipschitz Triangular Flows

Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential…

Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…

We propose a novel mechanism for the origin of non-Gaussian tails in the probability distribution functions (PDFs) of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields.…

Density varies spatiotemporally in low Mach number flows. Hence, incompressibility cannot be assumed, and the density must be accurately solved. Various methods have been proposed to analyze low Mach number flows, but their energy…

We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…

Input gradients have a pivotal role in a variety of applications, including adversarial attack algorithms for evaluating model robustness, explainable AI techniques for generating Saliency Maps, and counterfactual explanations.However,…

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…

Flow models transform data gradually from one modality (e.g. noise) onto another (e.g. images). Such models are parameterized by a time-dependent velocity field, trained to fit segments connecting pairs of source and target points. When the…

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…

We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…

A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate…

We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional…

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine…

Multifractal properties of a tracer density passively advected by a compressible random velocity field are characterized. A relationship is established between the statistical properties of mass on the dynamical fractal attractor towards…

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In…

Sequential user behavior modeling plays a crucial role in online user-oriented services, such as product purchasing, news feed consumption, and online advertising. The performance of sequential modeling heavily depends on the scale and…

We investigate the {\em survival-return} probability distribution and the eigenspectrum for the transition probability matrix, for diffusion in the presence of perfectly absorbing traps distributed with critical disorder in two and three…