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Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems…
Domains of attraction are identified for the universality classes of one-point asymptotic fluctuations for the Kardar-Parisi-Zhang (KPZ) equation with general initial data. The criterion is based on a large deviation rate function for the…
We study certain dynamical and metric aspects of Kiselman's semigroup $K_n$. The level function $\mathcal{L}$ is introduced and shown to admit a simple description in terms of right multiplication by generators. We show that every sequence…
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…
Sampling from high-dimensional and structured probability distributions is a fundamental challenge in computational physics, particularly in the context of lattice field theory (LFT), where generating field configurations efficiently is…
Linear wave theory captures the essential physics of free-surface flows at a fraction of the computational cost of nonlinear and viscous methods, making it attractive for design, real-time control, and surrogate modeling applications.…
A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter…
Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored.…
Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…
Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural…
Wireless channel models are a commonly used tool for the development of wireless telecommunication systems and standards. The currently prevailing geometry-based stochastic channel models (GSCMs) were manually specified for certain…
Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…
An essential problem in domain adaptation is to understand and make use of distribution changes across domains. For this purpose, we first propose a flexible Generative Domain Adaptation Network (G-DAN) with specific latent variables to…