Related papers: Riemannian Continuous Normalizing Flows
Extracting the maximum amount of cosmological and astrophysical information from upcoming large-scale surveys remains a challenge. This includes evaluating the exact likelihood, parameter inference and generating new diverse synthetic…
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically noninvertible in order to approximate the…
Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…
We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…
Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the…
Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…
Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…
Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this…
We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…
Normalizing flows are bijective mappings between inputs and latent representations with a fully factorized distribution. They are very attractive due to exact likelihood valuation and efficient sampling. However, their effective capacity is…
We show that the evolution of isoparametric hypersurfaces of Riemannian manifolds by the mean curvature flow is given by a reparametrization of the parallel family in short time, as long as the uniqueness of the mean curvature flow holds…
Sets related to positively curved invariant Riemannian metrics on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the normalized Ricci flow equation. For Riemannian metrics of…
In this study, we use Rational-Quadratic Neural Spline Flows, a sophisticated parametrization of Normalizing Flows, for inferring posterior probability distributions in scenarios where direct evaluation of the likelihood is challenging at…
In this article, we will study the isoperimetric problem by introducing a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow preserves the volume of the bounded domain enclosed…
We illustrate the flow or wave character of the metrics and curvatures of evolving manifolds, introducing the Riemann flow and the Riemann wave via the bialternate product Riemannian metric. This kind of evolutions are new and very natural…