相关论文: Gromov-Wasserstein Transfer Operators

We use the Ward identities corresponding to general linear transformations, and derive relations between transport coefficients of $(2+1)$-dimensional systems. Our analysis includes relativistic and Galilean invariant systems, as well as…

Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…

Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein…

This paper introduces a novel and generic framework to solve the flagship task of supervised labeled graph prediction by leveraging Optimal Transport tools. We formulate the problem as regression with the Fused Gromov-Wasserstein (FGW) loss…

Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…

This paper gives a spectral approach to time asymptotics of collisionless transport semi-groups with general diffuse boundary operators. The strong stability of the invariant density is derived from the classical Ingham theorem. A recent…

Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…

This paper develops a tractable analytical channel model for first-hitting-time molecular communication (MC) systems under time-varying drift. While existing studies of nonstationary transport rely primarily on numerical solutions of…

The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow's…

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high…

We propose a new driving scheme, when different parts of a system are driven with different, generally incommensurate, frequencies. Such driving provides a flexible handle to control various properties of the system and to obtain new types…

We study transport of local magnetization in a Heisenberg spin-1/2 chain at zero temperature. The system is initially prepared in a highly excited pure state far from equilibrium and its evolution is analyzed via exact diagonalization.…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of…

We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…

Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…

We present a dynamical and spectral study of Ostrowski's map based on the use of transfer operators. The Ostroswki dynamical system is obtained as a skew-product of the Gauss map (it has the Gauss map as a base and interval fibers) and…

We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…

The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data…

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…