Related papers: Localized Schr\"odinger Bridge Sampler
We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…
This paper presents a sampling-based motion planning framework that leverages the geometry of obstacles in a workspace as well as prior experiences from motion planning problems. Previous studies have demonstrated the benefits of utilizing…
This article presents an approach to the two-dimensional Schr\"odinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential,…
We introduce Bridged Clustering, a semi-supervised framework to learn predictors from any unpaired input $X$ and output $Y$ dataset. Our method first clusters $X$ and $Y$ independently, then learns a sparse, interpretable bridge between…
Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…
We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…
We present Path Integral Sampler~(PIS), a novel algorithm to draw samples from unnormalized probability density functions. The PIS is built on the Schr\"odinger bridge problem which aims to recover the most likely evolution of a diffusion…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
We study a martingale Schr\"odinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schr\"odinger potentials for this coupling. Namely, under…
We study the spreading dynamics of an initially localized wave packet in 1D nonlinear Schr\"{o}dinger lattices with random potential. It is shown that adding small dielectric coupling to surrounding random medium results in asymptotic…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
This paper describes a general formalism for obtaining localized solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems. This class includes the important cases of Schr\"odinger's…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
This paper investigates the localization properties of solutions to the semi-classical Schr\"odinger equation on closed Riemann surfaces. Unlike classical studies that assume a smooth potential, our work addresses the challenges arising…
The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in…
The local computation of Linial [FOCS'87] and Naor and Stockmeyer [STOC'93] concerns with the question of whether a locally definable distributed computing problem can be solved locally: for a given local CSP whether a CSP solution can be…
We propose a nonparametric bootstrap procedure for two-phase stratified sampling without replacement. In this design, a weighted likelihood estimator is known to have smaller asymptotic variance than under the convenient assumption of…
An ongoing challenge in animal ecology is developing movement models that account for the autocorrelation, and often temporal irregularity, in telemetry data. Continuous-time Langevin diffusion models have been proposed to model temporally…
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual…
Long-term traffic prediction has always been a challenging task due to its dynamic temporal dependencies and complex spatial dependencies. In this paper, we propose a model that combines hybrid Transformer and spatio-temporal…