Related papers: Light Schr\"odinger Bridge
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…
We introduce a numerical approach to computing the Schr\"odinger map (SM) based on the Hasimoto transform which relates the SM flow to a cubic nonlinear Schr\"odinger (NLS) equation. In exploiting this nonlinear transform we are able to…
We present a family of algorithms for the numerical approximation of the Schr\"odinger equation with potential concentrated at a finite set of points. Our methods belong to the so-called fast and oblivious convolution quadrature algorithms.…
Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting…
Leveraging connections between diffusion-based sampling, optimal transport, and stochastic optimal control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport…
In the light bulb problem, one is given uniformly random vectors $x_1, \ldots, x_n, y_1, \ldots, y_n \in \{-1,1\}^d$. They are all chosen independently except a planted pair $(x_{i^*}, y_{j^*})$ is chosen with correlation $\rho>0$. The goal…
A Schr\"{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the…
Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of…
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods.…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…
Convergence and generalization are two crucial aspects of performance in neural networks. When analyzed separately, these properties may lead to contradictory results. Optimizing a convergence rate yields fast training, but does not…
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…
We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…
The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
In a previous paper (Matsuno 2011 {\it J. Phys. A: Math. Theore.} {\bf 44} 495202), we have presented a determinantal expression of the bright $N$-soliton solution for a multi-component modified nonlinear Schr\"odinger (NLS) system with…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…