Related papers: Path Integral Optimiser: Global Optimisation via N…
We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
We investigate the sign problem in field theories by using the path optimization method with use of the neural network. For theories with the sign problem, integral in the complexified variable space is a promising approach to obtain a…
Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…
In this paper, we present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the…
Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener…
We consider anonymous multi-agent path finding (MAPF) where a set of robots is tasked to travel to a set of targets on a finite, connected graph. We show that MAPF can be cast as a special class of multi-marginal optimal transport (MMOT)…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
Atypically large fluctuations in macroscopic non-equilibrium systems continue to attract interest. Their probability can often be determined by the optimal fluctuation method (OFM). The OFM brings about a conditional variational problem,…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…