相关论文: A reduction methodology for fluctuation driven pop…
We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by…
Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…
Several perspectives of the cluster Gutzwiller method are briefly discussed. I show that the cluster mean-field method can be used for large inhomogeneous lattices, for computing local excitations, and for the time evolution of correlated…
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…
Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often…
In this paper, we propose an optimally structured gradient coding scheme to mitigate the straggler problem in distributed learning. Conventional gradient coding methods often assume homogeneous straggler models or rely on excessive data…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they…
We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…
Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…