Related papers: From Stationary Phase to Steepest Descent

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another.…

In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a {\em faster…

Deep learning has shown impressive results in a variety of time series forecasting tasks, where modeling the conditional distribution of the future given the past is the essence. However, when this conditional distribution is…

This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…

The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition,…

Pedestrian detection is a problem of considerable practical interest. Adding to the list of successful applications of deep learning methods to vision, we report state-of-the-art and competitive results on all major pedestrian datasets with…

Asymptotic expressions for an integral appearing in the solution of a d-bar problem are presented. The integral is a solid Cauchy transform of a function with a rapidly oscillating phase with a small parameter $h$, $0<h\ll 1$. Whereas…

This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…

We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Machine learning techniques have been shown to be effective to recognize different phases of matter and produce phase diagrams in the parameter space interested, while they usually require prior labeled data to perform well. Here, we…

A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic…

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior…

Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed,…