Related papers: Shadowing the rotating annulus. Part II: Gradient …
An intuitively necessary requirement of models used to provide forecasts of a system's future is the existence of shadowing trajectories that are consistent with past observations of the system: given a system-model pair, do model…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
Accurately modeling the effects of illumination and shadows during head rotation is critical in computer vision for enhancing image realism and reducing artifacts. This study delves into the latent space of denoising diffusion models to…
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected…
Depth estimation is an essential task toward full scene understanding since it allows the projection of rich semantic information captured by cameras into 3D space. While the field has gained much attention recently, datasets for depth…
The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $\rho$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
Recent years have seen increased interest in performance guarantees of gradient descent algorithms for non-convex optimization. A number of works have uncovered that gradient noise plays a critical role in the ability of gradient descent…