Related papers: Noise Stability is computable and low dimensional

In this paper we propose a notion of stability, that we call $\epsilon -N$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical…

Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…

Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural…

Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…

An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…

Quantum compilation is the problem of translating an input quantum circuit into the most efficient equivalent of itself, taking into account the characteristics of the device that will execute the computation. Compilation strategies are…

Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in…

We prove a vector-valued inequality for the Gaussian noise stability (i.e. we prove a vector-valued Borell inequality) for Euclidean functions taking values in the two-dimensional sphere, for all correlation parameters at most $1/10$ in…

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…

Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when…

We construct a noise stable sequence of transitive, monotone increasing Boolean functions $f_n: \{-1,1\}^{k_n} \longrightarrow \{-1,1\}$ which admit many pivotals with high probability. We show that such a sequence is volatile as well, and…

Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…

Advancements in quantum computing have spurred significant interest in harnessing its potential for speedups over classical systems. However, noise remains a major obstacle to achieving reliable quantum algorithms. In this work, we present…