相关论文: Effect of Noise on Patterns Formed by Growing Sand…

We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to an additive white noise. This setup uses noise to account for uncertainty in either…

The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural…

We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might…

While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…

Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…

The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization. Increasing the batch-size used typically improves optimization but degrades generalization. To address the…

In this study, we investigate whether noise-augmented training can concurrently improve adversarial robustness in automatic speech recognition (ASR) systems. We conduct a comparative analysis of the adversarial robustness of four different…

Gene expression levels exhibit stochastic variations among genetically identical organisms under the same environmental conditions (called gene expression "noise" or phenotype "fluctuation"). In yeast and Escherichia coli, positive…

We study the effects of additive and multiplicative noise on the solution landscape of nematic liquid crystals confined to a square domain within the Landau-de Gennes framework, as well as the impact of additive noise on the symmetric…

We introduce and study a non-conserving sandpile model, the autonomously adapting sandpile (AAS) model, for which a site topples whenever it has two or more grains, distributing three or two grains randomly on its neighboring sites,…

The leading workhorse of anomaly (and attack) detection in the literature has been residual-based detectors, where the residual is the discrepancy between the observed output provided by the sensors (inclusive of any tampering along the…

We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drives the evolution of the…

We propose a mathematical model for collective sensing in a population growing in a stochastically varying environment. In the population, individuals use an information channel for sensing the environment, and two channels for signal…

This work is about the synchronization of nonlinear coupled dynamical systems driven by $\alpha$-stable noise. Firstly, we provide a novel technique to construct the relationship between synchronized system and slow-fast system. Secondly,…

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…

The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically.…

In this paper, we introduce a noisy framework for SFTs, allowing some amount of forbidden patterns to appear. Using the Besicovitch distance, which permits a global comparison of configurations, we then study the closeness of noisy measures…

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term…

Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…