Related papers: Incremental Noising and its Fractal Behavior

Typical experimental measurement is set up as a study of the system's response to a stationary external excitation. This approach considers any random fluctuation of the signal as spurious contribution which is to be eliminated via…

Developability refers to the process of creating a surface without any tearing or shearing from a two-dimensional plane. It finds practical applications in the fabrication industry. An essential characteristic of a developable 3D surface is…

The microscopic dependence of glassy equilibration on sample history, both the initial configuration and the specific sequence of random noise, is examined. The temporal evolution of spin configurations in a two-dimensional Ising spin glass…

The speed at which one can minimize an expected loss using stochastic methods depends on two properties: the curvature of the loss and the variance of the gradients. While most previous works focus on one or the other of these properties,…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of…

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…

The advent of large-scale pre-trained language models has contributed greatly to the recent progress in natural language processing. Many state-of-the-art language models are first trained on a large text corpus and then fine-tuned on…

In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal…

In this work, we dive deep into the impact of additive noise in pre-training deep networks. While various methods have attempted to use additive noise inspired by the success of latent denoising diffusion models, when used in combination…

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…

In noisy label learning, estimating noisy class posteriors plays a fundamental role for developing consistent classifiers, as it forms the basis for estimating clean class posteriors and the transition matrix. Existing methods typically…

Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…

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…

In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…

In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation with this noise with a highly irregular coefficient. We employ a new method to…

Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…

The Langevin formulation of a number of well-known stochastic processes involves multiplicative noise. In this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise, which may…

The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…

This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…