Related papers: Noiseless regularisation by noise
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…
The generalisation and robustness properties of policies learnt through Maximum-Entropy Reinforcement Learning are investigated on chaotic dynamical systems with Gaussian noise on the observable. First, the robustness under noise…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization…
We study the stochastic Allen-Cahn equation driven by a noise term with intensity $\sqrt{\varepsilon}$ and correlation length $\delta$ in two and three spatial dimensions. We study diagonal limits $\delta, \varepsilon \to 0$ and describe…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
In this work we have considered a simple mechanical oscillator interacting with a single mode optical field inside a cavity in the generalized uncertainty principle framework (GUP). Our aim is to calculate the modified noise spectrum and…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
In this paper, we study the stochastic logrithmic Schr\"odinger equation with saturated nonlinear multiplicative L\'evy noise. The global well-posedness is established for the stochastic logrithmic Schr\"odinger equation in an appropriate…
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for…
In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to…
In this paper, based on the Tikhonov regularization technique, we study a monotone general variational inequality (GVI) by considering an associated strongly monotone GVI, depending on a regularization parameter $\alpha,$ such that the…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
This paper is devoted to the analysis of the incompressible Euler equation in a time-dependent fluid domain, whose interface evolution is governed by the law of linear elasticity. Our main result asserts that the Cauchy problem is globally…
It is demonstrated, by means of analogue electronic simulation and theoretically, that external noise can markedly change the character of the response of a nonlinear system to a low-frequency periodic field. In general, noise of sufficient…
An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem,…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…