Related papers: Smoothing Codes and Lattices: Systematic Study and…

In this paper, we consider a robust lattice alignment design for K-user quasi-static MIMO interference channels with imperfect channel knowledge. With random Gaussian inputs, the conventional interference alignment (IA) method has the…

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…

Designing resilient control strategies for mitigating stealthy attacks is a crucial task in emerging cyber-physical systems. In the design of anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however,…

In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…

The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…

-We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and…

We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We study the mixing time of the projected Langevin algorithm (LA) and the privacy curve of noisy Stochastic Gradient Descent (SGD), beyond nonexpansive iterations. Specifically, we derive new mixing time bounds for the projected LA which…

Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based…

We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$;…

We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image…

Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…

For a lattice/linear code, we define the Voronoi spherical cumulative density function (CDF) as the CDF of the $\ell_2$-norm/Hamming weight of a random vector uniformly distributed over the Voronoi cell. Using the first moment method…

We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…

When it comes to image compression in digital cameras, denoising is traditionally performed prior to compression. However, there are applications where image noise may be necessary to demonstrate the trustworthiness of the image, such as…