相关论文: L2-Stability Analysis of the SM-NLMS Algorithm

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the…

A wide variety of integral inequalities (IIs) have been developed and studied for the stability analysis of distributed parameter systems using the Lyapunov functional approach. However, no unified mathematical framework has been proposed…

We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem…

We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…

The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, and particularly in digital communications systems, the signal of interest (SOI) and the input signal are…

It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial…

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…

In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS)…

Large Language Models (LLMs) have emerged as a promising cornerstone for the development of natural language processing (NLP) and artificial intelligence (AI). However, ensuring the robustness of LLMs remains a critical challenge. To…

This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…

In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of…

Model averaging has received much attention in the past two decades, which integrates available information by averaging over potential models. Although various model averaging methods have been developed, there are few literatures on the…

We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…

We study the effect of fading in the communication channels between sensor nodes on the performance of the incremental least mean square (ILMS) algorithm, and derive steady state performance metrics, including the mean-square deviation…