Related papers: Robust blind methods using $\ell_p$ quasi norms

Machine learning image classifiers are susceptible to adversarial and corruption perturbations. Adding imperceptible noise to images can lead to severe misclassifications of the machine learning model. Using $L_p$-norms for measuring the…

Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^2(\Omega)$. In this paper we devise and analyze a variant thereof, which is defined for any load in the dual…

The practical implementation of maximum likelihood detection is limited by its high complexity as well as requiring perfect channel state information. Although conventional blind detection techniques reduce complexity, they degrade…

Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a…

We introduce the $\ell_0\ell_2$-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansion to describe configurational disorder in materials. The approach is implemented through mixed…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of…

Over the years, researchers have developed myriad attacks that exploit the ubiquity of adversarial examples, as well as defenses that aim to guard against the security vulnerabilities posed by such attacks. Of particular interest to this…

In this paper we provide an approach for deep learning that protects against adversarial examples in image classification-type networks. The approach relies on two mechanisms:1) a mechanism that increases robustness at the expense of…

This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…

We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to…

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…

Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…

Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…

The neural network with $1$-Lipschitz property based on $\ell_\infty$-dist neuron has a theoretical guarantee in certified $\ell_\infty$ robustness. However, due to the inherent difficulties in the training of the network, the certified…

In this paper we look at a particular problem related to under-determined linear systems of equations with sparse solutions. $\ell_1$-minimization is a fairly successful polynomial technique that can in certain statistical scenarios find…

Massive MIMO has been regarded as a key enabling technique for 5G and beyond networks. Nevertheless, its performance is limited by the large overhead needed to obtain the high-dimensional channel information. To reduce the huge training…

We consider classical Tsirelson-type norms of $T[A_r,\theta]$ and their modified versions on $\ell_p$ spaces. We show that for any $1<p<\infty$ there is a constant $\lambda_p$ such that considered Tsirelson-type norms do not…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

In this paper we investigate properties of several randomness generation protocols in the device independent framework. Using Bell-type inequalities it is possible to certify that the numbers generated by an untrusted device are indeed…