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Under extreme operating conditions, characterized by high particle multiplicity and heavily overlapping shower energy deposits, classical particle flow algorithms encounter pronounced limitations in resolution, efficiency, and accuracy. To…

We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…

This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…

We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…

This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…

In this paper we consider the $L_q$-approximation of multivariate periodic functions $f$ with $L_p$-bounded mixed derivative (difference). The (possibly non-linear) reconstruction algorithm is supposed to recover the function from function…

In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…

This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…

A new network with super approximation power is introduced. This network is built with Floor ($\lfloor x\rfloor$) or ReLU ($\max\{0,x\}$) activation function in each neuron and hence we call such networks Floor-ReLU networks. For any…

We consider the problem of recovering characteristic functions $u:=\chi_\Omega$ from cell-average data on a coarse grid, and where $\Omega$ is a compact set of $\mathbb{R}^d$. This task arises in very different contexts such as image…

The reconstruction of unknown functions from a finite number of samples is a fundamental challenge in pure and applied mathematics. This survey provides a comprehensive overview of recent developments in sampling recovery, focusing on the…

We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…

Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in $L^2$. In particular, we show that in relevant cases such as…

We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…

We study oblivious sketching for $k$-sparse linear regression under various loss functions such as an $\ell_p$ norm, or from a broad class of hinge-like loss functions, which includes the logistic and ReLU losses. We show that for sparse…

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate $\epsilon$-close to capacity, and aim to bound the dependence of the output list size $L$ on $\epsilon$,…

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…