Related papers: Injective Rank Metric Trapdoor Functions with Homo…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…
The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult;…
Implicit Neural Representations (INRs) have revolutionized continuous signal modeling, yet they struggle to recover fine-grained details within finite training budgets. While empirical techniques, such as positional encoding (PE),…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. Using this new concept, we derive properties of maximum rank distance (MRD) codes that parallel…
This study explores using embedding rank as an unsupervised evaluation metric for general-purpose speech encoders trained via self-supervised learning (SSL). Traditionally, assessing the performance of these encoders is resource-intensive…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Rank metric codes and constant-dimension codes (CDCs) have been considered for error control in random network coding. Since decoder errors are more detrimental to system performance than decoder failures, in this paper we investigate the…
In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank…
We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
In multiparametric programming an optimization problem which is dependent on a parameter vector is solved parametrically. In control, multiparametric quadratic programming (mp-QP) problems have become increasingly important since the…
We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\mathbb{Z}_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al.(2013)…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
Backdoor attack injects malicious behavior to models such that inputs embedded with triggers are misclassified to a target label desired by the attacker. However, natural features may behave like triggers, causing misclassification once…
In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…