Related papers: Module Lattice Security (Part II): Module Lattice …
In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules for weighted Korobov classes. The algorithm presented is a reduced fast component-by-component digit-by-digit…
This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…
Locally repairable codes (LRCs) have attracted a lot of attention due to their applications in distributed storage systems. In this paper, we provide new constructions of optimal $(2, \delta)$-LRCs over $\mathbb{F}_q$ with flexible…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
The purpose of this paper is to study convex bodies $C$ for which there exists no convex body $C^\prime\subsetneq C$ of the same lattice width. Such bodies shall be called ``lattice reduced'', and they occur naturally in the study of the…
We consider connections between similar sublattices and coincidence site lattices (CSLs), and more generally between similar submodules and coincidence site modules of general (free) $\mathbb{Z}$-modules in $\mathbb{R}^d$. In particular, we…
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards…
Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…
In the classical context, it is well known that, sometimes, if the search does not find its target, it is better to start the process anew again, known as resetting. The quantum counterpart of resetting also indicates speeding up the…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
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,…
A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant,…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no…
There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current…
This paper presents an efficient preference elicitation framework for uncertain matroid optimization, where precise weight information is unavailable, but insights into possible weight values are accessible. The core innovation of our…