相关论文: The Overlap Gap Property and Approximate Message P…

The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space $(V,d)$ with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V.…

In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…

In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset,…

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP)…

Approximate message-passing (AMP) method is a simple and efficient framework for the linear inverse problems. In this letter, we propose a faster AMP to solve the \emph{$L_1$-Split-Analysis} for the 2D sparsity separation, which is referred…

We study the problem of algorithmically optimizing the Hamiltonian $H_N$ of a spherical or Ising mixed $p$-spin glass. The maximum asymptotic value $\mathsf{OPT}$ of $H_N/N$ is characterized by a variational principle known as the Parisi…

We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems…

For any real number $p > 0$, we nearly completely characterize the space complexity of estimating $\|A\|_p^p = \sum_{i=1}^n \sigma_i^p$ for $n \times n$ matrices $A$ in which each row and each column has $O(1)$ non-zero entries and whose…

We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…

Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{multiple statistically asymmetric signal sources}, we introduce a multi-source AMP framework in which…

Orthogonal time frequency space (OTFS) modulation has emerged as a promising solution to support high-mobility wireless communications, for which, cost-effective data detectors are critical. Although graph neural network (GNN)-based data…

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner…

Orthogonal Matching pursuit (OMP) is a popular algorithm to estimate an unknown sparse vector from multiple linear measurements of it. Assuming exact sparsity and that the measurements are corrupted by additive Gaussian noise, the success…

Approximate message passing (AMP) algorithms are iterative methods for signal recovery in noisy linear systems. In some scenarios, AMP algorithms need to operate within a distributed network. To address this challenge, the distributed…

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

We study a variant of the sparse PCA (principal component analysis) problem in the "hard" regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio,…

The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such as…

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…

Path optimization is a fundamental concern across various real-world scenarios, ranging from traffic congestion issues to efficient data routing over the internet. The Traffic Assignment Problem (TAP) is a classic continuous optimization…

We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result \cite{ref:Has07}. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian…