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We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…
Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation…
We study the structure of the set of priority-neutral matchings. These matchings, introduced by Reny (AER, 2022), generalize stable matchings by allowing for priority violations in a principled way that enables Pareto-improvements to stable…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be…
The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their…
Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
Computational efficiency has remained a critical consideration in scaling high-capacity language models, with inference latency and resource consumption presenting significant constraints on real-time applications. The study has introduced…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
This paper investigates observability/controllability of a networked dynamic system (NDS) in which system matrices of its subsystems are expressed through linear fractional transformations (LFT). Some relations have been obtained between…
A networked dynamical system is composed of subsystems interconnected through prescribed interactions. In many engineering applications, however, one subsystem can also affect others through "unintended" interactions that can significantly…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
We study the class structure of finite-alphabet Markov chains with arbitrary memory length. To capture the structural constraints induced by prohibited transitions, we introduce the skeleton of a higher-order transition kernel, defined as a…
Network reconstruction is the first step towards understanding, diagnosing and controlling the dynamics of complex networked systems. It allows us to infer properties of the interaction matrix, which characterizes how nodes in a system…
Establishing reliable and interpretable structure-property relationships in glasses is a longstanding challenge in condensed matter physics. While modern data-driven machine learning techniques have proven highly effective in establishing…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is…