Related papers: Hierarchical Unambiguity
Randomized Hadamard Transforms (RHTs) have emerged as a computationally efficient alternative to the use of dense unstructured random matrices across a range of domains in computer science and machine learning. For several applications such…
This technical report considers worst-case robustness analysis of a network of locally controlled uncertain systems with uncertain parameter vectors belonging to the ellipsoid sets found by identification procedures. In order to deal with…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
In relation extraction for knowledge-based question answering, searching from one entity to another entity via a single relation is called "one hop". In related work, an exhaustive search from all one-hop relations, two-hop relations, and…
The Reconfiguration Inapproximability Hypothesis (RIH), recently established by Hirahara-Ohsaka (STOC'24) and Karthik-Manurangsi (ECCC'24), studies the hardness of reconfiguring one solution into another in constraint satisfaction problems…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
We assess the resources needed to identify a reversible quantum gate among a finite set of alternatives, including in our analysis both deterministic and probabilistic strategies. Among the probabilistic strategies we consider unambiguous…
Laplace approximations are classic, computationally lightweight means for constructing Bayesian neural networks (BNNs). As in other approximate BNNs, one cannot necessarily expect the induced predictive uncertainty to be calibrated. Here we…
A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is…
I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the…
We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…
Heuristic functions are central to the performance of search algorithms such as A-star, where admissibility - the property of never overestimating the true shortest-path cost - guarantees solution optimality. Recent deep learning approaches…
We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the $r$-matrix framework. An $r$-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The div-curl systems we are interested in stem from magnetostatics,…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Tiling recognizable two-dimensional languages, also known as REC, generalize recognizable string languages to two dimensions and share with them several theoretical properties. Nevertheless REC is not closed under complementation and the…