Related papers: Hierarchical Unambiguity
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable {(possibly nonconvex)} function and a nonsmooth (possibly nonseparable), convex one. The latter term is usually employed to enforce structure…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
Recently, there has been growing interest in unconventional computing as an approach for solving NP-hard problems, by developing dedicated hardware to find solutions more efficiently than conventional CPUs. In many of these approaches,…
Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…
Controlling complex dynamical systems to satisfy sophisticated specifications remains a significant challenge in modern engineering. A promising approach to this problem is the approximate simulation-based hierarchical control (ASHC)…
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…
We introduce semaphore codes associated to a Turing machine via resets. Semaphore codes provide an approximation theory for resets. In this paper we generalize the set-up of our previous paper "Random walks on semaphore codes and delay de…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
Consider the problem of imputing missing values in a dataset. One the one hand, conventional approaches using iterative imputation benefit from the simplicity and customizability of learning conditional distributions directly, but suffer…
This version is similar to math.CO/0210113. We've changed Conjectures 1.1 and 1.2 so that they cover arbitrary graphs(digraphs). Let G be an arbitrary graph(digraph). Then - in polynomial time - either an algorithm obtains a hamilton…
The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…