Related papers: Closure operators: Complexity and applications to …
We give some applications of closure operators in category of groups and link them with the join problem of subnormal subgroups.
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
This research investigates how Machine Learning (ML) algorithms can assist in workload allocation strategies by detecting tasks with node affinity operators (referred to as constraint operators), which constrain their execution to a limited…
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
The introduction of the categorical notion of closure operators has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen (\cite{DT})).…
In socio-technical settings, operators are increasingly assisted by decision support systems. By employing these, important properties of socio-technical systems such as self-adaptation and self-optimization are expected to improve further.…
Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables.…
Optimal shelflisting invites profit maximization to become sensitive to the ways in which purchasing decisions are order-dependent. We study the computational complexity of the corresponding product arrangement problem when consumers are…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…
Ensemble classifier refers to a group of individual classifiers that are cooperatively trained on data set in a supervised classification problem. In this paper we present a review of commonly used ensemble classifiers in the literature.…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…