Related papers: Algebraic Semantics of Generalized RIFs
Algorithmic generalization in machine learning refers to the ability to learn the underlying algorithm that generates data in a way that generalizes out-of-distribution. This is generally considered a difficult task for most machine…
This paper present a strong data mining method based on rough set, which can realize feature selection, classification and knowledge representation at the same time. Rough set has good interpretability, and is a popular method for feature…
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of…
Randomly perturbing networks during the training process is a commonly used approach to improving generalization performance. In this paper, we present a theoretical study of one particular way of random perturbation, which corresponds to…
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Machine learning models are susceptible to adversarial perturbations: small changes to input that can cause large changes in output. It is also demonstrated that there exist input-agnostic perturbations, called universal adversarial…
Despite the impressive advances achieved using deep learning for functional brain activity analysis, the heterogeneity of functional patterns and the scarcity of imaging data still pose challenges in tasks such as identifying neurological…
While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line via Riemann-Liouville or Caputo definitions. This constraint…
In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Rough set theory is a new method that deals with vagueness and uncertainty emphasized in decision making. Data mining is a discipline that has an important contribution to data analysis, discovery of new meaningful knowledge, and autonomous…
We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements of $\mathbb{F}_q[T]$ into primes and the factorizations of…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…
Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
Since Bustince et al. introduced the concepts of overlap and grouping functions, these two types of aggregation functions have attracted a lot of interest in both theory and applications. In this paper, the depiction of $(O,G)$-granular…