Related papers: A survey on difference hierarchies of regular lang…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
This paper is devoted to studying difference indices of quasi-regular difference algebraic systems. We give the definition of difference indices through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved.…
This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…
This report is a survey of the relationships between various state-of-the-art neural network architectures and formal languages as, for example, structured by the Chomsky Language Hierarchy. Of particular interest are the abilities of a…
In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.
Humans are naturally endowed with the ability to write in a particular style. They can, for instance, re-phrase a formal letter in an informal way, convey a literal message with the use of figures of speech or edit a novel by mimicking the…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope $\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a spectral metric,…
Deep learning has recently demonstrated its ability to rival the human brain for visual object recognition. As datasets get larger, a natural question to ask is if existing deep learning architectures can be extended to handle the 50+K…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
Distant supervision assumes that any sentence containing the same entity pairs reflects identical relationships. Previous works of distantly supervised relation extraction (DSRE) task generally focus on sentence-level or bag-level…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
Multilingual sequence labeling is a task of predicting label sequences using a single unified model for multiple languages. Compared with relying on multiple monolingual models, using a multilingual model has the benefit of a smaller model…
Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals {\`a} la…
Convolutional Neural Networks (CNNs) currently achieve state-of-the-art accuracy in image classification. With a growing number of classes, the accuracy usually drops as the possibilities of confusion increase. Interestingly, the class…
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study…
Effectively searching time-series data is essential for system analysis; however, traditional methods often require domain expertise to define search criteria. Recent advancements have enabled natural language-based search, but these…
Interleaved texts, where posts belonging to different threads occur in one sequence, are a common occurrence, e.g., online chat conversations. To quickly obtain an overview of such texts, existing systems first disentangle the posts by…
This is the first part of the lecture notes that grew out of the special course given during the 2021-2022 academic year. In these lecture notes we present an approach to the fundamental structures of differential geometry that uses the…