Related papers: A survey on difference hierarchies of regular lang…
Hierarchical attention networks have recently achieved remarkable performance for document classification in a given language. However, when multilingual document collections are considered, training such models separately for each language…
The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
We develop and explore the idea of recognition of languages (in the general sense of subsets of topological algebras) as preimages of clopen sets under continuous homomorphisms into Stone topological algebras. We obtain an Eilenberg…
Typography and layout lead to the hierarchical organisation of text in words, text lines, paragraphs. This inherent structure is a key property of text in any script and language, which has nonetheless been minimally leveraged by existing…
We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…
In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are…
We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.
This paper surveys the literature on theories of discrimination, focusing mainly on new contributions. Recent theories expand on the traditional taste-based and statistical discrimination frameworks by considering specific features of…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. This is a function version of the difference hierarchy for…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
Expansions in non-integer bases have been investigated abundantly since their introduction by R\'enyi. It was discovered by Erd\H{o}s et al. that the sets of numbers with a unique expansion have a much more complex structure than in the…
Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with $d$-ascents. We have recently extended the so-called hat map to…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
Generating explanations for neural networks has become crucial for their applications in real-world with respect to reliability and trustworthiness. In natural language processing, existing methods usually provide important features which…
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
The paper tries to extend results of the classical Descriptive Set Theory to as many countably based T_0-spaces (cb_0-spaces) as possible. Along with extending some central facts about Borel, Luzin and Hausdorff hierarchies of sets we…