Related papers: A Language Hierarchy of Binary Relations
The problem of determining the representation type of the full transformation monoid was resolved by Ponizovskii, Putcha, and Ringel. In this paper, we present a similar result for the monoid of binary relations, a partial result for the…
In this paper, we introduce a sociolinguistic perspective on language modeling. We claim that large language models are inherently models of varieties of language, and we consider how this insight can inform the development and deployment…
This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…
Online texts -- across genres, registers, domains, and styles -- are riddled with human stereotypes, expressed in overt or subtle ways. Word embeddings, trained on these texts, perpetuate and amplify these stereotypes, and propagate biases…
This is the first part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans -…
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an…
We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category.…
For the longest time, languages have been competing for their speakers to survive, although this problem has only recently gained rigorous attention from the scholarly community as a means to address the risk of losing speakers for the…
In this case study, we select a set of controversial Romanian historical questions and ask multiple Large Language Models to answer them across languages and contexts, in order to assess their biases. Besides being a study mainly performed…
Word alignments identify translational correspondences between words in a parallel sentence pair and is used, for instance, to learn bilingual dictionaries, to train statistical machine translation systems , or to perform quality…
In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state…
Multilingual programs, whose implementations are made of different languages, are gaining traction especially in domains, such as web programming, that particularly benefit from the additional flexibility brought by using multiple…
We characterize binary words that have exactly two unbordered conjugates and show that they can be expressed as a product of two palindromes.
Multilingualism is incredibly common around the world, leading to many important theoretical and practical questions about how children learn multiple languages at once. For example, does multilingual acquisition lead to delays in learning?…
Positional bias in binary question answering occurs when a model systematically favors one choice over another based solely on the ordering of presented options. In this study, we quantify and analyze positional bias across five large…
Language Models have ushered a new age of AI gaining traction within the NLP community as well as amongst the general population. AI's ability to make predictions, generations and its applications in sensitive decision-making scenarios,…
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
The aim of this note is to prove that monoids $\mathrm{Mon}\langle a,b:aUb=b\rangle$, with $aUb$ of relative length 6, admit finite complete rewriting systems. This is some advance in the understanding the long-standing open problem whether…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
This position paper discusses the problem of multilingual evaluation. Using simple statistics, such as average language performance, might inject linguistic biases in favor of dominant language families into evaluation methodology. We argue…