Related papers: Word maps with small image in simple groups
A simple graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ iff $xy\in E$. Word-representable graphs generalize several important classes of graphs. A graph…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
Learning representations for semantic relations is important for various tasks such as analogy detection, relational search, and relation classification. Although there have been several proposals for learning representations for individual…
We study the lexicographically least infinite $a/b$-power-free word on the alphabet of non-negative integers. Frequently this word is a fixed point of a uniform morphism, or closely related to one. For example, the lexicographically least…
We approach the problem of generalizing pre-trained word embeddings beyond fixed-size vocabularies without using additional contextual information. We propose a subword-level word vector generation model that views words as bags of…
We consider linear groups and Lie groups over a non-Archimedean local field $\mathbb F$ for which the power map $x\mapsto x^k$ has a dense image or it is surjective. We prove that the group of $\mathbb F$-points of such algebraic groups is…
We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of…
This paper presents a joint model for performing unsupervised morphological analysis on words, and learning a character-level composition function from morphemes to word embeddings. Our model splits individual words into segments, and…
We consider partial words with a unique position starting a power. We show that over a $k$ letter alphabet, a partial word with a unique position starting a square can contain at most $k$ squares. This is in contrast to full words which can…
It has been shown by Lubotzky in [10] that the set of verbal images of a fixed non-abelian finite simple group G is precisely the set of endomorphism invariant subsets of G. Here we use his result to determine the verbal images of certain…
The algebra of holomorphic polynomial Sp_{2n}-invariants of k complex 2n by 2n matrices (under diagonal conjugation action) is generated by the traces of words in these matrices and their symplectic adjoints. No concrete minimal generating…
Dense word embeddings, which encode semantic meanings of words to low dimensional vector spaces have become very popular in natural language processing (NLP) research due to their state-of-the-art performances in many NLP tasks. Word…
It is often useful to sort words into an order that reflects relations among their meanings as obtained by using a thesaurus. In this paper, we introduce a method of arranging words semantically by using several types of `{\sf is-a}'…
We generate all the Orthogonal Arrays (OAs) of a given size n and strength t as the union of a collection of OAs which belong to an inclusion-minimal set of OAs. We derive a formula for computing the (Generalized) Word Length Pattern of a…
Attention maps are a popular way of explaining the decisions of convolutional networks for image classification. Typically, for each image of interest, a single attention map is produced, which assigns weights to pixels based on their…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
Psychological research consistently finds that human ratings of words across diverse semantic scales can be reduced to a low-dimensional form with relatively little information loss. We find that the semantic associations encoded in the…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
There is a long line of research in the literature dedicated to word-representable graphs, which generalize several important classes of graphs. However, not much is known about word-representability of split graphs, another important class…
In the context of learning formal languages, data about an unknown target language L is given in terms of a set of (word,label) pairs, where a binary label indicates whether or not the given word belongs to L. A (polynomial-size)…