Related papers: Cobordism of words
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
The Isomorphism Conjectures are translated into the language of homotopical algebra, where they resemble Thomason's descent theorems.
We study a coderivation from a cobimodule into a coalgebra. Vector cofields are defined by the action of a codual bicomodule on a coalgebra. This action is induced by a codifferential. A construction of a codual object in the category of…
Word embeddings have been found to capture a surprisingly rich amount of syntactic and semantic knowledge. However, it is not yet sufficiently well-understood how the relational knowledge that is implicitly encoded in word embeddings can be…
Language has been a dynamic system and word meanings always have been changed over times. Every time a novel concept or sense is introduced, we need to assign it a word to express it. Also, some changes have happened because the result of a…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…
Skip-gram (word2vec) is a recent method for creating vector representations of words ("distributed word representations") using a neural network. The representation gained popularity in various areas of natural language processing, because…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
Children learn word meanings by tapping into the commonalities across different situations in which words are used and overcome the high level of uncertainty involved in early word learning experiences. We propose a modeling framework to…
We give a more detailed construction of the operation "intersection with a pseudo-divisor" in algebraic cobordism. Using arguments from Levine-Morel, Algebraic Cobordism, sections 6.2, 6.3, this gives a new proof of the contravariant…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity…
A new method presented for design of incoherent dictionaries.
Word embeddings allow natural language processing systems to share statistical information across related words. These embeddings are typically based on distributional statistics, making it difficult for them to generalize to rare or unseen…
(Co)bordisms of manifolds and maps are fundamental and important objects in algebraic and differential topology of manifolds and related studies were started by Thom etc.. Cobordisms of Morse functions were introduced and have been studied…
Models of bags of words typically assume topic mixing so that the words in a single bag come from a limited number of topics. We show here that many sets of bag of words exhibit a very different pattern of variation than the patterns that…
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…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…