Related papers: Cobordism of words
Cross-lingual word embeddings aim to bridge the gap between high-resource and low-resource languages by allowing to learn multilingual word representations even without using any direct bilingual signal. The lion's share of the methods are…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
The manifold hypothesis suggests that word vectors live on a submanifold within their ambient vector space. We argue that we should, more accurately, expect them to live on a pinched manifold: a singular quotient of a manifold obtained by…
We study the role of the second language in bilingual word embeddings in monolingual semantic evaluation tasks. We find strongly and weakly positive correlations between down-stream task performance and second language similarity to the…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
In [1] we introduced the notion of 'structured space', i.e. a space which locally resembles various algebraic structures. In [2] and [3] we studied some cohomology theories related to these space. In this paper we continue in this…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
An algebraic deformation theory of coalgebra morphisms is constructed.
In recent years several novel models were developed to process natural language, development of accurate language translation systems have helped us overcome geographical barriers and communicate ideas effectively. These models are…
A new word usage measure is proposed. It is based on psychophysical relations and allows to reveal words by its degree of "importance" for making basic dictionaries of sublanguages.
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
V. Turaev introduced the theory of topology of words and phrases in 2005. This is a combinatorialy extension of the theory of virtual knots and links. In this paper we generalize the notion of homotopy of words and phrases and we give…
We present an algorithm that takes an unannotated corpus as its input, and returns a ranked list of probable morphologically related pairs as its output. The algorithm tries to discover morphologically related pairs by looking for pairs…
In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…
A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…