Related papers: Cobordism of words
Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…
We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.
The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional…
Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…
We choose random points in the hyperbolic disc and claim that these points are already word representations. However, it is yet to be uncovered which point corresponds to which word of the human language of interest. This correspondence can…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
Word embeddings are a popular way to improve downstream performances in contemporary language modeling. However, the underlying geometric structure of the embedding space is not well understood. We present a series of explorations using…
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a…
We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded…
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…
Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…
Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…
Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…
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…
The study of semantic relationships has revealed a close connection between these relationships and the morphological characteristics of a language. Morphology, as a subfield of linguistics, investigates the internal structure and formation…
We explore the ability of word embeddings to capture both semantic and morphological similarity, as affected by the different types of linguistic properties (surface form, lemma, morphological tag) used to compose the representation of each…
Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…