Related papers: From Hyperbolic Geometry Back to Word Embeddings
Word embeddings are real-valued word representations able to capture lexical semantics and trained on natural language corpora. Models proposing these representations have gained popularity in the recent years, but the issue of the most…
Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…
While word embeddings are currently predominant for natural language processing, most of existing models learn them solely from their contexts. However, these context-based word embeddings are limited since not all words' meaning can be…
Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
Learning representations of words in a continuous space is perhaps the most fundamental task in NLP, however words interact in ways much richer than vector dot product similarity can provide. Many relationships between words can be…
Word embeddings represent language vocabularies as clouds of $d$-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically,…
The notions of concreteness and imageability, traditionally important in psycholinguistics, are gaining significance in semantic-oriented natural language processing tasks. In this paper we investigate the predictability of these two…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…
Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…
Word embeddings capture semantic relationships based on contextual information and are the basis for a wide variety of natural language processing applications. Notably these relationships are solely learned from the data and subsequently…
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…
We consider the problem of aligning continuous word representations, learned in multiple languages, to a common space. It was recently shown that, in the case of two languages, it is possible to learn such a mapping without supervision.…
Understanding human language has been a sub-challenge on the way of intelligent machines. The study of meaning in natural language processing (NLP) relies on the distributional hypothesis where language elements get meaning from the words…
A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infinite family of word-hyperbolic groups can be obtained by…
The meaning of a word is closely linked to sociocultural factors that can change over time and location, resulting in corresponding meaning changes. Taking a global view of words and their meanings in a widely used language, such as…
We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective)…
By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty. The uncertainty information can be particularly meaningful in…
Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully.…