Related papers: Text Has Curvature
Using the frequency of keywords is a classic approach in the formal analysis of text, but has the drawback of glossing over the relationality of word meanings. Word embedding models overcome this problem by constructing a standardized and…
Bending the edge of a thin elastic material promotes rigidity far from its clamped boundary. However, this curvature-induced rigidity can be overwhelmed by gravity or other external loading, resulting in elastic buckling and large…
Topology and geometry are deeply intertwined in the study of surfaces, though their interaction manifests differently in smooth and discrete settings. In the smooth category, a classical result asserts that any closed smooth surface…
Text embedding models from Natural Language Processing can map text data (e.g. words, sentences, documents) to supposedly meaningful numerical representations (a.k.a. text embeddings). While such models are increasingly applied in social…
Coherent discourse is distinguished from a mere collection of utterances by the satisfaction of a diverse set of constraints, for example choice of expression, logical relation between denoted events, and implicit compatibility with…
As an ubiquitous method in natural language processing, word embeddings are extensively employed to map semantic properties of words into a dense vector representation. They capture semantic and syntactic relations among words but the…
Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local…
Style is an integral component of a sentence indicated by the choice of words a person makes. Different people have different ways of expressing themselves, however, they adjust their speaking and writing style to a social context, an…
Multilingual (or cross-lingual) embeddings represent several languages in a unique vector space. Using a common embedding space enables for a shared semantic between words from different languages. In this paper, we propose to embed images…
Translations capture important information about languages that can be used as implicit supervision in learning linguistic properties and semantic representations. In an information-centric view, translated texts may be considered as…
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…
Language models based on the Transformer architecture achieve excellent results in many language-related tasks, such as text classification or sentiment analysis. However, despite the architecture of these models being well-defined, little…
We propose a novel framework to understand the text by converting sentences or articles into video-like 3-dimensional tensors. Each frame, corresponding to a slice of the tensor, is a word image that is rendered by the word's shape. The…
As language models such as GPT-3 become increasingly successful at generating realistic text, questions about what purely text-based modeling can learn about the world have become more urgent. Is text purely syntactic, as skeptics argue? Or…
In this work, we systematically investigate how well current models of coherence can capture aspects of text implicated in discourse organisation. We devise two datasets of various linguistic alterations that undermine coherence and test…
Recent years have seen an explosion of work and interest in text-to-3D shape generation. Much of the progress is driven by advances in 3D representations, large-scale pretraining and representation learning for text and image data enabling…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to…
An understandable concrete syntax and a comprehensible abstract syntax are two central aspects of defining a modeling language. Both representations of a language significantly overlap in their structure and also information, but may also…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…