Related papers: Text Has Curvature
We have written a Java applet to illustrate the meaning of curved geometry. The applet provides a mapping interface similar to MapQuest or Google Maps; features include the ability to navigate through a space and place permanent point…
Native speakers can judge whether a sentence is an acceptable instance of their language. Acceptability provides a means of evaluating whether computational language models are processing language in a human-like manner. We test the ability…
We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
Language grounding aims at linking the symbolic representation of language (e.g., words) into the rich perceptual knowledge of the outside world. The general approach is to embed both textual and visual information into a common space -the…
Grounding language in vision is an active field of research seeking to construct cognitively plausible word and sentence representations by incorporating perceptual knowledge from vision into text-based representations. Despite many…
Contextuality has long been associated with topological properties. In this work, such a relationship is elevated to identification in the broader framework of generalized contextuality. We employ the usual identification of states,…
Large language models encode the correlational structure present in natural language by fitting segments of utterances (tokens) into a high dimensional ambient latent space upon which the models then operate. We assert that in order to…
We demonstrate the utility of a new methodological tool, neural-network word embedding models, for large-scale text analysis, revealing how these models produce richer insights into cultural associations and categories than possible with…
In this work, we explore the challenging task of generating 3D shapes from text. Beyond the existing works, we propose a new approach for text-guided 3D shape generation, capable of producing high-fidelity shapes with colors that match the…
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…
Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference…
In this work, we develop intuitive controls for editing the style of 3D objects. Our framework, Text2Mesh, stylizes a 3D mesh by predicting color and local geometric details which conform to a target text prompt. We consider a disentangled…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Large language models use high-dimensional latent spaces to encode and process textual information. Much work has investigated how the conceptual content of words translates into geometrical relationships between their vector…
Text-to-image diffusion models have demonstrated an unparalleled ability to generate high-quality, diverse images from a textual prompt. However, the internal representations learned by these models remain an enigma. In this work, we…
Language understanding research is held back by a failure to relate language to the physical world it describes and to the social interactions it facilitates. Despite the incredible effectiveness of language processing models to tackle…
Curvature in biological membranes can be generated by a variety of different molecular mechanisms such as protein scaffolding, lipid or protein asymmetry, cytoskeletal forces, etc. These mechanisms have the net effect of generating stresses…
Analysis of word embedding properties to inform their use in downstream NLP tasks has largely been studied by assessing nearest neighbors. However, geometric properties of the continuous feature space contribute directly to the use of…
It has become a de-facto standard to represent words as elements of a vector space (word2vec, GloVe). While this approach is convenient, it is unnatural for language: words form a graph with a latent hierarchical structure, and this…