Related papers: Text Has Curvature
More than 80% of today's data is unstructured in nature, and these unstructured datasets evolve over time. A large part of these datasets are text documents generated by media outlets, scholarly articles in digital libraries, findings from…
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
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,…
Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether…
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…
Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…
With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative…
Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…
We propose Text2Scene, a method to automatically create realistic textures for virtual scenes composed of multiple objects. Guided by a reference image and text descriptions, our pipeline adds detailed texture on labeled 3D geometries in…
Natural Language Processing enables computers to understand human language by analysing and classifying text efficiently with deep-level grammatical and semantic features. Existing models capture features by learning from large corpora with…
Embeddings of words and concepts capture syntactic and semantic regularities of language; however, they have seen limited use as tools to study characteristics of different corpora and how they relate to one another. We introduce…
Information retrieval lies at the foundation of the modern digital industry. While natural language search has seen dramatic progress in recent years largely driven by embedding-based models and large-scale pretraining, the field still…
This Ph.D. proposal introduces a plan to develop a computational framework to identify Self-aspects in text. The Self is a multifaceted construct and it is reflected in language. While it is described across disciplines like cognitive…
The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges .…
Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature…
Text animation serves as an expressive medium, transforming static communication into dynamic experiences by infusing words with motion to evoke emotions, emphasize meanings, and construct compelling narratives. Crafting animations that are…
As language technologies gain prominence in real-world settings, it is important to understand how changes to language affect reader perceptions. This can be formalized as the causal effect of varying a linguistic attribute (e.g.,…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
When we speak, write or listen, we continuously make predictions based on our knowledge of a language's grammar. Remarkably, children acquire this grammatical knowledge within just a few years, enabling them to understand and generalise to…
Inspired by the concept of hyperconvexity and its relation to curvature, we translate geometric properties of a metric space encoded by the curvature inequalities into the persistent homology induced by the \v{C}ech filtration of that…