Related papers: An Internal Logic of Virtual Double Categories
Vision Language Models (VLMs) are becoming increasingly integral to multimedia understanding; however, they often struggle with domain-specific video classification tasks, particularly in cases with limited data. This stems from a critical…
We study monoidal categories that enjoy a certain weakening of the rigidity property, namely, the existence of a dualizing object in the sense of Grothendieck and Verdier. We call them Grothendieck-Verdier categories. Notable examples…
The successful application of large pre-trained models such as BERT in natural language processing has attracted more attention from researchers. Since the BERT typically acts as an end-to-end black box, classification systems based on it…
Reasoning is increasingly crucial for various tasks. While chain-of-thought prompting enables large language models to leverage reasoning effectively, harnessing the reasoning capabilities of Vision-Language Models (VLMs) remains…
We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…
We introduce $\infty$-type theories as an $\infty$-categorical generalization of the categorical definition of type theories introduced by the second named author. We establish analogous results to the previous work including the…
Motivated by its links to $\tau$-tilting theory, we introduce a generalization of cotorsion pairs in module categories. Such pairs are also linked to co-t-structures in corresponding triangulated categories, and to cotorsion pairs in…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
This article is the first in a series of articles that explain the formalization of a constructive model of cubical type theory in Nuprl. In this document we discuss only the parts of the formalization that do not depend on the choice of…
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We…
Let $\mathscr{C}$ be a $2$-Calabi-Yau triangulated category with two cluster tilting subcategories $\mathscr{T}$ and $\mathscr{U}$. Results by Demonet-Iyama-Jasso and J{\o}rgensen-Yakimov known as tropical duality says that the index with…
We prove that for any presentably symmetric monoidal $\infty$-category $\mathcal{V}$, the $\infty$-category $\mathbf{Mod}_\mathcal{V}(\mathbf{Pr}^{\mathrm{L}})^{\mathrm{dbl}}$ of dualizable presentable $\mathcal{V}$-modules and internal…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
We propose a Vision-Language Simulation Model (VLSM) that unifies visual and textual understanding to synthesize executable FlexScript from layout sketches and natural-language prompts, enabling cross-modal reasoning for industrial…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
The ability to cast values between related types is a leitmotiv of many flavors of dependent type theory, such as observational type theories, subtyping, or cast calculi for gradual typing. These casts all exhibit a common structural…
The proposed framework named IDEAL (Interpretable-by-design DEep learning ALgorithms) recasts the standard supervised classification problem into a function of similarity to a set of prototypes derived from the training data, while taking…
We propose the Vision-and-Augmented-Language Transformer (VAuLT). VAuLT is an extension of the popular Vision-and-Language Transformer (ViLT), and improves performance on vision-and-language (VL) tasks that involve more complex text inputs…
Visual question answering (VQA) task not only bridges the gap between images and language, but also requires that specific contents within the image are understood as indicated by linguistic context of the question, in order to generate the…