Related papers: An Internal Logic of Virtual Double Categories
Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye (KLT) double-copy formalisms have been recently generalized to a class of scattering matrix elements (so-called form factors) that involve local gauge-invariant…
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
We introduce and develop the notion of *displayed categories*. A displayed category over a category C is equivalent to "a category D and functor F : D --> C", but instead of having a single collection of "objects of D" with a map to the…
We introduce Displayed Type Theory (dTT), a multi-modal homotopy type theory with discrete and simplicial modes. In the intended semantics, the discrete mode is interpreted by a model for an arbitrary $\infty$-topos, while the simplicial…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
In recent years, the pre-training-then-fine-tuning paradigm has yielded immense success on a wide spectrum of cross-modal tasks, such as visual question answering (VQA), in which a visual-language (VL) model is first optimized via…
Let $\V$ be a mixed characteristic complete discrete valuation ring, let $\X$ and $\Y$ be two smooth formal $\V$-schemes, let $f_0$ : $X \to Y$ be a projective morphism between their special fibers, let $T$ be a divisor of $Y$ such that…
Open-Vocabulary Multi-Label Recognition (OV-MLR) aims to identify multiple seen and unseen object categories within an image, requiring both precise intra-class localization to pinpoint objects and effective inter-class reasoning to model…
This paper emerged as a result of tackling the following three issues. Firstly, we would like the well known embedding of bicategories into pseudo double categories to be monoidal, which it is not if one uses the usual notion of a monoidal…
The contribution of this paper is the development of the syntax and semantics of multi-sorted nominal abstract binding trees (abts), an extension of second order universal algebra to support symbol-indexed families of operators. Nominal…
The concept of_refinement_ in type theory is a way of reconciling the "intrinsic" and the "extrinsic" meanings of types. We begin with a rigorous analysis of this concept, settling on the simple conclusion that the type-theoretic notion of…
Two novel descriptions of weak {\omega}-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are {\omega}-categories. The second is a recursive description of a…
We present an open-source toolkit for neural machine translation (NMT). The new toolkit is mainly based on vaulted Transformer (Vaswani et al., 2017) along with many other improvements detailed below, in order to create a self-contained,…
Virtual Try-On (VTON) has seen rapid advancements, providing a strong foundation for generative fashion tasks. However, the inverse problem, Virtual Try-Off (VTOFF)-aimed at reconstructing the canonical garment from a draped-on…
We initiate a systematic study of 3-dimensional `defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes…
Visual prompt tuning offers significant advantages for adapting pre-trained visual foundation models to specific tasks. However, current research provides limited insight into the interpretability of this approach, which is essential for…
In a triangulated symmetric monoidal closed category, there are natural dualities induced by the internal Hom. Given a monoidal functor f^* between two such catgories and adjoint couples (f^*,f_*) and (f_*,f^!), we prove the necessary…
We introduce a notion of $\Theta$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-categories. We use this notion to prove a Tannakian duality statement, relating $\Theta$-categories with fpqc-stacks by means…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…