Related papers: Classification of Rank 5 Premodular Categories
In this short note we investigate the process of constructing auto-equivalences of modular tensor categories using invertible objects. We derive conditions on the invertible object for the resulting auto-equivalence to be either monoidal,…
We classify the gradings on the Kac superalgebra up to equivalence.
We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…
We introduce a new type of diagrams and prove the existence of a particular one, the "central tuned diagram", with some optimal features, for finitely generated modules of certain categories. This is achieved by getting to the idea of "the…
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
Extracting discriminative features plays a crucial role in the fine-grained visual classification task. Most of the existing methods focus on developing attention or augmentation mechanisms to achieve this goal. However, addressing the…
We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.
Recently, the success of pre-training in text domain has been fully extended to vision, audio, and cross-modal scenarios. The proposed pre-training models of different modalities are showing a rising trend of homogeneity in their model…
We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…
The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification (including parameterizations). Nowadays, parts of…
Hard cases of pronoun resolution have been used as a long-standing benchmark for commonsense reasoning. In the recent literature, pre-trained language models have been used to obtain state-of-the-art results on pronoun resolution. Overall,…
We investigate various types of squeezing in a collective su(2J+1) system consisting of spin-J particles (J>1/2). We show that the squeezing in the collective su(2J+1) system can be classified into unitary equivalence classes, each of which…
Recent breakthroughs in NLP research, such as the advent of Transformer models have indisputably contributed to major advancements in several tasks. However, few works research robustness and explainability issues of their evaluation…
We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an element of a Cu-semigroup by a rapidly increasing sequence.…
Research on computational argumentation is currently being intensively investigated. The goal of this community is to find the best pro and con arguments for a user given topic either to form an opinion for oneself, or to persuade others to…
Combining high-level and low-level visual tasks is a common technique in the field of computer vision. This work integrates the technique of image super resolution to semantic segmentation for document image binarization. It demonstrates…
This paper demonstrates how the limitations of pre-trained models and open evaluation datasets factor into assessing the performance of binary semantic similarity classification tasks. As (1) end-user-facing documentation around the…
We construct universal monoidal categories of topological tensor supermodules over the Lie superalgebras $\mathfrak{gl}(V\oplus \Pi V)$ and $\mathfrak{osp}(V\oplus \Pi V)$ associated with a Tate space $V$. Here $V\oplus \Pi V$ is a…
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the…