Related papers: Classification of Rank 5 Premodular Categories

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Recently, prefix-tuning was proposed to efficiently adapt pre-trained language models to a broad spectrum of natural language classification tasks. It leverages soft prefix as task-specific indicators and language verbalizers as…

We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebras and conformal nets, we also obtain a complete…

In this paper, we introduce the category of quasi-tempered automorphic D-modules, which is a rather natural class of D-modules from the point of view of geometric Langlands. We provide a characterization of this category in terms of…

Recent innovations in Transformer-based ranking models have advanced the state-of-the-art in information retrieval. However, these Transformers are computationally expensive, and their opaque hidden states make it hard to understand the…

Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…

We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

Self-supervised contrastive learning models, such as CLIP, have set new benchmarks for vision-language models in many downstream tasks. However, their dependency on rigid one-to-one mappings overlooks the complex and often multifaceted…

Motivated by the desire to exploit patterns shared across classes, we present a simple yet effective class-specific memory module for fine-grained feature learning. The memory module stores the prototypical feature representation for each…

Due to rapid advancements in the development of Large Language Models (LLMs), programming these models with prompts has recently gained significant attention. However, the sheer number of available prompt engineering techniques creates an…

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category ${\mathcal C}$ to be equivalent. This concludes the classification of such module…

The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

We classify the localising tensor ideal and colocalising hom-closed subcategories of the stable module category for $\mathrm{LH}\mathfrak{F}$ groups. Along the way we develop techniques to provide similar classifications for other…

Positive-Unlabelled (PU) learning is a growing area of machine learning that aims to learn classifiers from data consisting of labelled positive and unlabelled instances. Whilst much work has been done proposing methods for PU learning,…