Related papers: Modelling interface factorizations between Landau-…

In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

As a well-established approach, factorization machine (FM) is capable of automatically learning high-order interactions among features to make predictions without the need for manual feature engineering. With the prominent development of…

It is known that Lagrangian torus fibers of the moment map of a toric Fano manifold $X$, equipped with flat $U(1)$-connections, are mirror to matrix factorizations of the mirror superpotential $W:\check{X}\rightarrow\bC$. Via SYZ mirror…

This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite…

We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional…

Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal)…

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction…

In the manufacturing process of a filler-reinforced composite, the fillers in the matrix are aligned due to the shear flow occurring during the drawing stage, and the interface between the matrix and the fillers form various imperfections…

The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…

In this paper we study the relative tensor product of module categories over braided fusion categories using, in part, the notion of the relative center of a module category. In particular we investigate the canonical tensor category…

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

We propose semantic fusion, a lightweight scheme that augments a Transformer language model (LM) with a parallel, fuzzy-membership feature channel that encodes token-level semantics. Each token is represented by a vector of interpretable…

In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special…

We classify interacting topological insulators and superconductors with order-two crystal symmetries (reflection and twofold rotation), focusing on the case where interactions reduce the noninteracting classification. We find that the…

Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…

A pointed fusion category is a rigid tensor category with finitely many isomorphism classes of simple objects which moreover are invertible. Two tensor categories $C$ and $D$ are weakly Morita equivalent if there exists an indecomposable…

We prove that the Drinfeld center centralized by a symmetric fusion category is a symmetric monoidal functor if we choose proper domain and codomain categories. We also compute the factorization homology of stratified surfaces with…

Let $G$ be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for $G$ and biset functors defined on subgroups of $G$ and bifree bisets as morphisms. This paper proposes a…