Related papers: K-Knuth Equivalence for Increasing Tableaux
We compute the $K$-groups for the Cuntz-Krieger algebras $\mathcal{O}_{A_{\mathcal{K}(f_{\mu})}}$, where $A_{\mathcal{K}(f_{\mu})}$ is the Markov transition matrix arising from the \textit{kneading sequence }$\mathcal{K} (f_{\mu})$ of the…
Continuous word representations learned separately on distinct languages can be aligned so that their words become comparable in a common space. Existing works typically solve a least-square regression problem to learn a rotation aligning a…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
Khandelwal et al. (2020) use a k-nearest-neighbor (kNN) component to improve language model performance. We show that this idea is beneficial for open-domain question answering (QA). To improve the recall of facts encountered during…
In this short note, we derive an upper-bound for the sum of two comparison functions, namely for the sum of a class K and an extended class K function. To the best of our knowledge, the relations derived in this note have not been…
We generalize the notion of an admissible ideal from path algebras to (small) k-linear categories that satisfy the Krull--Remak--Schmidt--Azumaya assumption. In our treatment we first prove some general results that are analogous to general…
Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent…
Let R be a discrete unital ring, and let M be an R-bimodule. We extend Waldhausen's equivalence from the suspension of the Nil K-theory of R with coefficients in M to the K theory of the tensor algebra T_R(M), and get a map from the…
Recent table representation learning and data discovery methods tackle table union search (TUS) within data lakes, which involves identifying tables that can be unioned with a given query table to enrich its content. These methods are…
Large language models (LLMs) have been used to generate query expansions augmenting original queries for improving information search. Recent studies also explore providing LLMs with initial retrieval results to generate query expansions…
Lexical relations describe how concepts are semantically related, in the form of relation triples. The accurate prediction of lexical relations between concepts is challenging, due to the sparsity of patterns indicating the existence of…
Research on data generation and augmentation has been focused majorly on enhancing generation models, leaving a notable gap in the exploration and refinement of methods for evaluating synthetic data. There are several text similarity…
We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a…
We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition of the k-multiplication for which the rank is linear in n…
The Natural Language Processing (NLP) community has recently seen outstanding progress, catalysed by the release of different Neural Network (NN) architectures. Neural-based approaches have proven effective by significantly increasing the…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the set of positive integers. Two finite words $u$ and $v$ in…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
k-Nearest-Neighbor Machine Translation (kNN-MT) becomes an important research direction of NMT in recent years. Its main idea is to retrieve useful key-value pairs from an additional datastore to modify translations without updating the NMT…
A key feature of neural models is that they can produce semantic vector representations of objects (texts, images, speech, etc.) ensuring that similar objects are close to each other in the vector space. While much work has focused on…