Related papers: K-Knuth Equivalence for Increasing Tableaux
Search engines operate under a strict time constraint as a fast response is paramount to user satisfaction. Thus, neural re-ranking models have a limited time-budget to re-rank documents. Given the same amount of time, a faster re-ranking…
There are different ways to define similarity for grouping similar texts into clusters, as the concept of similarity may depend on the purpose of the task. For instance, in topic extraction similar texts mean those within the same semantic…
The classical K\"{u}nneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove K\"{u}nneth-type theorems for the persistent homology of the categorical and tensor…
Most existing work focuses on the generalization of KKT for nonsmooth convex optimization problems, but this paper explores a generalized form of Karush-Kuhn-Tucker (KKT) conditions for real continuous optimization problems.
We introduce twisted quantum $K$-rings, defined via twisted $K$-theoretic Gromov-Witten invariants. We develop a toolkit for computing relations by adapting some results about ordinary quantum K rings to our setting, and discuss some…
In this paper, we show how one may (efficiently) construct two types of extremal combinatorial objects whose existence was previously conjectural. (*) Panchromatic Graphs: For fixed integer k, a k-panchromatic graph is, roughly speaking, a…
Two words $u$ and $v$ are $k$-abelian equivalent if, for each word $x$ of length at most $k$, $x$ occurs equally many times as a factor in both $u$ and $v$. The notion of $k$-abelian equivalence is an intermediate notion between the abelian…
We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate $C^*$-correspondences. We use this to calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger algebras of…
This paper presents two new approaches to prove termination of rewrite systems with the Knuth-Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic and the…
Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space (RKHS) characterized by square-integrable first-order mixed…
The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First…
Large language models (LLM) have prioritized expanding the context window from which models can incorporate more information. However, training models to handle long contexts presents significant challenges. These include the scarcity of…
A $k$-truss is an edge-induced subgraph $H$ such that each of its edges belongs to at least $k-2$ triangles of $H$. This notion has been introduced around ten years ago in social network analysis and security, as a form of cohesive subgraph…
We show that the long exact sequence for K-groups of Leavitt path algebras deduced by Ara, Brustenga, and Cortinas extends to Leavitt path algebras of countable graphs with infinite emitters in the obvious way. Using this long exact…
Convolutional neural network (CNN) and recurrent neural network (RNN) models have become the mainstream methods for relation classification. We propose a unified architecture, which exploits the advantages of CNN and RNN simultaneously, to…
There is a huge imbalance between languages currently spoken and corresponding resources to study them. Most of the attention naturally goes to the "big" languages: those which have the largest presence in terms of media and number of…
We consider the problem of similarity search within a set of top-k lists under the Kendall's Tau distance function. This distance describes how related two rankings are in terms of concordantly and discordantly ordered items. As top-k lists…
In this paper, we propose an alternative to deep neural networks for semantic information retrieval for the case of long documents. This new approach exploiting clustering techniques to take into account the meaning of words in Information…
Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and…
Incorporating prior knowledge can improve existing pre-training models in cloze-style machine reading and has become a new trend in recent studies. Notably, most of the existing models have integrated external knowledge graphs (KG) and…