Related papers: K-Knuth Equivalence for Increasing Tableaux
Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In…
The goal of this paper is to prove the Riemann-Roch isomorphism for the higher equivariant K-theory of varieties with action of a linear algebraic group.
We study the problem of knowledge graph (KG) embedding. A widely-established assumption to this problem is that similar entities are likely to have similar relational roles. However, existing related methods derive KG embeddings mainly…
We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Sch\"{u}tzenberger '77] for standard Young tableaux. We apply this to give a new combinatorial rule for the K-theory Schubert calculus of…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…
Avoiding redundancy in query results has been extensively studied in relational databases and information retrieval, yet its implications for data lakes remain largely unexplored. We bridge this gap by investigating how to discover…
Given a $k$-vertex-connected graph $G$ and a set $S$ of extra edges (links), the goal of the $k$-vertex-connectivity augmentation problem is to find a set $S' \subseteq S$ of minimum size such that adding $S'$ to $G$ makes it…
Learning good representations on multi-relational graphs is essential to knowledge base completion (KBC). In this paper, we propose a new self-supervised training objective for multi-relational graph representation learning, via simply…
Catastrophic forgetting is a thorny challenge when updating keyword spotting (KWS) models after deployment. This problem will be more challenging if KWS models are further required for edge devices due to their limited memory. To alleviate…
Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for…
Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and K\'or\'odi to pseudo equality algebras which are aimed to find a…
kNN-MT, recently proposed by Khandelwal et al. (2020a), successfully combines pre-trained neural machine translation (NMT) model with token-level k-nearest-neighbor (kNN) retrieval to improve the translation accuracy. However, the…
We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theory of k-tableaux, and includes the introduction of a…
We prove a restriction of an analogue of the Robinson--Schensted--Knuth correspondence for semi-skyline augmented fillings, due to Mason, to multisets of cells of a staircase possibly truncated by a smaller staircase at the upper left end…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
Image-mixing augmentations (e.g., Mixup and CutMix), which typically involve mixing two images, have become the de-facto training techniques for image classification. Despite their huge success in image classification, the number of images…
Topics models, such as LDA, are widely used in Natural Language Processing. Making their output interpretable is an important area of research with applications to areas such as the enhancement of exploratory search interfaces and the…
Previous knowledge graph embedding approaches usually map entities to representations and utilize score functions to predict the target entities, yet they typically struggle to reason rare or emerging unseen entities. In this paper, we…
Word and sentence embeddings are useful feature representations in natural language processing. However, intrinsic evaluation for embeddings lags far behind, and there has been no significant update since the past decade. Word and sentence…