Related papers: K-Knuth Equivalence for Increasing Tableaux
In this work, we study several equivalence relations induced from the partitions of the sets of words of finite length. We have results on words over finite fields extending the work of Bacher (2002, Europ. J. Combinatorics, {\bf 23},…
Reference resolution on extended texts (several thousand references) cannot be evaluated manually. An evaluation algorithm has been proposed for the MUC tests, using equivalence classes for the coreference relation. However, we show here…
In this paper we combine an approach based on Runge-Kutta Nets considered in [Benning et al., J. Comput. Dynamics, 9, 2019] and a technique on augmenting the input space in [Dupont et al., NeurIPS, 2019] to obtain network architectures…
In the field of transformational music theory, which emphasizes the possible transformations between musical objects, Klumpenhouwer networks (K-Nets) constitute a useful framework with connections in both group theory and graph theory.…
This paper proposes K-NRM, a kernel based neural model for document ranking. Given a query and a set of documents, K-NRM uses a translation matrix that models word-level similarities via word embeddings, a new kernel-pooling technique that…
Co-occurrences between two words provide useful insights into the semantics of those words. Consequently, numerous prior work on word embedding learning have used co-occurrences between two words as the training signal for learning word…
Knowledge Tracing (KT) is to trace the knowledge of students as they solve a sequence of problems represented by their related skills. This involves abstract concepts of students' states of knowledge and the interactions between those…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…
In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of…
The key idea is that rewriting procedures can be enhanced so that they not only rewrite words but record (log) how the rewriting has taken place. We introduce logged rewrite systems and present a variation on the Knuth-Bendix algorithm for…
We present a dataset and experiments on applying recurrent neural networks (RNNs) for guiding clause selection in the connection tableau proof calculus. The RNN encodes a sequence of literals from the current branch of the partial proof…
Recursive neural networks (Tree-RNNs) based on dependency trees are ubiquitous in modeling sentence meanings as they effectively capture semantic relationships between non-neighborhood words. However, recognizing semantically dissimilar…
Increasing the capacity of recurrent neural networks (RNN) usually involves augmenting the size of the hidden layer, with significant increase of computational cost. Recurrent neural tensor networks (RNTN) increase capacity using distinct…
We define the relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs. We prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem for relative Cuntz-Krieger algebras.
Knowledge tracing (KT) is a popular approach for modeling students' learning progress over time, which can enable more personalized and adaptive learning. However, existing KT approaches face two major limitations: (1) they rely heavily on…
We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes…
In this paper, we extend Manin and Schechtman's higher Bruhat orders for the symmetric group to higher Bruhat orders for non-longest words $w$ in $S_n$. We prove that the higher Bruhat orders of non-longest words are ranked posets with…
We report on aggressive quantization strategies that greatly accelerate inference of Recurrent Neural Network Transducers (RNN-T). We use a 4 bit integer representation for both weights and activations and apply Quantization Aware Training…