相关论文: Fast Context-Free Parsing Requires Fast Boolean Ma…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

We introduce the use of the Fast Multipole Method (FMM) to speed up gravitational lensing ray tracing calculations. The method allows very fast calculation of ray deflections when a large number of deflectors, $N_*$, is involved, while…

We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and…

Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $\sigma$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

Compound probabilistic context-free grammars (C-PCFGs) have recently established a new state of the art for unsupervised phrase-structure grammar induction. However, due to the high space and time complexities of chart-based representation…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…

A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single computation task and batch processing of multiple distinct computation tasks. While these works…

This paper proposes a novel technique that applies case-based reasoning in order to generate templates for reusable parse tree fragments, based on PoS tags of bigrams and trigrams that demonstrate low variability in their syntactic analyses…

It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size…

Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and…

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…

Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…

Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…

We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…

Let $M$ be a transitive model of $ZFC$ and let ${\bf B}$ be a $M$-complete Boolean algebra in $M.$ (In general a proper class.) We define a generalized notion of forcing with such Boolean algebras, $^*$forcing. (A $^*$ forcing extension of…

A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…

Word Break is a prototypical factorization problem in string processing: Given a word $w$ of length $N$ and a dictionary $\mathcal{D} = \{d_1, d_2, \ldots, d_{K}\}$ of $K$ strings, determine whether we can partition $w$ into words from…

This research introduces a new parsing approach, based on earlier syntactic work on context free grammar (CFG) and generalized phrase structure grammar (GPSG). The approach comprises both a new parsing algorithm and a set of syntactic rules…

Classifier-Free Guidance (CFG) is a widely used technique for conditional generation and improving sample quality in continuous diffusion models, and its extensions to discrete diffusion has recently started to be investigated. In order to…