A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
3-manifold groups' word problem solved in nearly linear time.
Algorithm solves word problem in mapping class group quickly.
There are certain families of words and word sequences (words in the generators of a two-generator group) that arise frequently in the Teichm{ü}ller theory of hyperbolic three-manifolds and Kleinian and Fuchsian groups and in the discreteness problem for two generator matrix groups. We survey some of the families of su…
Existing approaches for automatically generating mathematical word problems are deprived of customizability and creativity due to the inherent nature of template-based mechanisms they employ. We present a solution to this problem with the use of deep neural language generation mechanisms. Our approach uses a Character …
We give a solution to the word problem for the singular braid monoid SB_n. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically reprove a result of Fenn, Keyman and Rourke that the monoid embeds into a group an…
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated group has the word problem solvable in subexponential time and has a subgroup of…
We show a simple and easily implementable solution to the word problem for virtual braid groups.
Among the six challenges of neural machine translation (NMT) coined by (Koehn and Knowles, 2017), rare-word problem is considered the most severe one, especially in translation of low-resource languages. In this paper, we propose three solutions to address the rare words in neural machine translation systems. First, we…
Word translation is a problem in machine translation that seeks to build models that recover word level correspondence between languages. Recent approaches to this problem have shown that word translation models can learned with very small seeding dictionaries, and even without any starting supervision. In this paper w…
Adyan and Rabin showed that most properties of groups cannot be algorithmically recognized from a finite presentation alone. We prove that, if one is also given a solution to the word problem, then the class of fundamental groups of closed, geometric 3-manifolds is algorithmically recognizable. In our terminology, the …
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our …
We describe a procedure which verifies that a group given by generators and relators is word-hyperbolic. This procedure always works with a group which is word-hyperbolic, provided there is sufficient memory and time devoted to the problem. If the group is not word-hyperbolic, the procedure continues indefinitely. We a…
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble s…
This paper proposes for every , linear time reductions of the word and conjugacy problems on the braid groups to the corresponding problems on the braid monoids and moreover only using positive words representations.
Graph-to-Tree Neural Networks improve structured input-output translation in tasks like semantic parsing and math word problems.
-stratifolds are a generalization of -manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of -stratifolds is solvable.
One of the most interesting questions about a group is if its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists and geometers, and is the target of intensive current research. We look at the braid group from a topological point of view (rather …
Text classification has become indispensable due to the rapid increase of text in digital form. Over the past three decades, efforts have been made to approach this task using various learning algorithms and statistical models based on bag-of-words (BOW) features. Despite its simple implementation, BOW features lack se…
Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categoriza…
We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w|^2 g for |w| > log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in the case of the closed surface is O(|w|^2 g^2). We also carry out the same method…
Simple framework decouples word alignment and multilingual embedding mapping.
Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learni…
Transformer model estimates keywords for better audio captioning.
Embedding words in a vector space has gained a lot of attention in recent years. While state-of-the-art methods provide efficient computation of word similarities via a low-dimensional matrix embedding, their motivation is often left unclear. In this paper, we argue that word embedding can be naturally viewed as a rank…
While the celebrated Word2Vec technique yields semantically rich representations for individual words, there has been relatively less success in extending to generate unsupervised sentences or documents embeddings. Recent work has demonstrated that a distance measure between documents called \emph{Word Mover's Distance…
The article introduces a new set of Polish word embeddings, built using KGR10 corpus, which contains more than 4 billion words. These embeddings are evaluated in the problem of recognition of temporal expressions (timexes) for the Polish language. We described the process of KGR10 corpus creation and a new approach to …
New algorithms solve word and conjugacy problems in braid group B3.
SFBoW provides sentence embeddings with predefined dimensions.
Time Series Motif Discovery (TSMD) is defined as searching for patterns that are previously unknown and appear with a given frequency in time series. Another problem strongly related with TSMD is Word Segmentation. This problem has received much attention from the community that studies early language acquisition in ba…
We investigate the fundamental group of Griffiths' space, and the first singular homology group of this space and of the Hawaiian Earring by using (countable) reduced tame words. We prove that two such words represent the same element in the corresponding group if and only if they can be carried to the same tame word b…
Constructing accurate and automatic solvers of math word problems has proven to be quite challenging. Prior attempts using machine learning have been trained on corpora specific to math word problems to produce arithmetic expressions in infix notation before answer computation. We find that custom-built neural networks…
Geometric approach for unsupervised word embedding alignment.
We outline a rigorous algorithm, first suggested by Casson, for determining whether a closed orientable 3-manifold M is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been given to solve the word problem in π_1(M).
Recently, Rips produced an example of a double of two free groups which has unsolvable generalized word problem. In this paper, we show that Rips's example fits into a large class of doubles of groups, each member of which contains F_2 x F_2 and therefore has unsolvable generalized word problem and is incoherent.
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…
Model learns image-word associations from captions using contrastive learning.
Generating high-quality and interpretable adversarial examples in the text domain is a much more daunting task than it is in the image domain. This is due partly to the discrete nature of text, partly to the problem of ensuring that the adversarial examples are still probable and interpretable, and partly to the proble…
Vector representations of words have heralded a transformational approach to classical problems in NLP; the most popular example is word2vec. However, a single vector does not suffice to model the polysemous nature of many (frequent) words, i.e., words with multiple meanings. In this paper, we propose a three-fold appr…
Cross-language learning allows us to use training data from one language to build models for a different language. Many approaches to bilingual learning require that we have word-level alignment of sentences from parallel corpora. In this work we explore the use of autoencoder-based methods for cross-language learning …
In this paper, we present Russian language datasets in the digital humanities domain for the evaluation of word embedding techniques or similar language modeling and feature learning algorithms. The datasets are split into two task types, word intrusion and word analogy, and contain 31362 task units in total. The chara…
A new presentation of the -string braid group is studied. Using it, a new solution to the word problem in is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes possible certain computational improvements. We also give a related solution to t…
Separable Non-negative Matrix Factorization (SNMF) is an important method for topic modeling, where "separable" assumes every topic contains at least one anchor word, defined as a word that has non-zero probability only on that topic. SNMF focuses on the word co-occurrence patterns to reveal topics by two steps: anchor…
Most existing word embedding approaches do not distinguish the same words in different contexts, therefore ignoring their contextual meanings. As a result, the learned embeddings of these words are usually a mixture of multiple meanings. In this paper, we acknowledge multiple identities of the same word in different co…
This paper gives a proof that the fundamental group of a class of closed orientable 3-manifolds constructed from three injective handlebodies has a solvable word problem. This is done by giving an algorithm to decide if a closed curve in the manifold is null-homotopic. Non-Haken and non-Seifert fibered examples are con…
Online harassment is a significant social problem. Prevention of online harassment requires rapid detection of harassing, offensive, and negative social media posts. In this paper, we propose the use of word embedding models to identify offensive and harassing social media messages in two aspects: detecting fast-changi…
A novel method extracts topological features from word embeddings for text classification.
Proves involutions on Right-angled Coxeter groups without fixed points.
Geometrically transforms word embeddings into a common space for better comparison.