Quantum Mathematics in Artificial Intelligence

In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time, quantum computers have become much more powerful, and announcements of major advances are frequently in the news. The mathematical techniques underlying both these areas have more in common than is sometimes realized. Vector spaces took a position at the axiomatic heart of quantum mechanics in the 1930s, and this adoption was a key motivation for the derivation of logic and probability from the linear geometry of vector spaces. Quantum interactions between particles are modelled using the tensor product, which is also used to express objects and operations in artificial neural networks. This paper describes some of these common mathematical areas, including examples of how they are used in artificial intelligence (AI), particularly in automated reasoning and natural language processing (NLP). Techniques discussed include vector spaces, scalar products, subspaces and implication, orthogonal projection and negation, dual vectors, density matrices, positive operators, and tensor products. Application areas include information retrieval, categorization and implication, modelling word-senses and disambiguation, inference in knowledge bases, decision making, and and semantic composition. Some of these approaches can potentially be implemented on quantum hardware. Many of the practical steps in this implementation are in early stages, and some are already realized. Explaining some of the common mathematical tools can help researchers in both AI and quantum computing further exploit these overlaps, recognizing and exploring new directions along the way.This paper describes some of these common mathematical areas, including examples of how they are used in artificial intelligence (AI), particularly in automated reasoning and natural language processing (NLP). Techniques discussed include vector spaces, scalar products, subspaces and implication, orthogonal projection and negation, dual vectors, density matrices, positive operators, and tensor products. Application areas include information retrieval, categorization and implication, modelling word-senses and disambiguation, inference in knowledge bases, and semantic composition. Some of these approaches can potentially be implemented on quantum hardware. Many of the practical steps in this implementation are in early stages, and some are already realized. Explaining some of the common mathematical tools can help researchers in both AI and quantum computing further exploit these overlaps, recognizing and exploring new directions along the way.

‘A patient act of adjustment’: Subjectivisation, adjectives and Jane Austen

Previous scholarship on Jane Austen has often commented on the moral overtones of her lexical choices; more specifically, the fact that “incorrect” lexical innovations and fashionable words (i.e. new usages) tend to be deployed as part of the idiolect of foolish, gullible or morally reprehensible characters. By contrast, ethically sound characters normally move within the limits of established (‘old’) usages and the “correct” Standard English repertoire. Taking the historical linguistic concept of subjectivisation as starting point, this case-study explores the use of two adjectives ( lovely and nice) in Austen’s novels. The article (a) demonstrates that a straightforward socio-moral classification of ‘old’ and ‘new’ word-senses in Austen’s fiction is not fully adequate and (b) advocates, in line with recent scholarship, a more nuanced approach to the study of her fictional vocabulary, where old and new senses of a word (in this case, lovely and nice) move across the idiolect of different character-types for ironic, character- and plot-building purposes.

Lexical Sense Labeling and Sentiment Potential Analysis Using Corpus-Based Dependency Graph

This paper describes a graph method for labeling word senses and identifying lexical sentiment potential by integrating the corpus-based syntactic-semantic dependency graph layer, lexical semantic and sentiment dictionaries. The method, implemented as ConGraCNet application on different languages and corpora, projects a semantic function onto a particular syntactical dependency layer and constructs a seed lexeme graph with collocates of high conceptual similarity. The seed lexeme graph is clustered into subgraphs that reveal the polysemous semantic nature of a lexeme in a corpus. The construction of the WordNet hypernym graph provides a set of synset labels that generalize the senses for each lexical cluster. By integrating sentiment dictionaries, we introduce graph propagation methods for sentiment analysis. Original dictionary sentiment values are integrated into ConGraCNet lexical graph to compute sentiment values of node lexemes and lexical clusters, and identify the sentiment potential of lexemes with respect to a corpus. The method can be used to resolve sparseness of sentiment dictionaries and enrich the sentiment evaluation of lexical structures in sentiment dictionaries by revealing the relative sentiment potential of polysemous lexemes with respect to a specific corpus. The proposed approach has the potential to be used as a complementary method to other NLP resources and tasks, including word disambiguation, domain relatedness, sense structure, metaphoricity, as well as a cross- and intra-cultural discourse variations of prototypical conceptualization patterns and knowledge representations.

Quantifying Lexical Ambiguity in Speech To and From English-Learning Children

Because words have multiple meanings, language users must often choose appropriate meanings according to the context of use. How this potential ambiguity affects first language learning, especially word learning, is unknown. Here, we present the first large-scale study of how children are exposed to, and themselves use, ambiguous words in their actual language learning environments. We tag 180,000 words in two longitudinal child language corpora with word senses from WordNet, focusing between 9 and 51 months and limiting to words from a popular parental vocabulary report. We then compare the diversity of sense usage in adult speech around children to that observed in a sample of adult-directed language, as well as the diversity of sense usage in children's own productions. To accomplish this we use a Bayesian model-based estimate of sense entropy, a measure of diversity that takes into account uncertainty inherent in small sample sizes. This reveals that sense diversity in caregivers' speech to children is similar to that observed in a sample of adult-directed written material, and that children' use of nouns --- but not verbs --- is similarly diverse to that of adults. Finally, we show that sense entropy is a significant predictor of vocabulary development: children begin to produce words with a higher diversity of adult sense usage at later ages. We discuss the implications of our findings for theories of word learning.

Geographical query reformulation using a geographical adjacency taxonomy builder and word senses

Purpose Geographical query formulation is one of the key difficulties for users in search engines. The purpose of this study is to improve geographical search by proposing a novel geographical query reformulation (GQR) technique using a geographical taxonomy and word senses. Design/methodology/approach This work introduces an approach for GQR, which combines a method of query components separation that uses GeoNames, a technique for reformulating these components using WordNet and a geographic taxonomy constructed using the latent semantic analysis method. Findings The proposed approach was compared to two methods from the literature, using the mean average precision (MAP) and the precision at 20 documents (P@20). The experimental results show that it outperforms the other techniques by 15.73% to 31.21% in terms of P@20 and by 17.81% to 35.52% in terms of MAP. Research limitations/implications According to the experimental results, the best created taxonomy using the geographical adjacency taxonomy builder contains 7.67% of incorrect links. This paper believes that using a very big amount of data for taxonomy building can give better results. Thus, in future work, this paper intends to apply the approach in a big data context. Originality/value Despite this, the reformulation of geographical queries using the new proposed approach considerably improves the precision of queries and retrieves relevant documents that were not retrieved using the original queries. The strengths of the technique lie in the facts of reformulating both thematic and spatial entities and replacing the spatial entity of the query with terms that explain the intent of the query more precisely using a geographical taxonomy.