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, 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.

The F-measure is widely used to assess the performance of classification algorithms. However, some researchers find it lacking in intuitive interpretation, questioning the appropriateness of combining two aspects of performance as conceptually distinct as precision and recall, and also questioning whether the harmonic mean is the best way to combine them. To ease this concern, we describe a simple transformation of the F-measure, which we call F* (F-star), which has an immediate practical interpretation.

Recently, a Quantum Language Model (QLM) was proposed to model term dependencies upon Quantum Theory (QT) framework and successively applied in Information Retrieval (IR). Nevertheless, QLM's dependency is based on co-occurrences of terms and has not yet taken into account the Quantum Entanglement (QE), which is a key quantum concept and has a significant cognitive implication. In QT, an entangled state can provide a more complete description for the nature of realities, and determine intrinsic correlations of considered objects globally, rather than those co-occurrences on the surface. It is, however, a real challenge to decide and measure QE using the classical statistics of texts in a post-measurement configuration. In order to circumvent this problem, we theoretically prove the connection between QE and statistically Unconditional Pure Dependence (UPD). Since UPD has an implementable deciding algorithm, we can in turn characterize QE by extracting the UPD patterns from texts. This leads to a measurable QE, based on which we further advance the existing QLM framework. We empirically compare our model with related models, and the results demonstrate the effectiveness of our model.

Fortunately, there are better alternatives… What the F- ‐measure is! F-measure, There are several motivations for this choice of mean. In particular, the harmonic mean is commonly appropriate when averaging rates or frequencies, but there is also a settheoretic reason we will discuss later. Precision is the frequency with which retrieved documents or predictions are relevant or'correct', and is properly a form of Accuracy, also known as Positive Predictive Value (PPV) or True Positive Accuracy (TPA). F is intended to combine these into a single measure of search'effectiveness'. One of the problems with Recall, Precision, F-measure and Accuracy as used in Information Retrieval is that they are easily biased. To better understand the relationships between these measures it is useful to give their formulae in two forms, one form related to the raw counts, and one related to normalized frequencies (Equation 1 and Table 1). These statistics are all appropriate when there is one class of items that is of interest or relevance out of a larger set of N items or instances.

This position paper provides an overview of work conducted and an outlook of future directions within the field of Information Retrieval (IR) that aims to develop novel models, methods and frameworks inspired by Quantum Theory (QT).