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Electronic workshops in computing

Selective Erasers: A Theoretical Framework for Representing Documents Inspired by Quantum Theory

Álvaro Francisco Huertas-Rosero

Published Sep 1, 2008• 4 citations
Publisher

Abstract

The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements on text are proposed as a way of representing documents which is akin to physical measurements on quantum states. The representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. These so called “Selective Erasers” provide the basis for representation [1]. During my presentation, the mathematical foundations of such a quantum representation of text will be presented and discussed in the context of indexing and retrieval within a “quantum like” Information Retrieval system. The presentation will then outline the various directions for future work using Selective Erasers.

DOI
10.14236/ewic/fdia2008.10

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The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements on text are proposed as a way of representing documents which is akin to physical measurements on quantum states. The representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. These so called “Selective Erasers” provide the basis for representation [1]. During my presentation, the mathematical foundations of such a quantum representation of text will be presented and discussed in the context of indexing and retrieval within a “quantum like” Information Retrieval system. The presentation will then outline the various directions for future work using Selective Erasers.
The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements of text are proposed as a way of representing documents which are akin to physical measurements on quantum states. Consequently, the representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. The mathematical foundations of such a quantum representation of text are provided in this position paper as a starting point for indexing and retrieval within a ``quantum like'' Information Retrieval system.
Since 2004, researchers have been using the mathematical framework of quantum theory in information retrieval (IR). Quantum theory offers a generalized probability and logic framework. Such a framework has been shown to be capable of unifying the representation, ranking, and user cognitive aspects of IR, and helpful in developing more dynamic, adaptive, and context-aware IR systems. Although quantum-inspired IR is still a growing area, a wide array of work in different aspects of IR has been done and produced promising results. This article presents a survey of the research done in this area, aiming to show the landscape of the field and draw a road map of future directions.
This thesis is fundamentally about using conceptual and mathematical constructs from the area of Quantum Theory in Information Retrieval (IR). The need and motivation for this is two-fold – firstly, it has been increasingly shown in decision sciences that human decision-making does not always conform to the norms of traditional probability and logic framework. The quantum framework offers a generalised probability and logic framework which can model decisions or judgements under dynamic context and ambiguity. Secondly, there is a need in IR for theories and models which improve our understanding of user behaviour. Hence it is worth exploring the combination of the quantum framework and IR, especially focused on the user aspects of IR. The overarching research question is whether there is evidence of user behaviour in IR scenarios which warrants the need for a quantum based approach by way of showing the limitations of the traditional (classical) approach. The methodology involves analysing data to detect quantum-like phenomena of interference, contextuality, incompatibility, etc. from two common data sources in IR–standard datasets like query log data, and through crowdsourced user studies designed similar to some quantum physics or cognitive science experiments. While the evidence of quantum-like phenomena from standard datasets is not convincing, we find that some of the user studies reveal the quantum-like structure of document judgements. One of the key findings which has implication for IR is the dynamic interactions between the different dimensions of relevance. For example, a user’s judgement of reliability of a document depends significantly on whether they found it understandable or not. Thus, the consideration of one relevance dimension or document feature can provide a context for another dimension, contrary to the current IR models which consider these features to be independent of each other and an objective property of the document. The quantum framework has been especially designed to deal with such scenarios where properties of systems or objects do not exist independent of measurement context. The thesis concludes with suggestions about incorporating quantum mathematical constructs into state-of-art IR algorithms.
The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval. In this paper, we overview the quantum cognition approach developed in our Brussels team during the last two decades, specifically our identification of quantum structures in human concepts and language, and the modeling of data from psychological and corpus-text-based experiments. We discuss our quantum-theoretic framework for concepts and their conjunctions/disjunctions in a Fock-Hilbert space structure, adequately modeling a large amount of data collected on concept combinations. Inspired by this modeling, we put forward elements for a quantum contextual and meaning-based approach to information technologies in which 'entities of meaning' are inversely reconstructed from texts, which are considered as traces of these entities' states.
The article considers the epistemology of quantum phenomena and the quantum eraser experiments as reflecting certain essential features of these phenomena, and uses these experiments to introduce a new concept, that of ‘erasure’. This concept is defined by the fact that a given quantum measurement destroys, ‘erases’, the usefulness of actual or even possible information associated with a given quantum system prior to this measurement, for the purposes of predictions concerning the experiments performed on this system after this measurement. The concept of ‘erasure’ allows one to capture certain fundamental aspects of quantum phenomena more sharply than previously, and to differentiate classical and quantum phenomena, and theories in a new way.