Quantum aspects of semantic analysis and symbolic artificial intelligence

Abstract. Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) have ignored complex numbers. In this paper, we argue that in order to advance the use of quantum models of IR, one has to lift the constraint of real-valued representations of the information space, and package more information within the representation by means of complex numbers. As a first attempt, we propose a complex-valued representation for IR, which explicitly uses complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complex-valued vectors. The proposal consists of integrating distributional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component. Our proposal has the merit of lifting the role of complex numbers from a computational byproduct of the model to the very mathematical texture that unifies different levels of semantic information. An empirical instantiation of our proposal is tested in the TREC Medical Record task of retrieving cohorts for clinical studies.

Section: Resultsmentioning

confidence: 99%

Combining Word Semantics within Complex Hilbert Space for Information Retrieval

Wittek

Koopman

Zuccon

et al. 2014

“…Technically this distance corresponds to the angle between the real and imaginary components of information objects (terms, documents, etc.). The representation invites the study of the compositionality of meaning in noun compounds from a new perspective, a field of intensive study within Quantum Interaction [32,33]. In addition, user relevance is an indirect but inherent component in our framework as the sources of referential semantics within the representation (e.g., SNOMED-CT in the medical domain) are constructed with domain-specific relevance in mind.…”

Section: Discussionmentioning

confidence: 99%

Combining Word Semantics within Complex Hilbert Space for Information Retrieval

Wittek

Koopman

Zuccon

et al. 2014

Abstract. Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to advance the use of quantum models of IR, one has to lift the constraint of real-valued representations of the information space, and package more information within the representation by means of complex numbers. As a first attempt, we propose a complex-valued representation for IR, which explicitly uses complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complex-valued vectors. The proposal consists of integrating distributional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component. Our proposal has the merit of lifting the role of complex numbers from a computational byproduct of the model to the very mathematical texture that unifies different levels of semantic information. An empirical instantiation of our proposal is tested in the TREC Medical Record task of retrieving cohorts for clinical studies.

“…Thus, with the assumption that the symmetries in quantum-like models will be continuous, we find ourselves to be looking for unitary operators satisfying equations (1) and (2).…”

Section: Transformations In Quantum Theorymentioning

confidence: 99%

“…In extracting the generators of a Galileian group describing a QT it is necessary to couple the symmetry structure of the transformations in the group with the unitary requirements of (1) and (2). In doing this we find that the standard commutation relationships of QT must be satisfied [5].…”

Section: How Do Commutation Relations Relate To Symmetry?mentioning

confidence: 99%

See 1 more Smart Citation

Generalising Unitary Time Evolution

Kitto

Bruza

Sitbon

2009

Abstract. In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified. Quantum Interactions are not EvolvingAs a field Quantum Interaction (QI) has progressed well in recent years [10,8]. It is clear that something is to be gained from applying the quantum formalism to the description of systems not generally considered physical [1,4,14,16,23]. However, despite this initial promise, there are many elements of quantum theory that have yet to be properly applied within this framework. Perhaps most notably, it is clear that time evolution has yet to be properly implemented (i.e. derived) for any of these systems. This is a very significant weakness. Without an appreciation of how an entangled quantum-like system might come about it becomes rather difficult to justify the quantum collapse model that is very often leveraged in the quantum interaction community. This paper will explore the notion of time evolution in standard quantum theory (QT), sketching out the modern approach to extracting Hamiltonians and unitary operators. We shall then utilise this approach to suggest some interesting avenues that might be pursued in the future extraction of a fully-fledged quantum-like theory capable of evolving, entangling and then collapsing.There is no apriori reason to expect that the Schrödinger equation is the only form of time evolution equation available in a quantum-like theory. This paper will discuss the reasons lying behind this, and propose ways in which the QI community might work to establish a new time dynamics, or to prove that the application of Schrödinger dynamics is appropriate. Even if some justification can be found for the application of the Schrödinger equation beyond the description of physical systems, it is highly unlikely that the common techniques used in the extraction of a quantum description will work. This is because the standard approach to constructing a quantum theory generally involves finding a 2 Kirsty Kitto, Peter Bruza, and Laurianne Sitbon