Quantum-like non-separability of concept combinations, emergent associates and abduction

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

“…Thus, the joint probability of relevance is calculated as a product of individual relevance probabilities. However, in [1,2,6,7] the Bell inequality has been violated. In those experiments, the users are asked to report their judgments on composite states.…”

Section: Resultsmentioning

confidence: 99%

“…The non-compositionality of entangled systems opened also the door to developing quantum-like models of cognitive phenomena which are not decompositional in nature. Concept combinations have been widely modeled as composite systems [1,2,6,7,22]. The state of the composite system between two words can be modeled by taking the tensor product of the states of the individual words respectively.…”

Section: Related Workmentioning

confidence: 99%

Investigating Non-classical Correlations Between Decision Fused Multi-modal Documents

Gkoumas

Uprety

Song

2019

Correlation has been widely used to facilitate various information retrieval methods such as query expansion, relevance feedback, document clustering, and multi-modal fusion. Especially, correlation and independence are important issues when fusing different modalities that influence a multi-modal information retrieval process. The basic idea of correlation is that an observable can help predict or enhance another observable. In quantum mechanics, quantum correlation, called entanglement, is a sort of correlation between the observables measured in atomic-size particles when these particles are not necessarily collected in ensembles. In this paper, we examine a multimodal fusion scenario that might be similar to that encountered in physics by firstly measuring two observables (i.e., text-based relevance and image-based relevance) of a multi-modal document without counting on an ensemble of multimodal documents already labeled in terms of these two variables. Then, we investigate the existence of non-classical correlations between pairs of multi-modal documents. Despite there are some basic differences between entanglement and classical correlation encountered in the macroscopic world, we investigate the existence of this kind of non-classical correlation through the Bell inequality violation. Here, we experimentally test several novel association methods in a small-scale experiment. However, in the current experiment we did not find any violation of the Bell inequality. Finally, we present a series of interesting discussions, which may provide theoretical and empirical insights and inspirations for future development of this direction.

“…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.