Index

A

Akaike information criterion, 45, 47 Arithmetic formula on operands, 141 Aspect model, 101

B

Bag-of-words approach, 36

Bayesian information criterion, 45, 47 Bell test

inequality and interpretation, 36Ð37 semantic retrieving, 37Ð38

Bell test parameter vs. HAL window size, 39 Best Match N. 25 (BM25) extension, 146 BiLSTM-CRF architecture, 91

Binary Independence Retrieval (BIR) model, 146

Bloch representation of quantum mechanics, 26

Borel σ -algebra, 53

Brussels quantum approach, see Double-slit experiment

C

Car components

atomic conditions, 116, 117 car management, 116 properties, 116

Classical (Boolean) logic, 36

Classical probability, see KolmogorovÕs axiomatics

ClauserÐHorneÐShimonyÐHolt (CHSH) type, 37

Cognitive semantic information retrieval, see Bell test

Cognitivistic/conceptualistic interpretation, 12Ð14

Collobert and Weston (C&W) approach, 87

Commuting quantum query language (CQQL)

database condition, 135 information retrieval, 134 proximity condition, 135 QM mathematics, 134

set of commutative conditions, 135Ð137 vector spaces, query processing, 134

Compatible and incompatible observables BornÕs rule, joint measurements, 62 commutativityÐnoncommutativity, 62 deÞned, 61Ð62

projection postulate Hermitian operator, 63 LŸders, 63Ð64

von Neumann, 63 Complex-valued embedding, 100 Conceptual entities

printed or printable webpages, 2 QWeb composite entity, 16

Context effects, 21, 23, 24 Contextuality

CHSH inequality, 37

compatibility of different queries, 36 user and smart information system, 36

Contextualized word embedding, 99 Copenhagen interpretation, 64Ð65

suai.ru/our-contacts

170

D

Database query language

Boolean model, information retrieval, 130

user search and text retrieval search, 129 See also Weighting formula

Data type construction, 121Ð123 Decision-making

classical (Boolean) logic violations, 36 psychological aspects, 36

Degree of purity, 59 Density operators, 59 Diagonal values, 119

Distributional hypothesis, 86Ð87 Documental entities, see Double-slit

experiment; Information retrieval (IR)

Document-level representation, 92 Document ranking, 156Ð158 Double-slit experiment

Born rule, 10 classical, 7

classical probabilistic average, 12 cognitivistic/conceptualistic interpretation,

12Ð14

conceptual and classical logical thoughts, 21

conÞgurations, 6

conjunction and disjunction, 23 descriptions of, 6

detection screen, 8 DiracÕs notation, 9 effective Hilbert space, 10 experimental probability, 8 ÒÞrst sectorÓ modeling, 23

interference contribution, 7 paradigmatic projection operators, 23 probabilities, 25

projection operator, 24 properties, 11 quantum, 7, 8

quantum Þeld theory, 22 real functions, 9 superposition principle, 11

Venn-diagram representation, 21 weighted average, 25

written documents, 6 Downstream task, 96Ð97

E

Elementary data types deÞned, 117

Þnite domains, 118

quantum machine learning

Index

non-orthogonal data type, 117, 119Ð121 orthogonal data type, 117, 118

Ensemble interpretation, 64 Entangled/non-separable state, 37

F

FaginÕs approach, 140

Formula of total probability (FTP), 55 Hermitian matrices, 67 incompatible observables, 67 quantum conditional probability, 68 VŠxjš interpretation, 68Ð70

Fuzzy logic theory

score function, 132Ð133 t-conorm function, 132 t-norm function, 132

weighted score function function, 133Ð134

G

Gaussian embedding, 100

H

Hilbert space multi-dimensional (HSM) modeling

choice probabilities, 47 compatibility relations, 45 computer programs, 48 contingency data tables, 42 description, 41

dimension determination, 45 four-way joint distribution, 42 initial state, deÞned, 46

model parameters and test models, 47 projectors, 46Ð47

See also Quantum probability theory Hyperbolic embedding, 100

Hyperspace analogue to language (HAL) algorithm, 37Ð38

I

Information retrieval (IR) Boolean model, 149

click-through activity and natural language phrases, 145

cognitive experiments with human participants, 2

CQQL, 134 decision making, 83 description of, 2, 3

deterministic processes, 3 physical and conceptual entities, 2 quantumness, 83

suai.ru/our-contacts

Index

query, 3, 84 QWeb, 2

relevance and information need, 3 user/item embedding, 84

Information retrieving approach, 35 Interference contribution, 7 Interference effects, 17, 20, 21 Interference plus context effect, 28Ð30 Irreducible quantum randomness, 65

K

Ket-and Bra-vectors, 73Ð74

Ket vectors, one-qubit-vectors, 121 Kolmogorov probability space, 53 KolmogorovÕs axiomatics

σ -algebra, 53 Bayes formula, 55

Bayesian inference, 55 Borel σ -algebra, 53 discrete random variable, 55 Ω elementary events, 53 experimental contexts, 53 FTP, 55

Kolmogorov probability space, 53 observables, 53

probability distribution, 54 probability measure, 53Ð54 transition probabilities, 55

Kolmogorov theory, 43Ð44

L

Latent Dirichlet Allocation (LDA), 84, 164 Latent semantic analysis (LSA), 84, 164 Linguistically enhanced word embedding,

99Ð100

Logic-based weighting, 137Ð140

M

Machine learning paradigms, 35

Maximum likelihood estimation (MLE), 152 Meaning bond concept, 30Ð32

Meet and join operators bi-dimensional subspace, rays, 154 deÞnition, 153

intersection and union of sets, 154 one-dimensional subspace, planes, 154 See also Query-by-theme language (QTL)

Meta embedding, 100

N

Named Entity Recognition (NER), 91

Neural Network Language Model (NNLM), 87

quantum machine learning

171

Non-commutativity, 62

Non-negative matrix factorization (NMF), 160

O

Out-Of-Vocabulary (OOV) Problem, 98

OWA approach, 141

P

Part-Of-Speech (POS) tagging, 91 Point-wise Mutual Information (PMI) matrix,

102 Poly-representation, 164 Polysemy problem, 98

Positive operator valued measures (POVMs), 67

Probabilistic models, 152Ð153 Pseudo relevance feedback (PRF), 163

Q

Quantum-based data type constructors set data, 125Ð126

tuple, 123Ð125

Quantum Bayesianism (QBism), 65 Quantum cognition, 27

Quantum cognitive science, 36

Quantum conditional (transition) probability, 65Ð66

Quantum entanglement, 39 Quantum formalism, 36 Quantum interference effect, 36 Quantum mathematics

Hermitian operators, Hilbert space, 56Ð58 normalized vectors and density operators,

58Ð59 Quantum mechanics (QM)

Boolean logics, 52 BornÕs rule, 60Ð61

Copenhagen interpretation, 64Ð65 ensemble interpretation, 64 Hermitian operators, 52 information interpretations, 65 Ket-and Bra-vectors, 73Ð74 logic, 70Ð71

mathematical description physical observables, 60 quantum states, 59Ð60

non-physicists, 51

probability calculus, linear algebra and logic, 115

projection postulate, 52 qubit space, 74Ð75

separable and non-separable entanglement, 75Ð76

suai.ru/our-contacts

172

Quantum mechanics (QM) (cont.) spectral, 60

square integrable functions, 71 statistical theory, 51Ð52

tensor product operation, 72Ð73 time evolution, wave function, 61 two-slit experiment, 76Ð79

See also KolmogorovÕs axiomatics Quantum probability theory

human judgments, 43

Kolmogorov concept, random variable, 43Ð44

logical, vector space and probabilistic approach, 43

Quantum Query Language (QQL), 164

Quantum state tomography, 27 Quantum structures

abstractness and concreteness, 4 human culture, 5, 6

meaning and concept, 3Ð4 physical objects, 5

See also Double-slit experiment Quantum Web (QWeb)

composite entity, 16 concepts, 17Ð19 deÞned, 2

documental entities, 14 interference effects, 20 interrogative process, 14 measurements, 15 n-dimensional Hilbert space, 16 uniform meaning connection, 16 VSM, 15Ð16

webpages, 15 Qubit space, 74Ð75

Query-by-theme language (QTL) document ranking, 156Ð158 features and terms, 155Ð156 JOIN function, 161

meet and join operators, 158Ð160 MEET function, 162

NMF, 160 notations, 155

one-and bi-dimensional themes, 161 themes, 156

Query expansion (QE), 162, 164 Question answering, 94

R

Reading Comprehension (RC) task, 92

Relevance feedback (RF), 162Ð163

quantum machine learning

Index

S

Schmidt orthogonalization algorithm, 38 Set data type constructor, 125Ð126

Sets vs. vector spaces, 147Ð148 Sentence classiÞcation, 90Ð91 Sentence-level applications

classiÞcation, 89, 90 document-level representation, 92 sentence classiÞcation, 90Ð91 sequential labeling, 91Ð92

Sentence-pair level application question answering, 94 RC task, 92

sentence-pair vs. sentence based task, 92, 93

Seq2seq application, 94Ð95 Sequential labeling, 91Ð92

Singular Value Decomposition (SVD), 84, 164 Skip-gram, 87, 88

SQuAD dataset, 94

Square-rooted positive semi-deÞniteness, 119 Sub-word embedding, 100

T

Tensor product operation, 72Ð73

Term Relevance Weight (TRW) function, 152 Thematic modeling, 35

Topic model, 101 Transition probabilities, 55

degenerate spectra and POVMs, 67 doubly stochastic, 67 nondegenerate observables, 66

Tuple data type constructor, 123Ð125 Two-slit experiment, QM, 76Ð79

U

Unit interval, 119

User and smart information system, 36

V

VŠxjš interpretation, 68Ð70 Vector-space based approach

contextual windows, 102Ð103

topic distribution derivation, 101Ð102 Vector space model (VSM), 15Ð16, 150Ð152 Vector spaces

basis and dimension, 147 deÞnition, 147

linear independence, 147 vs. sets, 147Ð148

suai.ru/our-contacts

Index

W

Weighted sum, 141 Weighting formula

arithmetic formula on operands, 141 atomic conditions, 130, 131 contributions, 130

database condition, 131 FaginÕs approach, 140

logic-based weighting approach on min/max, 141

OWA approach, 141 proximity condition, 131 query language, 130

summer cottages and weighted condition tree, 131, 132

text retrieval, 131 types, 140 weighted sum, 141

Word co-occurrence, 20, 21, 25 Word embedding

advanced word embedding, 100 categories, 84

CBOW, 88 contextualized, 99 CV and NLP, 85 C&W, 87 description, 84

quantum machine learning

173

distributional hypothesis, 86Ð87 evaluations

downstream task, 96Ð97 word property, 95Ð96

Glove, 89 ÒinterpretabilityÓ, 99 limitations

distributional hypothesis, 98 lack of theoretical explanation,

98

OOV problem, 98 polysemy problem, 98

semantic change over time, 98 linguistically enhanced, 99Ð100 LSA, 84

NNLM, 87

sentence-level applications, 89Ð92 sentence-pair level application, 92Ð94 Seq2seq application, 94Ð95 Skip-gram, 87, 88

sub-word embedding, 100 towards dynamic version, 103Ð106

visualization of selected words, 85, 86 word-level applications, 89

See also Vector-space based approach Word-level applications, 89

Word representation, 104

LNCS 11690

Quantum Interaction