- •Preface
- •Contents
- •Contributors
- •Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach
- •1 Introduction
- •2 The Double-Slit Experiment
- •3 Interrogative Processes
- •4 Modeling the QWeb
- •5 Adding Context
- •6 Conclusion
- •Appendix 1: Interference Plus Context Effects
- •Appendix 2: Meaning Bond
- •References
- •1 Introduction
- •2 Bell Test in the Problem of Cognitive Semantic Information Retrieval
- •2.1 Bell Inequality and Its Interpretation
- •2.2 Bell Test in Semantic Retrieving
- •3 Results
- •References
- •1 Introduction
- •2 Basics of Quantum Probability Theory
- •3 Steps to Build an HSM Model
- •3.1 How to Determine the Compatibility Relations
- •3.2 How to Determine the Dimension
- •3.5 Compute the Choice Probabilities
- •3.6 Estimate Model Parameters, Compare and Test Models
- •4 Computer Programs
- •5 Concluding Comments
- •References
- •Basics of Quantum Theory for Quantum-Like Modeling Information Retrieval
- •1 Introduction
- •3 Quantum Mathematics
- •3.1 Hermitian Operators in Hilbert Space
- •3.2 Pure and Mixed States: Normalized Vectors and Density Operators
- •4 Quantum Mechanics: Postulates
- •5 Compatible and Incompatible Observables
- •5.1 Post-Measurement State From the Projection Postulate
- •6 Interpretations of Quantum Mechanics
- •6.1 Ensemble and Individual Interpretations
- •6.2 Information Interpretations
- •7 Quantum Conditional (Transition) Probability
- •9 Formula of Total Probability with the Interference Term
- •9.1 Växjö (Realist Ensemble Contextual) Interpretation of Quantum Mechanics
- •10 Quantum Logic
- •11 Space of Square Integrable Functions as a State Space
- •12 Operation of Tensor Product
- •14 Qubit
- •15 Entanglement
- •References
- •1 Introduction
- •2 Background
- •2.1 Distributional Hypothesis
- •2.2 A Brief History of Word Embedding
- •3 Applications of Word Embedding
- •3.1 Word-Level Applications
- •3.2 Sentence-Level Application
- •3.3 Sentence-Pair Level Application
- •3.4 Seq2seq Application
- •3.5 Evaluation
- •4 Reconsidering Word Embedding
- •4.1 Limitations
- •4.2 Trends
- •4.4 Towards Dynamic Word Embedding
- •5 Conclusion
- •References
- •1 Introduction
- •2 Motivating Example: Car Dealership
- •3 Modelling Elementary Data Types
- •3.1 Orthogonal Data Types
- •3.2 Non-orthogonal Data Types
- •4 Data Type Construction
- •5 Quantum-Based Data Type Constructors
- •5.1 Tuple Data Type Constructor
- •5.2 Set Data Type Constructor
- •6 Conclusion
- •References
- •Incorporating Weights into a Quantum-Logic-Based Query Language
- •1 Introduction
- •2 A Motivating Example
- •5 Logic-Based Weighting
- •6 Related Work
- •7 Conclusion
- •References
- •Searching for Information with Meet and Join Operators
- •1 Introduction
- •2 Background
- •2.1 Vector Spaces
- •2.2 Sets Versus Vector Spaces
- •2.3 The Boolean Model for IR
- •2.5 The Probabilistic Models
- •3 Meet and Join
- •4 Structures of a Query-by-Theme Language
- •4.1 Features and Terms
- •4.2 Themes
- •4.3 Document Ranking
- •4.4 Meet and Join Operators
- •5 Implementation of a Query-by-Theme Language
- •6 Related Work
- •7 Discussion and Future Work
- •References
- •Index
- •Preface
- •Organization
- •Contents
- •Fundamentals
- •Why Should We Use Quantum Theory?
- •1 Introduction
- •2 On the Human Science/Natural Science Issue
- •3 The Human Roots of Quantum Science
- •4 Qualitative Parallels Between Quantum Theory and the Human Sciences
- •5 Early Quantitative Applications of Quantum Theory to the Human Sciences
- •6 Epilogue
- •References
- •Quantum Cognition
- •1 Introduction
- •2 The Quantum Persuasion Approach
- •3 Experimental Design
- •3.1 Testing for Perspective Incompatibility
- •3.2 Quantum Persuasion
- •3.3 Predictions
- •4 Results
- •4.1 Descriptive Statistics
- •4.2 Data Analysis
- •4.3 Interpretation
- •5 Discussion and Concluding Remarks
- •References
- •1 Introduction
- •2 A Probabilistic Fusion Model of Trust
- •3 Contextuality
- •4 Experiment
- •4.1 Subjects
- •4.2 Design and Materials
- •4.3 Procedure
- •4.4 Results
- •4.5 Discussion
- •5 Summary and Conclusions
- •References
- •Probabilistic Programs for Investigating Contextuality in Human Information Processing
- •1 Introduction
- •2 A Framework for Determining Contextuality in Human Information Processing
- •3 Using Probabilistic Programs to Simulate Bell Scenario Experiments
- •References
- •1 Familiarity and Recollection, Verbatim and Gist
- •2 True Memory, False Memory, over Distributed Memory
- •3 The Hamiltonian Based QEM Model
- •4 Data and Prediction
- •5 Discussion
- •References
- •Decision-Making
- •1 Introduction
- •1.2 Two Stage Gambling Game
- •2 Quantum Probabilities and Waves
- •2.1 Intensity Waves
- •2.2 The Law of Balance and Probability Waves
- •2.3 Probability Waves
- •3 Law of Maximal Uncertainty
- •3.1 Principle of Entropy
- •3.2 Mirror Principle
- •4 Conclusion
- •References
- •1 Introduction
- •4 Quantum-Like Bayesian Networks
- •7.1 Results and Discussion
- •8 Conclusion
- •References
- •Cybernetics and AI
- •1 Introduction
- •2 Modeling of the Vehicle
- •2.1 Introduction to Braitenberg Vehicles
- •2.2 Quantum Approach for BV Decision Making
- •3 Topics in Eigenlogic
- •3.1 The Eigenlogic Operators
- •3.2 Incorporation of Fuzzy Logic
- •4 BV Quantum Robot Simulation Results
- •4.1 Simulation Environment
- •5 Quantum Wheel of Emotions
- •6 Discussion and Conclusion
- •7 Credits and Acknowledgements
- •References
- •1 Introduction
- •2.1 What Is Intelligence?
- •2.2 Human Intelligence and Quantum Cognition
- •2.3 In Search of the General Principles of Intelligence
- •3 Towards a Moral Test
- •4 Compositional Quantum Cognition
- •4.1 Categorical Compositional Model of Meaning
- •4.2 Proof of Concept: Compositional Quantum Cognition
- •5 Implementation of a Moral Test
- •5.2 Step II: A Toy Example, Moral Dilemmas and Context Effects
- •5.4 Step IV. Application for AI
- •6 Discussion and Conclusion
- •Appendix A: Example of a Moral Dilemma
- •References
- •Probability and Beyond
- •1 Introduction
- •2 The Theory of Density Hypercubes
- •2.1 Construction of the Theory
- •2.2 Component Symmetries
- •2.3 Normalisation and Causality
- •3 Decoherence and Hyper-decoherence
- •3.1 Decoherence to Classical Theory
- •4 Higher Order Interference
- •5 Conclusions
- •A Proofs
- •References
- •Information Retrieval
- •1 Introduction
- •2 Related Work
- •3 Quantum Entanglement and Bell Inequality
- •5 Experiment Settings
- •5.1 Dataset
- •5.3 Experimental Procedure
- •6 Results and Discussion
- •7 Conclusion
- •A Appendix
- •References
- •Investigating Bell Inequalities for Multidimensional Relevance Judgments in Information Retrieval
- •1 Introduction
- •2 Quantifying Relevance Dimensions
- •3 Deriving a Bell Inequality for Documents
- •3.1 CHSH Inequality
- •3.2 CHSH Inequality for Documents Using the Trace Method
- •4 Experiment and Results
- •5 Conclusion and Future Work
- •A Appendix
- •References
- •Short Paper
- •An Update on Updating
- •References
- •Author Index
- •The Sure Thing principle, the Disjunction Effect and the Law of Total Probability
- •Material and methods
- •Experimental results.
- •Experiment 1
- •Experiment 2
- •More versus less risk averse participants
- •Theoretical analysis
- •Shared features of the theoretical models
- •The Markov model
- •The quantum-like model
- •Logistic model
- •Theoretical model performance
- •Model comparison for risk attitude partitioning.
- •Discussion
- •Authors contributions
- •Ethical clearance
- •Funding
- •Acknowledgements
- •References
- •Markov versus quantum dynamic models of belief change during evidence monitoring
- •Results
- •Model comparisons.
- •Discussion
- •Methods
- •Participants.
- •Task.
- •Procedure.
- •Mathematical Models.
- •Acknowledgements
- •New Developments for Value-based Decisions
- •Context Effects in Preferential Choice
- •Comparison of Model Mechanisms
- •Qualitative Empirical Comparisons
- •Quantitative Empirical Comparisons
- •Neural Mechanisms of Value Accumulation
- •Neuroimaging Studies of Context Effects and Attribute-Wise Decision Processes
- •Concluding Remarks
- •Acknowledgments
- •References
- •Comparison of Markov versus quantum dynamical models of human decision making
- •CONFLICT OF INTEREST
- •Endnotes
- •FURTHER READING
- •REFERENCES
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quantum machine learning |
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
© Springer Nature Switzerland AG 2019 |
169 |
D. Aerts et al. (eds.), Quantum-Like Models for Information Retrieval and Decision-Making, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, https://doi.org/10.1007/978-3-030-25913-6
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
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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
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quantum machine learning |
Bob Coecke
Ariane Lambert-Mogiliansky (Eds.)
LNCS 11690
Quantum Interaction
11th International Conference, QI 2018
Nice, France, September 3–5, 2018
Revised Selected Papers
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Lecture Notes in Computer Science |
11690 |
Founding Editors
Gerhard Goos
Karlsruhe Institute of Technology, Karlsruhe, Germany
Juris Hartmanis
Cornell University, Ithaca, NY, USA
Editorial Board Members
Elisa Bertino
Purdue University, West Lafayette, IN, USA
Wen Gao
Peking University, Beijing, China
Bernhard Steffen
TU Dortmund University, Dortmund, Germany
Gerhard Woeginger
RWTH Aachen, Aachen, Germany
Moti Yung
Columbia University, New York, NY, USA
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More information about this series at http://www.springer.com/series/7407
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Bob Coecke • Ariane Lambert-Mogiliansky (Eds.)
Quantum Interaction
11th International Conference, QI 2018
Nice, France, September 3–5, 2018
Revised Selected Papers
123
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quantum machine learning |
Editors |
Ariane Lambert-Mogiliansky |
Bob Coecke |
|
University of Oxford |
Paris School of Economics |
Oxford, UK |
Paris, France |
ISSN |
0302-9743 |
ISSN 1611-3349 (electronic) |
Lecture Notes in Computer Science |
|
|
ISBN |
978-3-030-35894-5 |
ISBN 978-3-030-35895-2 (eBook) |
https://doi.org/10.1007/978-3-030-35895-2
LNCS Sublibrary: SL1 – Theoretical Computer Science and General Issues
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