Statistical mechanics of neural networks:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
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Singapore
Springer
[2021]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Chapter 1: Introduction; Chapter 2: Spin Glass Models and Cavity Method; Chapter 3: Variational Mean-Field Theory and Belief Propagation; Chapter 4: Monte-Carlo Simulation Methods; Chapter 5: High-Temperature Expansion Techniques; Chapter 6: Nishimori Model; Chapter 7: Random Energy Model; Chapter 8: Statistical Mechanics of Hopfield Model; Chapter 9: Replica Symmetry and Symmetry Breaking; Chapter 10: Statistical Mechanics of Restricted Boltzmann Machine; Chapter 11: Simplest Model of Unsupervised Learning with Binary Synapses; Chapter 12: Inherent-Symmetry Breaking in Unsupervised Learning; Chapter 13: Mean-Field Theory of Ising Perceptron; Chapter 14: Mean-Field Model of Multi-Layered Perceptron; Chapter 15: Mean-Field Theory of Dimension Reduction in Neural Networks; Chapter 16: Chaos Theory of Random Recurrent Networks; Chapter 17: Statistical Mechanics of Random Matrices; Chapter 18: Perspectives |
| Beschreibung: | xviii, 296 Seiten Diagramme (teilweise farbig) 631 grams |
| ISBN: | 9789811675720 9789811675690 |
Internformat
MARC
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| 500 | |a Chapter 1: Introduction; Chapter 2: Spin Glass Models and Cavity Method; Chapter 3: Variational Mean-Field Theory and Belief Propagation; Chapter 4: Monte-Carlo Simulation Methods; Chapter 5: High-Temperature Expansion Techniques; Chapter 6: Nishimori Model; Chapter 7: Random Energy Model; Chapter 8: Statistical Mechanics of Hopfield Model; Chapter 9: Replica Symmetry and Symmetry Breaking; Chapter 10: Statistical Mechanics of Restricted Boltzmann Machine; Chapter 11: Simplest Model of Unsupervised Learning with Binary Synapses; Chapter 12: Inherent-Symmetry Breaking in Unsupervised Learning; Chapter 13: Mean-Field Theory of Ising Perceptron; Chapter 14: Mean-Field Model of Multi-Layered Perceptron; Chapter 15: Mean-Field Theory of Dimension Reduction in Neural Networks; Chapter 16: Chaos Theory of Random Recurrent Networks; Chapter 17: Statistical Mechanics of Random Matrices; Chapter 18: Perspectives | ||
| 650 | 4 | |a Neural networks (Computer science) | |
| 650 | 4 | |a Statistical Mechanics | |
| 650 | 4 | |a Computational intelligence | |
| 650 | 4 | |a Artificial intelligence | |
| 650 | 4 | |a Statistical Physics | |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text |
Contents 1 Introduction . References . 2 Spin Glass Models and Cavity Method . 2.1 Multi-spin Interaction Models. 2.2 Cavity Method . 2.3 From Cavity Method to Message Passing Algorithms. References . 3 Variational Mean-Field Theory and Belief Propagation . Variational Method . Variational Free Energy . 3.2.1 Mean-Field Approximation . 3.2.2 Bethe Approximation . 3.2.3 From the Bethe to Naive Mean-Field Approximation . 3.3 Mean-Field Inverse Ising Problem . References . 3.1 3.2 4 Monte Carlo Simulation Methods. Monte Carlo
Method. Importance Sampling . Markov Chain Sampling . Monte Carlo Simulations in Statistical Physics . 4.4.1 Metropolis Algorithm . 4.4.2 Parallel Tempering Monte Carlo . References . 4.1 4.2 4.3 4.4 5 High-Temperature Expansion . 5.1 Statistical Physics Setting . 5.2 High-Temperature Expansion . 5.3 Properties of the TAP Equation. References . 1 З 5 5 8 12 14 17 17 18 20 22 27 29 30 33 33 34 35 36 37 39 42 43 43 46 51 52 xi
Contents xii 6 Nishimori Line. 6.1 Model Setting . 6.2 Exact Result for Internal Energy. 6.3 Proof of No RSB Effects on the Nishimori Line. References . 7 Random Energy Model . 7.1 Model Setting . 7.2 Phase Diagram. References . 8 Statistical Mechanical Theory of Hopfield Model . Hopfield Model . Replica Method . 8.2.1 Replica-Symmetric Ansatz . 8.2.2 Zero-Temperature Limit . 8.3 Phase Diagram. 8.4 Hopfield Model with Arbitrary Hebbian Length. 8.4.1 Computation of the Disorder-Averaged Free Energy
. 81 8.4.2 Derivation of Saddle-Point Equations . 8.4.3 Computation Transformation to Solve the SDE. 8.4.4 Zero-Temperature Limit . References . 8.1 8.2 9 Replica Symmetry and Replica Symmetry Breaking . 9.1 Generalized Free Energy and Complexity of States. 9.2 Applications to Constraint Satisfaction Problems. 9.3 More Steps of Replica Symmetry Breaking . References . 10 Statistical Mechanics of Restricted Boltzmann Machine 10.1 10.2 10.3 10.4 10.5 10.6 . Boltzmann Machine . Restricted Boltzmann Machine . Free Energy Calculation . Thermodynamic Quantities Related to Learning . Stability Analysis . Variational Mean-Field Theory for Training Binary RBMs . 10.6.1 RBMs with Binary Weights . 10.6.2 Variational Principle . 10.6.3
Experiments . References . 55 55 56 57 58 59 59 61 62 63 63 66 73 78 79 81 91 92 94 98 99 99 102 106 108 Ill Ill 113 115 117 121 123 124 125 130 132
xiii Contents 11 Simplest Model of Unsupervised Learning with Binary Synapses . 133 Model Setting . Derivation of sMP and AMP Equations. Replica Computation . 11.3.1Explicit form of (Z") . 11.3.2 Estimation of (Z") Under Replica Symmetry Ansatz . 11.3.3 Derivation of Free Energy and Saddle-Point Equations. 142 11.4 Phase Transitions. 11.5 Measuring the Temperature of Dataset. References . 11.1 11.2 11.3 12 Inherent-Symmetry Breaking in Unsupervised Learning. 12.1 Model Setting . 12.1.1 Cavity Approximation . 12.1.2 Replica Computation . 12.1.3 Stability Analysis . 12.2 Phase
Diagram. 12.3 Hyper-Parameters Inference . References . 13 Mean-Field Theory of Ising Perceptron . Ising Perceptron model. Message-Passing-Based Learning. Replica Analysis . 13.3.1 Replica Symmetry . 13.3.2 Replica Symmetry Breaking. 13.4 Further Theory Development. References . 13.1 13.2 13.3 14 Mean-Field Model of Multi-layered Perceptron . Random Active Path Model. 14.1.1 Results from Cavity Method. 14.1.2 An Infinite Depth Analysis . 14.2 Mean-Field Training Algorithms . 14.3 Spike and Slab Model. 14.3.1 Ensemble Perspective
. 14.3.2 Training Equations. References . 14.1 15 Mean-Field Theory of Dimension Reduction . 15.1 Mean-Field Model. 15.2 Linear Dimensionality and Correlation Strength . 15.2.1 Iteration Equations for Correlation Strength . 15.2.2 Mechanism of Dimension Reduction . 133 135 138 139 140 145 148 151 153 153 156 161 182 186 190 193 195 195 197 199 201 205 210 211 213 213 215 216 220 221 221 222 225 227 227 231 232 234
Contents xiv 16 15.3 Dimension Reduction with Correlated Synapses . 15.3.1 Model Setting . 15.3.2 Mean-Field Calculation. 15.3.3 Numerical Results Compared with Theory . References . 237 238 239 247 250 Chaos Theory of Random Recurrent Neural Networks . 253 253 255 255 259 262 264 268 268 268 272 16.1 16.2 Spiking and Rate Models . Dynamical Mean-Field Theory . 16.2.1 Dynamical Mean-Field Equation . 16.2.2 Regimes of Network Dynamics . 16.3 Lyapunov Exponent and Chaos. 16.4 Excitation-Inhibition Balance Theory . 16.5 Training Recurrent Neural Networks . 16.5.1 Force-Training . 16.5.2 Backpropagation Through Time . References . 17 Statistical Mechanics of Random Matrices . 17.1 Spectral Density
. 17.2 Replica Method and Semi-circle Law . 17.3 Cavity Approach and Marchenko-Pastur Law . 17.4 Spectral Densities of Random Asymmetric Matrices. References . 18 Perspectives . References . 275 275 277 281 285 289 291 294 |
| adam_txt |
Contents 1 Introduction . References . 2 Spin Glass Models and Cavity Method . 2.1 Multi-spin Interaction Models. 2.2 Cavity Method . 2.3 From Cavity Method to Message Passing Algorithms. References . 3 Variational Mean-Field Theory and Belief Propagation . Variational Method . Variational Free Energy . 3.2.1 Mean-Field Approximation . 3.2.2 Bethe Approximation . 3.2.3 From the Bethe to Naive Mean-Field Approximation . 3.3 Mean-Field Inverse Ising Problem . References . 3.1 3.2 4 Monte Carlo Simulation Methods. Monte Carlo
Method. Importance Sampling . Markov Chain Sampling . Monte Carlo Simulations in Statistical Physics . 4.4.1 Metropolis Algorithm . 4.4.2 Parallel Tempering Monte Carlo . References . 4.1 4.2 4.3 4.4 5 High-Temperature Expansion . 5.1 Statistical Physics Setting . 5.2 High-Temperature Expansion . 5.3 Properties of the TAP Equation. References . 1 З 5 5 8 12 14 17 17 18 20 22 27 29 30 33 33 34 35 36 37 39 42 43 43 46 51 52 xi
Contents xii 6 Nishimori Line. 6.1 Model Setting . 6.2 Exact Result for Internal Energy. 6.3 Proof of No RSB Effects on the Nishimori Line. References . 7 Random Energy Model . 7.1 Model Setting . 7.2 Phase Diagram. References . 8 Statistical Mechanical Theory of Hopfield Model . Hopfield Model . Replica Method . 8.2.1 Replica-Symmetric Ansatz . 8.2.2 Zero-Temperature Limit . 8.3 Phase Diagram. 8.4 Hopfield Model with Arbitrary Hebbian Length. 8.4.1 Computation of the Disorder-Averaged Free Energy
. 81 8.4.2 Derivation of Saddle-Point Equations . 8.4.3 Computation Transformation to Solve the SDE. 8.4.4 Zero-Temperature Limit . References . 8.1 8.2 9 Replica Symmetry and Replica Symmetry Breaking . 9.1 Generalized Free Energy and Complexity of States. 9.2 Applications to Constraint Satisfaction Problems. 9.3 More Steps of Replica Symmetry Breaking . References . 10 Statistical Mechanics of Restricted Boltzmann Machine 10.1 10.2 10.3 10.4 10.5 10.6 . Boltzmann Machine . Restricted Boltzmann Machine . Free Energy Calculation . Thermodynamic Quantities Related to Learning . Stability Analysis . Variational Mean-Field Theory for Training Binary RBMs . 10.6.1 RBMs with Binary Weights . 10.6.2 Variational Principle . 10.6.3
Experiments . References . 55 55 56 57 58 59 59 61 62 63 63 66 73 78 79 81 91 92 94 98 99 99 102 106 108 Ill Ill 113 115 117 121 123 124 125 130 132
xiii Contents 11 Simplest Model of Unsupervised Learning with Binary Synapses . 133 Model Setting . Derivation of sMP and AMP Equations. Replica Computation . 11.3.1Explicit form of (Z") . 11.3.2 Estimation of (Z") Under Replica Symmetry Ansatz . 11.3.3 Derivation of Free Energy and Saddle-Point Equations. 142 11.4 Phase Transitions. 11.5 Measuring the Temperature of Dataset. References . 11.1 11.2 11.3 12 Inherent-Symmetry Breaking in Unsupervised Learning. 12.1 Model Setting . 12.1.1 Cavity Approximation . 12.1.2 Replica Computation . 12.1.3 Stability Analysis . 12.2 Phase
Diagram. 12.3 Hyper-Parameters Inference . References . 13 Mean-Field Theory of Ising Perceptron . Ising Perceptron model. Message-Passing-Based Learning. Replica Analysis . 13.3.1 Replica Symmetry . 13.3.2 Replica Symmetry Breaking. 13.4 Further Theory Development. References . 13.1 13.2 13.3 14 Mean-Field Model of Multi-layered Perceptron . Random Active Path Model. 14.1.1 Results from Cavity Method. 14.1.2 An Infinite Depth Analysis . 14.2 Mean-Field Training Algorithms . 14.3 Spike and Slab Model. 14.3.1 Ensemble Perspective
. 14.3.2 Training Equations. References . 14.1 15 Mean-Field Theory of Dimension Reduction . 15.1 Mean-Field Model. 15.2 Linear Dimensionality and Correlation Strength . 15.2.1 Iteration Equations for Correlation Strength . 15.2.2 Mechanism of Dimension Reduction . 133 135 138 139 140 145 148 151 153 153 156 161 182 186 190 193 195 195 197 199 201 205 210 211 213 213 215 216 220 221 221 222 225 227 227 231 232 234
Contents xiv 16 15.3 Dimension Reduction with Correlated Synapses . 15.3.1 Model Setting . 15.3.2 Mean-Field Calculation. 15.3.3 Numerical Results Compared with Theory . References . 237 238 239 247 250 Chaos Theory of Random Recurrent Neural Networks . 253 253 255 255 259 262 264 268 268 268 272 16.1 16.2 Spiking and Rate Models . Dynamical Mean-Field Theory . 16.2.1 Dynamical Mean-Field Equation . 16.2.2 Regimes of Network Dynamics . 16.3 Lyapunov Exponent and Chaos. 16.4 Excitation-Inhibition Balance Theory . 16.5 Training Recurrent Neural Networks . 16.5.1 Force-Training . 16.5.2 Backpropagation Through Time . References . 17 Statistical Mechanics of Random Matrices . 17.1 Spectral Density
. 17.2 Replica Method and Semi-circle Law . 17.3 Cavity Approach and Marchenko-Pastur Law . 17.4 Spectral Densities of Random Asymmetric Matrices. References . 18 Perspectives . References . 275 275 277 281 285 289 291 294 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T19:04:59Z |
| indexdate | 2024-12-09T17:01:26Z |
| institution | BVB |
| isbn | 9789811675720 9789811675690 |
| language | English |
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| spelling | Huang, Haiping Verfasser (DE-588)1299857248 aut Statistical mechanics of neural networks Haiping Huang Singapore Springer [2021] Higher Education Press © 2021 xviii, 296 Seiten Diagramme (teilweise farbig) 631 grams txt rdacontent n rdamedia nc rdacarrier Chapter 1: Introduction; Chapter 2: Spin Glass Models and Cavity Method; Chapter 3: Variational Mean-Field Theory and Belief Propagation; Chapter 4: Monte-Carlo Simulation Methods; Chapter 5: High-Temperature Expansion Techniques; Chapter 6: Nishimori Model; Chapter 7: Random Energy Model; Chapter 8: Statistical Mechanics of Hopfield Model; Chapter 9: Replica Symmetry and Symmetry Breaking; Chapter 10: Statistical Mechanics of Restricted Boltzmann Machine; Chapter 11: Simplest Model of Unsupervised Learning with Binary Synapses; Chapter 12: Inherent-Symmetry Breaking in Unsupervised Learning; Chapter 13: Mean-Field Theory of Ising Perceptron; Chapter 14: Mean-Field Model of Multi-Layered Perceptron; Chapter 15: Mean-Field Theory of Dimension Reduction in Neural Networks; Chapter 16: Chaos Theory of Random Recurrent Networks; Chapter 17: Statistical Mechanics of Random Matrices; Chapter 18: Perspectives Neural networks (Computer science) Statistical Mechanics Computational intelligence Artificial intelligence Statistical Physics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Neuronales Netz (DE-588)4226127-2 gnd rswk-swf Hardcover, Softcover / Physik, Astronomie/Allgemeines, Lexika Neuronales Netz (DE-588)4226127-2 s Statistische Mechanik (DE-588)4056999-8 s DE-604 Erscheint auch als Online-Ausgabe 978-981-16-7570-6 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033193686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huang, Haiping Statistical mechanics of neural networks Neural networks (Computer science) Statistical Mechanics Computational intelligence Artificial intelligence Statistical Physics Statistische Mechanik (DE-588)4056999-8 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4226127-2 |
| title | Statistical mechanics of neural networks |
| title_auth | Statistical mechanics of neural networks |
| title_exact_search | Statistical mechanics of neural networks |
| title_exact_search_txtP | Statistical mechanics of neural networks |
| title_full | Statistical mechanics of neural networks Haiping Huang |
| title_fullStr | Statistical mechanics of neural networks Haiping Huang |
| title_full_unstemmed | Statistical mechanics of neural networks Haiping Huang |
| title_short | Statistical mechanics of neural networks |
| title_sort | statistical mechanics of neural networks |
| topic | Neural networks (Computer science) Statistical Mechanics Computational intelligence Artificial intelligence Statistical Physics Statistische Mechanik (DE-588)4056999-8 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| topic_facet | Neural networks (Computer science) Statistical Mechanics Computational intelligence Artificial intelligence Statistical Physics Statistische Mechanik Neuronales Netz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033193686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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