# Statistical Mechanics of Learning

Cambridge University Press, 29.3.2001 - 329 sivua
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Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.

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### Sisältö

 Getting Started 1 12 A simple example 4 13 General setup 8 14 Problems 13 Perceptron Learning Basics 14 22 The annealed approximation 18 23 The Gardner analysis 22 24 Summary 27
 93 Optimal online learning 155 94 Perceptron with a smooth transfer function 159 95 Queries 160 96 Unsupervised online learning 165 97 The natural gradient 169 98 Discussion 170 99 Problems 171 Making Contact with Statistics 176

 25 Problems 29 A Choice of Learning Rules 33 32 The perceptron rule 36 33 The pseudoinverse rule 37 34 The adaline rule 39 35 Maximal stability 40 36 The Bayes rule 42 37 Summary 46 Augmented Statistical Mechanics Formulation 49 42 Gibbs learning at nonzero temperature 52 43 General statistical mechanics formulation 56 44 Learning rules revisited 59 45 The optimal potential 63 46 Summary 64 47 Problems 65 Noisy Teachers 69 52 Trying perfect learning 72 53 Learning with errors 78 54 Refinements 80 55 Summary 82 56 Problems 83 The Storage Problem 85 the Cover analysis 89 the Ising perceptron 93 64 The distribution of stabilities 98 65 Beyond the storage capacity 102 66 Problems 104 Discontinuous Learning 109 72 The Ising perceptron 111 73 The reversed wedge perceptron 114 74 The dynamics of discontinuous learning 118 75 Summary 121 76 Problems 122 Unsupervised Learning 125 82 The deceptions of randomness 129 83 Learning a symmetrybreaking direction 133 84 Clustering through competitive learning 137 85 Clustering by tuning the temperature 142 87 Problems 147 Online Learning 149 92 Specific examples 152
 102 Sauers lemma 178 103 The VapnikChervonenkis theorem 180 104 Comparison with statistical mechanics 182 105 The CramérRao inequality 186 106 Discussion 189 107 Problems 190 A Birds Eye View Multifractals 193 112 The multifractal spectrum of the perceptron 195 113 The multifractal organization of internal representations 203 114 Discussion 207 Multilayer Networks 209 121 Basic architectures 210 122 Bounds 214 123 The storage problem 218 124 Generalization with a parity tree 222 125 Generalization with a committee tree 225 126 The fully connected committee machine 228 127 Summary 230 128 Problems 232 Online Learning in Multilayer Networks 237 132 The parity tree 243 133 Soft committee machine 246 134 Backpropagation 251 135 Bayesian online learning 253 136 Discussion 255 137 Problems 256 What Else? 259 142 Complex optimization 263 143 Errorcorrecting codes 266 144 Game theory 270 Appendices 275 A2 The Gardner Analysis 282 A3 Convergence of the Perceptron Rule 289 A4 Stability of the Replica Symmetric Saddle Point 291 A5 Onestep Replica Symmetry Breaking 300 A6 The Cavity Approach 304 A7 The VC theorem 310 Bibliography 313 Index 327 Tekijänoikeudet

### Suositut otteet

Sivu 318 - K. Rose, E. Gurewitz, and GC Fox, "Statistical mechanics and phase transitions in clustering," Physical Review Letters, vol.

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