## Statistical Mechanics of LearningThe effort to build machines that are able to learn and undertake tasks such as datamining, image processing and pattern recognition has led to the development of artificial neural networks in which learning from examples may be described and understood. The contribution to this subject made over the past 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. |

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### Contents

II | 1 |

III | 4 |

IV | 8 |

V | 13 |

VI | 14 |

VIII | 18 |

IX | 22 |

X | 27 |

LIV | 155 |

LV | 159 |

LVI | 160 |

LVII | 165 |

LVIII | 169 |

LIX | 170 |

LX | 171 |

LXI | 176 |

XI | 29 |

XII | 33 |

XIII | 36 |

XIV | 37 |

XV | 39 |

XVI | 40 |

XVII | 42 |

XVIII | 46 |

XX | 49 |

XXI | 52 |

XXII | 56 |

XXIII | 59 |

XXIV | 63 |

XXV | 64 |

XXVI | 65 |

XXVII | 69 |

XXVIII | 72 |

XXIX | 78 |

XXX | 80 |

XXXI | 82 |

XXXII | 83 |

XXXIII | 85 |

XXXIV | 89 |

XXXV | 93 |

XXXVI | 98 |

XXXVII | 102 |

XXXVIII | 104 |

XXXIX | 109 |

XLI | 111 |

XLII | 114 |

XLIII | 118 |

XLIV | 121 |

XLV | 122 |

XLVI | 125 |

XLVII | 129 |

XLVIII | 133 |

XLIX | 137 |

L | 142 |

LI | 147 |

LII | 149 |

LIII | 152 |

LXII | 178 |

LXIII | 180 |

LXIV | 182 |

LXV | 186 |

LXVI | 189 |

LXVII | 190 |

LXVIII | 193 |

LXIX | 195 |

LXX | 203 |

LXXI | 207 |

LXXIII | 209 |

LXXIV | 210 |

LXXV | 214 |

LXXVI | 218 |

LXXVII | 222 |

LXXVIII | 225 |

LXXIX | 228 |

LXXX | 230 |

LXXXI | 232 |

LXXXII | 237 |

LXXXIII | 243 |

LXXXIV | 246 |

LXXXV | 251 |

LXXXVI | 253 |

LXXXVII | 255 |

LXXXVIII | 256 |

LXXXIX | 259 |

XC | 263 |

XCI | 266 |

XCII | 270 |

XCIII | 275 |

XCIV | 282 |

XCV | 289 |

XCVI | 291 |

XCVII | 300 |

XCVIII | 304 |

XCIX | 310 |

313 | |

327 | |

### Common terms and phrases

adatron algorithm alignment annealed annealed approximation ansatz architecture asymptotic behaviour average Bayes Boolean function bound calculation cells chapter characterized classification cluster committee machine Consider convergence corresponding cost function coupling vector defined denotes determined exponentially Fisher information free energy Gaussian Gibbs learning given gives rise Hebb rule hence hidden units hyperplane indicator function input integral internal representations introduced Ising perceptron learning from examples learning process learning rules matrix maximal minimal mixed strategies multifractal spectrum multilayer networks neural networks neurons obtained off-line on-line learning optimal order parameters output noise overlap parity tree perceptron learning performance probability distribution quenched entropy random variables realize replica symmetry breaking replica trick result reversed wedge perceptron saddle point equations self-averaging Show simple stability statistical mechanics storage capacity storage problem student vector thermodynamic limit training error training set typical unsupervised unsupervised learning VC dimension version space W-sphere zero

### Popular passages

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