## An Introduction to the Modeling of Neural NetworksThis text is a graduate-level introduction to neural networks, focusing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence, and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final section of the book reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual neuronal supercomputers, with the potential for one-hundred fold increase in speed over contemporary serial machines. |

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### Contents

Introduction | 1 |

a brief historical overview | 6 |

13 Organization of the book | 11 |

The biology of neural networks a few features for the sake of nonbiologists | 13 |

22 The anatomy of central nervous systems | 15 |

23 A brief survey of neurophysiology | 29 |

a summary of experimental observations | 41 |

The dynamics of neural networks a stochastic approach | 57 |

Solving the problem of credit assignment | 269 |

82 Handling internal representations | 278 |

83 Learning in Boolean networks | 292 |

Selforganization | 299 |

92 Ontogenesis | 307 |

93 Three questions about learning | 319 |

Neurocomputation | 325 |

102 Optimization | 326 |

32 Noiseless neural networks | 64 |

33 Taking synaptic noise into account | 78 |

Hebbian models of associative memory | 99 |

42 Stochastic Hebbian neural networks in the limit of finite numbers of memorized patterns | 112 |

the technique of field distributions | 130 |

44 The replica method approach | 141 |

45 General dynamics of neural networks | 149 |

Temporal sequences of patterns | 153 |

52 Stochastic dynamics | 155 |

53 An example of conditioned behavior | 168 |

The problem of learning in neural networks | 173 |

62 Linear separability | 183 |

63 Computing the volume of solutions | 196 |

Learning dynamics in visible neural networks | 209 |

72 Constraining the synaptic efficacies | 212 |

73 Projection algorithms | 218 |

74 The perceptron learning rules | 230 |

75 Correlated patterns | 248 |

103 Lowlevel signal processing | 350 |

104 Pattern matching | 357 |

105 Some speculations on biological systems | 366 |

106 Higher associative functions | 371 |

Neurocomputers | 379 |

112 Semiparallel neurocomputers | 391 |

A critical view of the modeling of neural networks | 403 |

122 The neural code | 404 |

123 The synfire chains | 405 |

124 Computing with attractors versus computing with flows of information | 406 |

125 The issue of low neuronal activities | 408 |

126 Learning and cortical plasticity | 413 |

127 Taking the modular organization of the cortex into account | 414 |

the problem of artificial intelligence | 416 |

129 Concluding remarks | 418 |

421 | |

467 | |

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### Common terms and phrases

according action potential algorithm architecture associated assume average activity axon basins of attraction behavior binary Boolean function cells classical conditioning coding comprising computation connected networks consider constraints correlations cortex cortical cost function defined determined distribution eigenvalues equations example excitatory exist feedforward Figure fixed points fully connected fully connected networks given Hamming distance Hebbian rule hidden units hippocampus Hopfield inhibitory input units interactions internal representation Kohonen learning dynamics learning rule limit linear machine maps matrix mechanism membrane potential memorized patterns memory storage capacity modified neural networks neurocomputers neuronal dynamics noise number of patterns observed optimization order parameters output unit parallel perceptron perceptron algorithm perceptron rule phase space possible postsynaptic probability problem properties random semi-parallel signals solution spin glasses stimuli stored structure symmetrical synaptic efficacies theory of neural threshold updated vector visible units visual yields zero

### Popular passages

Page 447 - Fast adaptive formation of orthogonalizing filters and associative memory in recurrent networks of neuron-like elements.

Page 444 - 'Neural' Computation of Decisions in Optimization Problems".

Page 462 - Feigel'man MV 1988 The enhanced storage capacity in neural networks with low activity level Europhys.

Page 432 - Simulation of anticipatory responses in classical conditioning by a neuron-like adaptive element.

Page 449 - Nonlinear signal processing using neural networks: Prediction and system modeling.

Page 448 - W. Krauth, J.-P. Nadal, and M.Mezard (1988) The Roles of Stability and Symmetry in the Dynamics of Neural Networks. J. Phys. A: Math. Gen. 21 pp2995-3011.

Page 451 - Llinas, R. , Sugimori, M. and Simon, SM , Transmission by presynaptic spike-like depolarization in the squid giant synapse, Proc. Natl. Acad. Sci. (USA) 79:2415-2419 (1982).

Page 437 - Del Castillo J, Katz B: Statistical factors involved in neuromuscular facilitation and depression. J. Physiol.

Page 447 - Associative neural network model for the generation of temporal patterns: Theory and application to central pattern generators. Biophysical J. 54, 1039-1051. 11. Kleinfeld, D. and Sompolinsky, H. (1989). Associative network models for central pattern generators. In "Methods in Neuronal Modeling: From Synapses to Networks