Plausible Neural Networks for Biological Modelling / Edition 1

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Overview

This book has the unique intention of returning the mathematical tools of neural networks to the biological realm of the nervous system, where they originated a few decades ago. It aims to introduce, in a didactic manner, two relatively recent developments in neural network methodology, namely recurrence in the architecture and the use of spiking or integrate-and-fire neurons. In addition, the neuro-anatomical processes of synapse modification during development, training, and memory formation are discussed as realistic bases for weight-adjustment in neural networks.
While neural networks have many applications outside biology, where it is irrelevant precisely which architecture and which algorithms are used, it is essential that there is a close relationship between the network's properties and whatever is the case in a neuro-biological phenomenon that is being modelled or simulated in terms of a neural network. A recurrent architecture, the use of spiking neurons and appropriate weight update rules contribute to the plausibility of a neural network in such a case.
Therefore, in the first half of this book the foundations are laid for the application of neural networks as models for the various biological phenomena that are treated in the second half of this book. These include various neural network models of sensory and motor control tasks that implement one or several of the requirements for biological plausibility.
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Product Details

Table of Contents

Preface 1
Part I Fundamentals
1 Biological Evidence for Synapse Modification Relevant for Neural Network Modelling
1. Introduction 7
2. The Synapse 11
3. Long Term Potentiation 13
4. Two Characteristic Types of Experiment 15
4.1 Food Discrimination Learning in Chicks 15
4.2 Electrical Stimulation of Nervous Cell Cultures 18
5. Conclusion 19
References and Further Reading 20
2 What is Different with Spiking Neurons?
1. Spikes and Rates 23
1.1 Temporal Average-Spike Count 24
1.2 Spatial Average-Population Activity 26
1.3 Pulse Coding-Correlations and Synchrony 27
2. 'Integrate and Fire' Model 28
3. Spike Response Model 30
4. Rapid Transients 33
5. Perfect Synchrony 36
6. Coincidence Detection 38
7. Spike Time Dependent Hebbian Learning 39
8. Temporal Coding in the Auditory System 42
9. Conclusion 43
References 45
3 Recurrent Neural Networks: Properties and Models
1. Introduction 49
2. Universality of Recurrent Networks 52
2.1 Discrete Time Dynamics 52
2.2 Continuous Time Dynamics 54
3. Recurrent Learning Algorithms for Static Tasks 56
3.1 Hopfield Network 56
3.2 Boltzmann Machines 58
3.3 Recurrent Backpropagation Proposed by Fernando Pineda 60
4. Recurrent Learning Algorithms for Dynamical Tasks 63
4.1 Backpropagation Through Time 63
4.2 Jordan and Elman Networks 64
4.3 Real Time Recurrent Learning (RTRL) 65
4.3.1 Continuous Time RTRL 65
4.3.2 Discrete Time RTRL 66
4.3.3 Teacher Forced RTRL 67
4.3.4 Considerations about the Memory Requirements 67
4.4 Time Dependent Recurrent Backpropagation (TDRBP) 68
5. Other Recurrent Algorithms 69
6. Conclusion 70
References 72
4 A Derivation of the Learning Rules for Dynamic Recurrent Neural Networks
1. A Look into the Calculus of Variations 75
2. Conditions of Constraint 77
3. Applications in Physics: Lagrangian and Hamiltonian Dynamics 78
4. Generalized Coordinates 80
5. Application to Optimal Control Systems 82
6. Time Dependent Recurrent Backpropagation: Learning Rules 85
References 88
Part II Applications to Biology
5 Simulation of the Human Oculomotor Integrator Using a Dynamic Recurrent Neural Network
1. Introduction 92
2. The Different Neural Integrator Models 95
3. The Biologically Plausible Improvements 99
3.1 Fixed Sign Connection Weights 100
3.2 Artificial Distance between Inter-Neurons 101
3.3 Numerical Discretization of the Continuous Time Model 101
3.4 The General Supervisor 102
3.5 The Modified Network 103
4. Emergence of Clusters 104
4.1 Definition 105
4.2 Mathematical Identification of Clusters 106
4.3 Characterization of the Clustered Structure 106
4.4 Particular Locations 110
5. Discussion and Conclusion 110
References 112
6 Pattern Segmentation in an Associative Network of Spiking Neurons
1. The Binding Problem 117
2. Spike Response Model 118
3. Simulation Results 121
3.1 Pattern Retrieval and Synchronization 123
3.2 Pattern Segmentation 124
3.3 Context Sensitive Binding in a Layered Network with Feedback 126
4. Related Work 129
4.1 Segmentation with LEGION 129
4.2 How about Real Brains? 130
References 131
7 Cortical Models for Movement Control
1. Introduction: Constraints on Modeling Biological Neural Networks 135
2. Cellular Firing Patterns in Monkey Cortical Areas 4 and 5 137
3. Anatomical Links between Areas 4 and 5, Spinal Motoneurons, and Sensory Systems 140
4. How Insertion of a Time Delay can Create a Niche for Deliberation 141
5. A Volition-Deliberation Nexus and Voluntary Trajectory Generation 142
6. Cortical-Subcortical Cooperation for Deliberation and Task-Dependent Configuration 146
7. Cortical Layers, Neural Population Codes, and Posture-Dependent Recruitment of Muscle Synergies 150
8. Trajectory Generation in Handwriting and Viapoint Movements 151
9. Satisfying Constraints of Reaching to Intercept or Grasp 155
10. Conclusions: Online Action Composition by Cortical Circuits 156
References 157
8 Implications of Activity Dependent Processes in Spinal Cord Circuits for the Development of Motor Control; a Neural Network Model
1. Introduction 164
2. Sensorimotor Development 165
3. Reflex Contributions to Joint Stiffness 166
4. The Model 167
4.1 Neural Model 168
4.2 Musculo-Skeletal Model 170
4.3 Muscle Model 172
4.4 Sensory Model 173
4.5 Model Dynamics 174
5. Experiments 174
5.1 Training 176
5.2 Neural Control Properties 177
5.3 Perturbation Experiments 179
6. Discussion 182
References 185
9 Cortical Maps as Topology-Representing Neural Networks Applied to Motor Control: Articulatory Speech Synthesis
1. Lateral Connections in Cortical Maps 190
2. A Neural Network Model 191
3. Spatial Maps as Internal Representations for Motor Planning 193
3.1 Dynamical Behavior of Spatial Maps 194
3.2 Function Approximation by Interconnected Maps 196
3.3 Dynamical Inversion 199
4. Application of Cortical Maps to Articulatory Speech Synthesis 200
4.1 Cortical Control of Speech Movements 202
4.2 An Experimental Study 203
4.2.1 The Training Procedure 204
4.2.2 Field Representation of Phonemic Targets 208
4.2.3 Non-Audible Gestures and Compensation 211
4.2.4 Generation of VVV ... Sequences 211
5. Conclusions 215
References 216
10 Line and Edge Detection by Curvature-Adaptive Neural Networks
1. Introduction 220
2. Biological Constraints 223
3. Construction of the Gabor Filters 224
4. The One-Dimensional Case 224
5. The Two-Dimensional Case 225
6. Simple Detection Scheme 225
7. An Extended Detection Scheme 226
8. Intermezzo: A Multi-Scale Approach 230
9. Advanced Detection Scheme 231
10. Biological Plausibility of the Adaptive Algorithm 233
11. Conclusion and Discussion 235
References 238
11 Path Planning and Obstacle Avoidance Using a Recurrent Neural Network
1. Introduction 241
2. Problem Description 242
3. Task Descriptions 243
3.1 Representations 243
3.2 Fusing the Representations into a Neuronal Map 245
3.3 Path Planning and Heading Decision 246
4. Results 248
5. Conclusions 251
References 253
Index 255
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