COMPLEX NEURAL COMPUTATION WITH SIMPLE DIGITAL

by

Andrew Thomas Nere

A dissertation submitted in partial fulfillment of

the requirements for the degree of

Doctor of Philosophy

(Electrical Engineering)

at the

UNIVERSITY OF WISCONSIN–MADISON

2013 © Copyright by Andrew Thomas Nere 2013

All Rights Reserved i

dedication ii acknowledgments iii table of contents

Table of Contents ...... iii

List of Tables ...... ix

List of Figures ...... x

Abstract ...... xiii

1. Introduction ...... 1

1.1 Motivation: Challenges Faced by the von Neumann Architecture ...... 1

1.2 Inspiration: The Cortex as a Computing Model ...... 2

1.3 Spiking Models and Neuromorphic Hardware ...... 3

1.4 Objectives and Contributions ...... 4

1.4.1 Computing Capabilities of Simple Spiking Neurons ...... 4

1.4.2 Identifying Useful Complex Neuronal Dynamics ...... 4

1.4.3 Modeling the Visual Cortex as a Hierarchical Attractor Network . . . 5

1.4.4 Visual Cortex Model Applications ...... 5

1.4.5 Addressing the Neuromorphic Semantic Gap ...... 5

1.4.6 Automatic Approaches for Deploying Cortical Models on Neuromor-

phic Substrates ...... 6

1.5 Related Published Work ...... 6

1.6 Dissertation Structure ...... 7 iv

2. Artificial Neuron Models and Neural Networks ...... 9

2.1 A Brief History of Artificial Neural Networks ...... 9

2.2 Spiking Neuron Models ...... 12

2.2.1 The Hodgkin-Huxley Model ...... 14

2.2.2 The Izhikevich Model ...... 15

2.2.3 The Leaky Integrate and Fire Model ...... 17

2.3 Biologically Inspired Learning Mechanisms ...... 20

2.3.1 Hebbian Learning ...... 20

2.3.2 Spike Timing Dependent Plasticity ...... 21

2.3.3 Variants of STDP ...... 22

2.3.4 Reward Based Learning Paradigms ...... 23

2.4 Introduction to the ...... 24

2.5 The Visual Cortex ...... 26

2.6 Recurrent Neural Networks ...... 30

2.6.1 The Hopfield Attractor Neural Network ...... 30

2.6.2 Transient and Metastable Attractor Networks ...... 32

2.6.3 Liquid State Machines ...... 36

2.6.4 Recurrent Neural Networks Summary ...... 37

2.7 Summary ...... 38

3. Neuromorphic Hardware ...... 39

3.1 Neurogrid ...... 39 v

3.2 The BrainScaleS Neuromorphic Processor ...... 40

3.3 SpiNNaker ...... 42

3.4 IBM’s Neurosynaptic Core ...... 43

3.4.1 Why Target the Neurosynaptic Core? ...... 44

3.4.2 Description and Operation of the Neurosynaptic Core ...... 46

3.4.3 The Neurosynaptic Core with Online Learning ...... 50

3.5 Summary ...... 51

4. Modeling Spiking Neurons and Biologically Inspired Learning Mechanisms . 52

4.1 Leaky Integrate-and-Fire Spiking Neuron Model ...... 52

4.2 Learning with Bursts of Spikes ...... 54

4.3 Value Dependent Learning ...... 56

4.4 Homeostatic Renormalization ...... 57

4.5 Preliminary Spiking Model of the Visual System ...... 59

4.5.1 Shape Categorization Module ...... 59

4.5.2 Motion Detection Module ...... 63

4.5.3 Attention Module ...... 66

4.5.4 Decision Module and Motor Outputs ...... 67

4.6 Experimental Results ...... 67

4.6.1 Experiment 1: Shape Categorization ...... 68

4.6.2 Experiment 2: Catching Targets and Avoiding Obstacles ...... 69 vi

4.6.3 Experiment 3: Anticipating a Target Object Location with Multiple

Objects ...... 71

4.7 Summary ...... 72

5. Visual Cortex Model ...... 73

5.1 Extending the LLIF Neuron Model ...... 73

5.1.1 Short-Term Plasticity ...... 73

5.1.2 NMDA Modulated Synapses ...... 76

5.2 The Visual Cortex as a Hierarchical Metastable Attractor ...... 79

5.2.1 Hierarchical Organization and the Feedforward Pathways ...