LEARNING IN SILICON: A NEUROMORPHIC MODEL OF THE HIPPOCAMPUS John Vernon Arthur A DISSERTATION in Bioengineering Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2006 Kwabena Boahen, Christopher S. Chen, Supervisor of Dissertation Graduate Group Chair COPYRIGHT John Vernon Arthur 2006 Acknowledgements Many people contributed in many ways to my time at Penn. I thank them all. Specifically, I thank my advisor, Kwabena Boahen. He has guided me through many challenges and has provided a constant example of what a researcher should be and can accomplish. Our interactions taught me a great deal and shaped my vision of research, science, and engineering for the better. I thank my committee - Matt Dalva, Leif Finkel, and John Hopfield - who provided advice as well as new insights and different viewpoints that challenged my assumptions, improving my work. I thank those that I had the opportunity to work with - Kareem Zaghloul, Kai Hynna, Brian Taba, Paul Merolla, Bo Wen, John Wittig, Thomas Choi, Rodrigo Alvarez, and Joe Lin - for the time we spent at work and at play. I thank them and many others for their friendship. I thank my family, my parents for exemplifying integrity and work ethic, and my sib- lings for their encouragement. Finally, I thank my wife, Amy, for immeasurable contributions— her enduring support, her constant willingness to help, and her extraordinary tolerance. iii Abstract LEARNING IN SILICON: A NEUROMORPHIC MODEL OF THE HIPPOCAMPUS John Vernon Arthur Supervisor: Kwabena Boahen The human brain is the most complex computing structure in the known universe; it excels at many tasks that digital computers perform poorly, such as learning input patterns and later retreiving them with only a part of the original patterns as input, realizing associa- tive memory. Our brains perform these feats rapidly and with unmatched energy efficiency, using only about 10W, far less than a typical light bulb. To explore neurobiological process- ing, neuromorphic engineers use existing silicon technology to duplicate neural structure and function down to the level of ion channels, efficiently morphing brain-like computation into mixed analog and digital integrated circuits. In this dissertation, we present a neuromorphic model of the hippocampus, a brain region critical in associative memory. We model hippocampal rhythmicity for the first time in a neuromorphic model by developing a new class of silicon neurons that synchronize by using shunting inhibition (conductance-based) with a synaptic rise-time. Synaptic rise-time promotes synchrony by delaying the effect of inhibition, providing an opportune period for neurons to spike together. Shunting inhibition, through its voltage dependence, inhibits neurons that spike out of phase more strongly (delaying the spike further), pushing them into phase (in the next cycle). In addition, we use these neurons to implement associative memory in a recurrent net- work that uses binary-weighted synpases with spike timing-dependent plasticity (STDP) to iv learn stimulated patterns of neuron activity and to compensate for variability in excitability. STDP preferentially potentiates (turns on) synapses that project from excitable neurons, which fire early, to lethargic neurons, which fire late. The additional excitatory synaptic current makes lethargic neurons fire earlier, thereby causing neurons that belong to the same pattern to fire in synchrony. Potentiation among neurons in the same pattern store it such that, once learned, an entire pattern can be recalled by stimulating a subset, which recruits the inactive members of the original pattern. v Contents Acknowledgements iii Abstract iv Contents vi List of Figures xv 1 Introduction 1 1.1 Dissertation Structure . 2 1.2 Original Contributions . 4 2 A Model of the Episodic Hippocampus 6 2.1EpisodicMemory............................... 7 vi 2.2 The Episodic Hippocampus . 8 2.3 Hippocampal Biology . 12 2.3.1 Hippocampal Neurons . 14 2.3.1.1 Granule Neurons . 16 2.3.1.2 Mossy Neurons . 16 2.3.1.3 CA3 Pyramidal Neurons . 17 2.3.1.4 CA1 Pyramidal Neurons . 17 2.3.1.5 Inhibitory Interneurons . 18 2.3.2 Connections . 18 2.3.2.1 Trisynaptic Circuit . 18 2.3.2.2 Dentate Gyrus Excitatory Connectivity . 19 2.3.2.3 CA3 Excitatory Connectivity . 20 2.3.2.4 CA1 Excitatory Connectivity . 21 2.3.2.5 Inhibitory Interneuron Connectivity . 22 2.3.3 Long-Term Synaptic Plasticity . 22 2.3.3.1 Hebb’s Rule . 22 vii 2.3.3.2 Long-Term Potentiation and Depression . 23 2.3.3.3 Spike Timing-Dependent Plasticity . 26 2.3.4 Rhythmicity . 27 2.3.4.1 Theta Rhythm . 28 2.3.4.2 Gamma Rhythm . 29 2.4 Components of Sequence Memory . 30 2.4.1 Autoassociation . 30 2.4.2 Heteroassociation . 32 2.4.3 Abstract Sequence Memory . 34 2.5 Models of the Hippocampus . 34 2.5.1 Models of Hippocampal Autoassociation . 35 2.5.2 Models of Hippocampal Sequence Memory . 36 2.6 Dual Autoassociation Model of Sequence Memory . 41 2.6.1 Autoassociative and Heteroassociative Memory Regions . 42 2.6.2 Sequence Memory Storage . 43 2.6.3 Sequence Memory Recall . 46 viii 2.6.4 The Role of the CA1 . 46 2.7 Neuromorphic CA3 . 47 3 A Neuromorphic Neuron 48 3.1 Neuromorphic Design Methodology: In the Valley of Death . 49 3.2 Conductance-Based Neuron Design . 52 3.3NeuronCircuit................................ 58 3.3.1 Low-pass Filter . 58 3.3.2 Pulse Extender . 64 3.3.3 SomaCircuit............................. 67 3.3.4 Synapse Circuit . 70 3.4 Characterization . 73 3.4.1 Frequency-Current Curve . 74 3.4.2 Synaptic Rise and Decay . 81 3.4.3 Synaptic Summation . 81 3.4.4 Phase-Response . 86 3.5Discussion................................... 87 ix 4 Silicon Gamma Synchrony 89 4.1 Gamma Synchrony in the Hippocampal Formation . 90 4.2PreviousModels............................... 91 4.2.1 Silicon Models . 92 4.2.2 Analytical Models . 92 4.2.3 Computational models . 93 4.3 Including Synaptic Rise-Time . 96 4.4 Interneuron Circuit . 100 4.4.1 Phase-Response Curve . 100 4.5 Interneuron Network . 102 4.5.1 Experimental Setup . 103 4.5.2 Quantifying Synchrony . 103 4.5.3 Computing Network Frequency and Period . 106 4.6Results.....................................107 4.6.1 Gabaergic Rise-time . 109 4.6.2 Other Gabaergic Parameters . 112 x 4.6.3 Input Current . 115 4.6.4 Poisson Input . 116 4.6.5 Pyramidal Neuron Entrainment . 117 4.7Discussion...................................119 5 Silicon Synaptic Spike Timing-Dependent Plasticity 124 5.1 STDP in the Hippocampus . 125 5.2 Plastic Silicon Synapses . 126 5.2.1 Membrane Voltage-Dependent Plasticity . 127 5.2.2 Spike Timing-Dependent Plasticity . 128 5.3 The Silicon STDP Circuit . 129 5.3.1 Specifications . 130 5.3.2 Circuit Design . 131 5.3.3 Analysis...............................134 5.4 Characterization . 136 5.4.1 Spike Timing-Dependent Plasticity Results . 137 5.4.2 Curve Parameters . 137 xi 5.4.3 Variability...............................139 5.4.4 Transition Verification . 142 5.4.5 Poisson Stimulus . 143 5.5Discussion...................................146 6 Timing in Silicon Autoassociation 150 6.1 Hippocampal Associative Memory . 151 6.2 Previous Silicon Autoassociation . 153 6.3 Neuromorphic CA3 . 159 6.3.1 Pyramidal Neuron . 160 6.3.2 Pyramidal Network . 161 6.4 Neuromorphic Autoassociation . 163 6.4.1 Variability Compensation . 163 6.4.2 Pattern Storage and Recall . 167 6.5 Sources of Spike-Timing Variation . 169 6.5.1 Components of Variation . 172 6.5.2 Timing Variation . 174 xii 6.6Discussion...................................176 7 Conclusions 179 7.1 Appropriate Level of Abstraction . 180 7.1.1 Silicon Gamma Synchrony . 180 7.1.2 Silicon Synaptic Plasticity . 181 7.2 Mismatch Matters . 182 7.2.1 Bane of Mismatch . 182 7.2.2 Boon of Mismatch . 183 7.3FutureWork..................................183 7.3.1 Sequence Memory . 184 7.3.2 Neural Scale . 185 7.3.3 Silicon Dendrites . 186 7.4 Insights into Neurobiology . 186 7.5Conclusion..................................187 A Phase Response 189 A.1 Instantaneous Inhibition . 189 xiii A.1.1 Integrator-Type Neuron . 189 A.1.2 Conductance-Type Neuron . 191 A.2 Instantaneous Excitation . 193 A.2.1 Integrator-Type Neuron . 194 A.2.2 Conductance-Type Neuron . 195 B Low-Pass Filter 198 C SRAM Scanner 203 C.1Architecture..................................203 C.2Segments...................................205 Bibliography 208 xiv List of Figures 2.1 The Human Hippocampus . 9 2.2PlaceCells.................................. 10 2.3 The Episodic Hippocampus . 12 2.4 Memory Space Not Space Memory . 13 2.5 Hippocampal Sequence Activity . 14 2.6 Neurons of the.