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Observation and Characterization of Memristor Current Spikes and their Application to Neuromorphic Computation. Ella Gale , Ben de Lacy Costello and Andrew Adamatzky. Contents. How do Neurons Compute? Competing Models for the Memristor Making Spiking Neural Networks with Memristors
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Observation and Characterization of Memristor Current Spikes and their Application to Neuromorphic Computation Ella Gale, Ben de Lacy Costello and Andrew Adamatzky
Contents • How do Neurons Compute? • Competing Models for the Memristor • Making Spiking Neural Networks with Memristors • The Memristor Acting as a Neuron • Characteristics and Properties • Where do the Spikes come from?
How Does the Brain Differ From a Modern-Day Computer? • Slow • Parallel Processing • High degree of interconnectivity • Spiking Neural Nets • Ionic • Analogue
The Memristor as a Synapse Before learning Before learning After learning After learning During learning
Spike-Time Dependent Plasticity, STDP • Process by which synapses are potentiated • Related to Hebb’s Rule • Possibly a cause of memory and learning • Relative timing of spike inputs to a synapse important Bi and Poo, Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength and Postsynaptic Cell Type, J. Neurosci., 1998
Phenomenological Model = ionic mobility of the O+ vacancies Roff = resistance of TiO2 Ron = resistance of TiO(2-x) Strukov et al, The Missing Memristor Found, Nature, 2008
Chua’s Definitions of Types of Memristors Charge-Controlled Memristor Flux-Controlled Memristor L. Chua, Memristor – The Missing Circuit Element, IEEE Trans. Circuit Theory, 1971
What the Flux? But, where is the magnetic flux? Strukov et al, 2008 Chua, 1971
Starting From The Ions… • Memristance is a phenomenon associated with ionic current flow • Therefore calculate the magnetic flux of the IONS • Vacancy Volume Current , L = eLectric field • Vacancy Magnetic Field • Vacancy Magnetic Flux
Memristance, as Derived from Ion Flow • Universal constants: • X, Experimental constants: product of surface area and electric field • , material variable, = Gale, The Missing Magnetic Flux in the HP Memristor Found, 2011
Mem-Con Theory Gale, The Missing Magnetic Flux in the HP Memristor Found, Submitted, 2011
Our Intent: • To make a memristor brain • & thus a machine intelligence
Connecting Memristors with Spiking Neurons to Implement STDP Simulation Results 1. Zamarreno-Ramos et al, On Spike Time Dependent Plasticity, Memristive Devices and Building a Self-Learning Visual Cortex, Frontiers in Neuroscience, 2011 0. Linares-Barranco and Serrano-Gotarredona, Memristance can explain Spike-Time-Dependent-Plasticity in Neural Synapses, Nature Preceedings, 2009
But, Memristors Spike Naturally!
Our Memristors • Crossed Aluminium electrodes • Thin-film (40nm) TiO2 sol-gel layer 1. Gergel-Hackett et al, A Flexible Solution Processed Memristor, IEEE Elec. Dev. Lett., 2009 2. Gale et al, Aluminium Electrodes Effect the Operation of Titanium Dioxide Sol-Gel Memristors, Submitted 2012
Spikes are Reproducible Current Spike Response Voltage Square Wave
Spikes are Repeatable Current Response Voltage Ramp
Memristor Behaviour Looks Similar to Neurons Neuron Memristor Bal and McCormick, Synchronized Oscilliations in the Inferior Olive are controlled by the Hyperpolarisation-Activated Cation Current Ih, J. Neurophysiol, 77, 3145-3156, 1997
SpintronicMemristor Current Spikes Pershinand Di Ventra, Spin Memristive Systems: Spin Memory Effects in Semi-conductor Spintronics, Phys. Rev. B, 2008
Properties of Spikes • Direction of Spikes is related to not V • The switch to 0V has a associated current spike • Spikes are repeatable • Spikes are reproducable • Spikes are seen in bipolar switching memristors/ReRAM • Spikes are not seen in unipolar switching, UPS ReRAM type memristors
Two Different Types of Memristor Behaviour Seen in Our Lab Curved (BPS-like) Memristors Triangular (UPS-like) Memristors • Pictures
Two Different Types of Memristor Behaviour Seen in Our Lab Triangular (UPS-like) Memristors Curved (BPS-like) Memristors
Where do the Spikes Come From? Does Current Theory Predict Their Existence?
Mem-Con Model Applied to Memristor Spikes Memristors Neurons
In Chua’s Model Neuron Voltage Spikes Memristor Current Spikes • Dynamics related to min. response time, τ, related to speed of ion diffusion across membrane • Memory property = ??? • Neuron operated in a current-controlled way • Dynamics related to τ, which is related to • Memory property = qv • Memristor operated in voltage controlled way
What is the Memory Property of Neurons? • More complex system than a single memristor • Short-term memory associated with membrane potential • Long term memory associated with the number of synaptic buds
Memristor Models Fit the Data Sol-Gel MemristorPositiveV Sol-Gel Memristor Negative V
Au-TiO2-Au WORMS Memory Time Dependent I-V I-t Response to Stepped Voltage
Al-TiO2-Al Current Response to Voltage Ramp Current Response Voltage Ramp
Further Work • Neurology: • Modelling Neurons with the Mem-Con Theory to prove that they are Memristive • Investigate the Memory Property for neurons • Unconventional Computing: • Further Investigation of memristor and ReRAM properties • Attempt to build a neuromorphic control system for a navigation robot
Summary • Neurons May Be Biological Memristors • Neurons Operate via Voltage Spikes • Memristors can Operative via Current Spikes • Thus, Memristors are Good Candidates for Neuromorphic Computation • A Memristor-based Neuromorphic Computer will be Voltage Controlled and transmit data via Current Spikes
With Thanks to • Victor Erokhin and his group (University of Parma) • Steve Kitson (HP UK) • David Pearson (HP UK) • Bristol Robotics Laboratory • Ben de Lacy Costello • Andrew Adamatzky • David Howard • Larry Bull