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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 How does a Neuron Compute? Influx of Ionic I Voltage Spike Axon: Transmission along neuron Synapse: Transmission between neurons Memristive Systems to Describe Nerve Axon Membranes Synapse Long-Term Potentiation 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 Memristor Structure and Function Phenomenological Model 𝑀 𝑞 𝑡 𝜇𝑣 = 𝑅off − 2 𝑅off 𝑅on 𝑞(𝑡) 𝐷 𝜇𝑣 = 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 𝑣 𝑡 = 𝑀 𝑞 𝑡 𝑖(𝑡) 𝑑𝜑(𝑞) 𝑀 𝑞 ≡ 𝑑𝑞 F lux-Controlled Memristor 𝑖 𝑡 =𝑊 𝜑 𝑡 𝑣(𝑡) 𝑑𝑞(𝜑) 𝑊(𝜑) ≡ 𝑑𝜑 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 𝑀 𝑞 𝑡 Chua, 1971 𝜇𝑣 = 𝑅𝑜𝑓𝑓 − 2 𝑅𝑜𝑓𝑓 𝑅𝑜𝑛 𝑞(𝑡) 𝐷 𝑉=𝑀 𝑡 𝐼 𝑑𝜑 = 𝑀 𝑞 𝑡 𝑑𝑞 Starting From The Ions… • Memristance is a phenomenon associated with ionic current flow • Therefore calculate the magnetic flux of the IONS Vacancy Volume Current 𝐉 = 𝑞 𝑡 𝜇𝑣 𝐋 𝑉𝑜𝑙𝑇𝑖𝑂(2−𝑥) Vacancy Magnetic Field 𝐁 = Vacancy Magnetic Flux 𝜑 = , L = eLectric field 𝝁𝟎 𝟒𝝅 𝐉×𝐫 |𝐫| 𝑑𝜏 𝜇0 |𝐋|𝜇𝑣 𝑃𝑘 (𝑞 4𝜋 𝑡 ) Memristance, as Derived from Ion Flow • Universal constants: 𝜇0 4𝜋 • X, Experimental constants: product of surface area and electric field • 𝛽, material variable, 𝛽=𝜇𝑣 𝑝𝑘 (𝑞 𝑡 ) 𝑀 𝑞 𝑡 𝜇0 = 𝑋𝛽(𝑞(𝑡)) 4𝜋 Gale, The Missing Magnetic Flux in the HP Memristor Found, 2011 Mem-Con Theory • 𝑅𝑡𝑜𝑡𝑎𝑙 = 𝑅𝑚𝑒𝑚 + 𝑅𝐶𝑜𝑛 • 𝑅𝑀𝑒𝑚 = 𝑐 𝑀 𝑞 𝑡 • 𝑅𝐶𝑜𝑛 = (𝐷−𝑤 𝑡 )𝜌TiO2 𝐸𝐹 𝑞 ↔ 𝑀(𝑞) ↔ 𝜑 Ionic ↑ 𝑉 ↔ 𝑅𝑡𝑜𝑡 (𝑡) ↔ 𝐼 Electronic Gale, The Missing Magnetic Flux in the HP Memristor Found, Submitted, 2011 Memristor I-V Behaviour 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-TimeDependent-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 Current Spikes Seen in I-t Plots Spikes are Reproducible Volta ge Square Wave Cur rent Spike Response Spikes are Repeatable Voltage Ramp Current Response Memristor Behaviour Looks Similar to Neurons Memristor Neuron Bal and McCormick, Synchronized Oscilliations in the Inferior Olive are controlled by the Hyperpolarisation-Activated Cation Current Ih, J. Neurophysiol, 77, 3145-3156, 1997 SPIKES SEEN IN THE LITERATURE Spintronic Memristor Current Spikes Pershin and 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 ∆𝑉 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 C ur ved (BP S - li ke) M em ri s to r s Pictures Tri a n gu la r ( U P S - li ke) M em ri s to r s Two Different Types of Memristor Behaviour Seen in Our Lab Cur ved (BPS-like) Memristor s Triangular (UPS -like) Memristor s Where do the Spikes Come From? Does Current Theory Predict Their Existence? Mem-Con Model Applied to Memristor Spikes Neurons Memristors q φ q φ I V V I In Chua’s Model Neuron Volta ge Spikes ∆𝑉 = 𝑀(𝑞(𝑡))∆𝑖 • Dynamics related to min. response time, τ, related to speed of ion diffusion across membrane • Memory property = ??? • Neuron operated in a current-controlled way Memristor Cur rent Spikes ∆𝑖 = 𝑀 𝑞 𝑡 ∆𝑉 • Dynamics related to τ, which is related to 𝜇𝑣 • 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 Memristor Negative V Sol-Gel Memristor Positive V Memristor Model Fits the PEO-PANI Memristor Al-TiO2-Al Sol-Gel Memristor Time & Frequency Dependence of Hysteresis for Al-TiO2-Al Au-TiO2-Au WORMS Memory Au-TiO2-Au WORMS Memory I-t Response to Stepped Voltage Time Dependent I-V Al-TiO2-Al Current Response to Voltage Ramp Voltage Ramp Cur rent Response 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 • Ben de Lacy Costello • Victor Erokhin and his group (University of Parma) • Andrew Adamatzky • David Howard • Larry Bull • Steve Kitson (HP UK) • David Pearson (HP UK) • Bristol Robotics Laboratory