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Ella Gale, Ben de Lacy Costello and Andrew
Adamatzky
Observation and Characterization of Memristor
Current Spikes and their Application to Neuromorphic
Computation
• 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?
Contents
• Slow• Parallel Processing• High degree of interconnectivity• Spiking Neural Nets• Ionic• Analogue
How Does the Brain Differ From a Modern-Day Computer?
Influx of Ionic I
Voltage Spike
Axon:Transmission along
neuron
Synapse:Transmission
between neurons
How does a Neuron Compute?
The Memristor as a Synapse
Before learning Before learning
During learning
After learningAfter learning
• 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
Spike-Time Dependent Plasticity, STDP
Bi and Poo, Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength and Postsynaptic Cell Type, J. Neurosci., 1998
Phenomenological Model
𝑀 (𝑞 (𝑡 ) )=𝑅off−𝜇𝑣
𝐷2 𝑅off 𝑅on𝑞 (𝑡)
Strukov et al, The Missing Memristor Found, Nature, 2008
= ionic mobility of the O+ vacancies
Roff = resistance of TiO2
Ron = resistance of TiO(2-x)
Charge-Controlled Memristor
Flux-Controlled Memristor
Chua’s Definitions of Types of Memristors
L. Chua, Memristor – The Missing Circuit Element, IEEE Trans. Circuit Theory, 1971
What the Flux?
𝑑𝜑=𝑀 (𝑞 (𝑡 ) )𝑑𝑞𝑀 (𝑞 (𝑡 ) )=𝑅𝑜𝑓𝑓−𝜇𝑣
𝐷2 𝑅𝑜𝑓𝑓 𝑅𝑜𝑛𝑞(𝑡)
But, where is the magnetic flux?
𝑉=𝑀 (𝑡 ) 𝐼
Chua, 1971Strukov et al, 2008
• 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
Starting From The Ions…
• Universal constants:
• X, Experimental constants: product of surface area and electric field
• , material variable, =
Memristance, as Derived from Ion Flow
Gale, The Missing Magnetic Flux in the HP Memristor Found, 2011
Mem-Con Theory
𝑞 ↔ 𝑀(𝑞) ↔ 𝜑 ↑ 𝑉 ↔ 𝑅𝑡𝑜𝑡(𝑡) ↔ 𝐼
Ionic Electronic
Gale, The Missing Magnetic Flux in the HP Memristor Found, Submitted, 2011
Connecting Memristors with Spiking Neurons to Implement STDP
1. Zamarreno-Ramos et al, On Spike Time Dependent Plasticity, Memristive Devices and Building a Self-Learning Visual Cortex, Frontiers in Neuroscience, 20110. Linares-Barranco and Serrano-Gotarredona, Memristance can explain Spike-Time-Dependent-Plasticity in Neural Synapses, Nature Preceedings, 2009
Simulation Results
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., 20092. Gale et al, Aluminium Electrodes Effect the Operation of Titanium Dioxide Sol-Gel Memristors, Submitted 2012
Neuron
Memristor
Memristor Behaviour Looks Similar to Neurons
Bal and McCormick, Synchronized Oscilliations in the Inferior Olive are controlled by the Hyperpolarisation-Activated Cation Current Ih, J. Neurophysiol, 77, 3145-3156, 1997
Pershin and Di Ventra, Spin Memristive Systems: Spin Memory Effects in Semi-conductor Spintronics, Phys. Rev. B, 2008
Spintronic Memristor Current 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
Properties of Spikes
Pictures
Curved (BPS-like) Memristors
Triangular (UPS-like) Memristors
Two Different Types of Memristor Behaviour Seen in Our Lab
Curved (BPS-like) Memristors
Triangular (UPS-like) Memristors
Two Different Types of Memristor Behaviour Seen in Our Lab
• 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
Neuron Voltage SpikesMemristor Current
Spikes
In Chua’s Model
• More complex system than a single memristor
• Short-term memory associated with membrane potential
• Long term memory associated with the number of synaptic buds
What is the Memory Property of Neurons?
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
Further Work
• 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
Summary
• Ben de Lacy Costello
• Andrew Adamatzky• David Howard• Larry Bull
With Thanks to
• Victor Erokhin and his group (University of Parma)
• Steve Kitson (HP UK)• David Pearson (HP
UK)
• Bristol Robotics Laboratory