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?

Memristive Systems to Describe Nerve Axon

Membranes

Synapse Long-Term Potentiation

The Memristor as a Synapse

Before learning Before learning

During learningAfter learning

After 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

Memristor Structure and Function

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

Memristor I-V Behaviour

To make a memristor brain

& thus a machine intelligence

Our Intent:

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

Memristors Spike

Naturally!

But,

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

Current Spikes Seen in I-t Plots

Voltage Square Wave Current Spike Response

Spikes are Reproducible

Voltage Ramp Current Response

Spikes are Repeatable

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

SPIKES SEEN IN THE LITERATURE

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

Where do the Spikes Come From?

Does Current Theory Predict Their Existence?

q φI V

q φV I

Neurons Memristors

Mem-Con Model Applied to Memristor 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

Neuron Voltage Spikes Memristor 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?

Sol-Gel Memristor Negative V

Sol-Gel Memristor Positive V

Memristor Models Fit the Data

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

I-t Response to Stepped Voltage

Time Dependent I-V

Au-TiO2-Au WORMS Memory

Voltage Ramp Current Response

Al-TiO2-Al Current Response to Voltage Ramp

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