Application to Neuromorphic

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20 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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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?

Memristive

Systems to Describe
Nerve Axon Membranes

Synapse Long
-
Term Potentiation

The
M
emristor

as a Synapse

Before learning

Before learning

During learning

After 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

𝑡
=
𝑅
off

𝜇

𝐷
2
𝑅
off
𝑅
on

(
𝑡
)

Strukov

et al, The Missing
Memristor

Found, Nature, 2008

𝜇



= ionic mobility of the O
+


vacancies

R
off

= resistance of TiO
2

R
on

= resistance of
TiO
(2
-
x
)


𝑣
𝑡
=
𝑀

𝑡
𝑖
(
𝑡
)


𝑀



𝜑
(

)



𝑖
𝑡
=

𝜑
𝑡

𝑣
(
𝑡
)



(
𝜑
)


(
𝜑
)
𝜑

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?


𝜑
=
𝑀

𝑡



𝑀

𝑡
=
𝑅


𝜇

𝐷
2
𝑅

𝑅


(
𝑡
)

But, where is the magnetic flux?


=
𝑀
𝑡
𝐼

Chua, 1971

Strukov

et al, 2008


Memristance is a phenomenon associated with ionic current flow


Therefore


calculate the magnetic flux of the IONS


Vacancy Volume Current


𝐉
=
𝑞
𝑡
𝜇
𝑣
𝐋
𝑉
𝑇𝑖
𝑂
(
2

𝑥
)

,
L =
eLectric

field


Vacancy Magnetic Field


𝐁
=
𝝁
𝟎
𝟒
𝝅

𝐉
×
𝐫
|
𝐫
|


𝜏


Vacancy Magnetic Flux

𝜑
=
𝜇
0
4

|
𝐋
|
𝜇

𝑃

(

𝑡
)

Starting
F
rom
T
he Ions…


Universal constants:
𝜇
0
4




X
, Experimental constants: product of surface area
and electric field



𝛽
, material variable,
𝛽
=
𝜇



(

𝑡
)



𝑀

𝑡
=
𝜇
0
4
𝜋


𝛽
(

(
𝑡
)
)

Memristance
, as Derived from Ion
F
low

Gale, The Missing Magnetic Flux in the HP
Memristor

Found, 2011


𝑅
𝑡𝑡𝑎
=
𝑅
 
+
𝑅




𝑅
𝑀 
=


𝑀

𝑡



𝑅

=

(



𝑡
)

Ti
O
2





Mem
-
Con Theory

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, 2011

0. 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
Memristor
s


Crossed Aluminium
electrodes


Thin
-
film (40nm)
TiO
2

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

Voltage Square Wave

Cur rent Spike Response

Spikes are Reproducible

Voltage Ramp

Current Response

Spikes are Repeatable

Neur on

Memr i st or

Memristor

Behaviour Looks Similar to
Neurons

Bal

and McCormick, Synchronized
Oscilliations

in the Inferior Olive are controlled by
the Hyperpolarisation
-
Activated
Cation

Current
I
h
, 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

Cur ved (BPS
-
l i ke)
Memri stors

Tri angul ar (UPS
-
l i ke)
Memri stors

Two Different Types of Memristor
Behaviour Seen in Our Lab

Cur ved (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

φ

I

V

q

φ

V

I

Neurons

Memristors

Mem
-
Con Model Applied to
Memristor

Spikes



=
𝑀
(

(
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


𝑖
=
𝑀

𝑡





Dynamics related to
τ
,
which is related to
𝜇



Memory property =
q
v


Memristor

operated in
voltage controlled way

Neuron Voltage Spikes

Memristor

Cur rent 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
-
TiO
2
-
Al Sol
-
Gel Memristor

Time & Frequency Dependence of Hysteresis for
Al
-
TiO
2
-
Al

Au
-
TiO
2
-
Au WORMS Memory

I
-
t Response to
Stepped Voltage

Time Dependent I
-
V

Au
-
TiO
2
-
Au WORMS Memory

Voltage Ramp

Current Response

Al
-
TiO
2
-
Al Current Response to Voltage Ramp

Neurology:


Modelling Neurons with the
Mem
-
Con Theory to
p
rove
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