FOCUSED REVIEW
published: 18 Feb ua y 2013
doi: 10.3389/ nins.2013.00002
STDP and STDP a ia ions wi h mem is o s
o spiking neu omo phic lea ning sys ems
T. Se ano-Go a edona1,T. Masquelie 2,3,T. P od omakis4,G. Indi e i5
and B. Lina es-Ba anco 1*
1Depa men o Analog and Mixed-Signal Design, Ins i u o de Mic oelec ónica de Se illa, IMSE-CNM-CSIC, Se illa,
Spain
2Uni o B ain and Cogni ion, Depa men o In o ma ion and Communica ion Technologies, Uni e si a Pompeu Fab a,
Ba celona, Spain
3Labo a o y o Neu obiology o Adap i e P ocesses, UMR 7102, CNRS - Uni e si y Pie e and Ma ie Cu ie, Pa is, F ance
4Cen e o Bio-inspi ed Technology, Ins i u e o Biomedical Enginee ing, Impe ial College London
5Ins i u e o Neu oin o ma ics, Uni e si y o Zu ich and ETH Zu ich, Zu ich, Swi ze land
In his pape we e iew se e al ways o ealizing asynch onous Spike-Timing-Dependen -
Plas ici y (STDP) using mem is o s as synapses. Ou ocus is on how o use indi idual
mem is o s o implemen synap ic weigh mul iplica ions, in a way such ha i is no
necessa y o (a) in oduce global synch oniza ion and (b) o sepa a e mem is o lea ning
phases om mem is o pe o ming phases. In he app oaches desc ibed, neu ons i e
spikes asynch onously when hey wish and mem is i e synapses pe o m compu a ion
and lea n a hei own pace, as i happens in biological neu al sys ems. We dis inguish
be ween wo di e en mem is o physics, depending on whe he hey espond o he
o iginal “mo ing wall” o o he “ ilamen c ea ion and annihila ion” models. Independen
o he mem is o physics, we discuss wo di e en ypes o STDP ules ha can be
implemen ed wi h mem is o s: ei he he pu e iming-based ule ha akes in o accoun
he a i al ime o he spikes om he p e- and he pos -synap ic neu ons, o a hyb id ule
ha akes in o accoun only he iming o p e-synap ic spikes and he memb ane po en ial
and o he s a e a iables o he pos -synap ic neu on. We show how o implemen hese
ules in c oss-ba a chi ec u es ha comp ise massi e a ays o mem is o s, and we
discuss applica ions o a i icial ision.
Keywo ds: mem is o /cmos, a i icial-lea ning-synapses, spike- iming-dependen -plas ici y, spiking-neu al-
ne wo ks
Edi ed by:
Ge Cauwenbe ghs, Uni e si y o
Cali o nia, San Diego, USA
Re iewed by:
Em e O. Ne ci, Ins i u e o
Neu oin o ma ics, Swi ze land
Siddha h Joshi, Uni e si y o Cali o nia,
San Diego, USA
*Co espondence:
B. Lina es-Ba anco, BSc Physics 1986,
MSc 1987, PhD 1990 om Uni e si y o
Se ille, Spain, and 2nd PhD 1991 om
Texas A&M Uni e si y, USA. He is Full
p o esso o Resea ch a he Ins i u o de
Mic oelec ónica de Se illa
(IMSE-CNM-CSIC). He has been
in ol ed wi h ci cui design o
elecommunica ion ci cui s, VLSI
emula o s o biological neu ons, VLSI
neu al based pa e n ecogni ion sys ems,
hea ing aids, p ecision ci cui design o
ins umen a ion equipmen , bio-inspi ed
VLSI ision p ocessing sys ems, AER,
mem is o s and eme ging nanode ices,
and VLSI ansis o misma ch
pa ame e s cha ac e iza ion. He is IEEE
Fellow.
be [email protected]
1. INTRODUCTION
Fo many yea s, he ield o neu omo phic
enginee ing has s uggled o de elop p ac i-
cal neu o-compu ing de ices ha mimicked he
p inciples and ope a ions o biological b ains,
by di ec ly exploi ing he physics o elec onic
de ices in mixed analog/digi al VLSI (Indi e i
and Ho iuchi, 2011). Howe e , he e always was
aclamo o acompac anddis ibu ednon-
ola ile memo y, possibly igh ly coupled o
he signal p ocessing componen s (neu ons), so
ha he biological synapses coun e pa s could
be p ope ly emula ed. The ecen ad en o
nanoscale mem is i e-like de ices (Wu ig and
Yamada, 2007; S uko e al., 2008; Yang e al.,
2008; Jo e al., 2010; Go o eanu e al., 2011; Lee
e al., 2011; Chan hbouala e al., 2012; Kuzum
e al., 2012; P od omakis e al., 2012a)opens
he possibili y o la ge-scale bio-inspi ed neu al
ne wo k implemen a ions wi h minimal size-
equi emen s o hose elemen s in he ci cui
ha a e mos nume ous and he e o e mos
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |1
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
space-in ense: plas ic synap ic connec ions. The
s eng h o a synap ic link be ween wo neigh-
bo ing neu ons depends on i s his o y and mo e
explici ly by he o e all amoun o neu o ans-
mi e s ha has been p opaga ed h ough i a e
a ele an neu al spike. In simila ashion, he
s eng h o a mem is o , i.e., i s mem is ance
Mem is o
Two e minal elec onic de ice which
ope a es simila o a esis o , bu whose
esis ance changes dynamically as he
de ice is being used.
Spike-Timing-Dependen -Plas ici y
(STDP)
One ype o lea ning ule o a i icial
synapses in spiking neu al ne wo ks,
whe e he synap ic upda e depends on
he iming cha ac e is ics o indi idual
spikes a he synapse e minals.
(o ins an aneous esis ance) is dic a ed by he
amoun o cha ge q ha has lown h ough i
o he accumula ed ol age lux φ. Addi ionally,
he in insic non-linea na u e o p ac ical solid-
s a e mem is o s esembles he beha io o neu-
al synapses.
On he o he hand, and independen ly o
he new nanoscale de ices a ailabili y, he neu-
omo phic enginee ing ield e ol ed na u ally
owa d ci cui s and sys ems exploi ing spik-
ing signal encoding, as in biology. Fo exam-
ple, a la ge collec ion o spike-d i en ision
senso s ha e been epo ed, such as senso s
o luminance (Culu ciello e al., 2003; Chen
e al., 2011), empo al con as (Ba ba o e al.,
2002; Mallik e al., 2005; Chan e al., 2007a;
Lich s eine e al., 2008; Leñe o-Ba dallo e al.,
2011; Posch e al., 2011; Se ano-Go a edona
e al., 2013), mo ion (K ame , 1996; Sa peshka
e al., 1996; Ozale li and Higgins, 2005), and
spa ial con as (Ruedi e al., 2003; Zaghloul
and Boahen, 2004; Cos as-San os e al., 2007;
Massa i e al., 2008; Leñe o-Ba dallo e al.,
2010). Spike-d i en p inciples ha e also been
used o audi o y sys ems (Sa peshka e al.,
2005; Wen and Boahen, 2006, 2009; Chan
e al., 2007b), compe i ion and Winne -Take-
All ne wo ks (Indi e i, 2000; Chicca e al., 2007;
Os e e al., 2008), lea ning (Mill e al., 2011),
classi ica ion (Mi a e al., 2009), all de ec-
ion (Fu e al., 2008), and sys ems dis ibu ed
o e wi eless senso ne wo ks (Teixei a e al.,
2005; Massa i e al., 2008). Apa om eal-
ime sensing, spike-d i en p ocessing sys ems
can p oduce ex emely as esponses. Examples
o spike-d i en p ocessing modules (chips)
a e hose ha , emula ing biological neoco i-
cal s uc u es, pe o m spa io- empo al ea u e
ex ac ion such as ixed-ke nel (Venie e al.,
1997; Choi e al., 2005) o p og ammable ke nel
(Se ano-Go a edona e al., 2006; Camuñas-
Mesa e al., 2011, 2012) 2D con olu ions, and
gene ic massi e neu al p ocessing (Vogels ein
e al., 2007; Fie es e al., 2008; Khan e al., 2008;
Se ano-Go a edona e al., 2009; Zama eno-
Ramos, 2012).
Una oidably, he lea ning capabili y is one
key cha ac e is ic ha is equi ed o building
cogni i e a i icial neu al sys ems. Recen ly p o-
posed a i icial neu al p ocessing sys ems spend
g ea esou ces o his ask: he mul i-million
Eu opean ini ia i e FACETS/B ainScales (Fie es
e al., 2008) is de eloping a 200.000 neu on
wa e 1whe e mos o he silicon a ea is used
o implemen ing Spike-Timing-Dependen -
Plas ici y (STDP) lea ning mechanisms in
he synapses. The UK ini ia i e SpiNNake
(Khan e al., 2008) based on mul i-p ocesso s
ARM echnology has o use hyb id packaging
echnology in o de o encapsula e wo sepa a e
Silicon chips in o each chip package: one chip
is being he genuine SpiNNake chip wi h
18 ARM 2CPUs, and he second chip being
a comme cial 128MB DRAM chip o local
synap ic s o age. Bo h he lea ning mechanisms
and he s o age o lea ned pa ame e s equi e
subs an ial silicon eal-es a e in adi ional
silicon-based chip echnology.
Howe e , he ad en o new nanoscale ech-
nologies has shed new expec a ions, gi ing
hopes o he de elopmen o ul a-compac ,
as and e icien lea ning and s o age mecha-
nisms ha may esul in a o dable, low powe ,
compac , la ge scale, a i icial neu al sys ems
(Wu ig and Yamada, 2007; S uko e al., 2008;
Yang e al., 2008; Jo e al., 2010; Go o eanu e al.,
2011; Lee e al., 2011; Chan hbouala e al., 2012;
Kuzum e al., 2012; P od omakis e al., 2012a).
A e y p omising new class o nanoscale de ices
is he one ha comp ises he so called mem is-
o s (Chua, 1971; Chua and Kang, 1976; S uko
e al., 2008; Bo ghe i e al., 2009; Jo e al., 2009,
2010), whose dis inc cha ac e is ic is ha hey
ha e memo y while hey ope a e like a iable
wo- e minal esis o s.I was ecen lypos u-
la ed ha such iny nanoscale de ices, when
d i en by app op ia ely shaped ol age pulses,
could be embedded wi hin adi ional CMOS3
mic ochips, esul ing in uly asynch onous4
a i icial lea ning neu al “ issue” equipped
1Wa e : mic ochips a e ab ica ed on silicon wa e s (wi h
diame e anging om 1 o abou 18), which can hold
se e al hund eds o housands o indi idual chips ha
a e la e on cu and encapsula ed in o chip packages.
The FACETS/B ainScaleS p ojec is a wa e -scale design,
meaning ha he wa e is no cu in o indi idual chips,
bu he whole wa e is used as a uni ci cui .
2ARM s ands o “Aco n Risk Mic op ocesso ” and is he
name o a company p o iding embedded mic op oces-
so s o a a ie y o mo e complex chips, like cellula
phones, usb-s icks, e c.
3CMOS s ands o “Complemen a y Me al Oxide
Semiconduc o ” and e e s o he mos s anda d echnol-
ogy used o mic ochip ab ica ion.
4In asynch onous sys ems no clock is equi ed, as
opposed o con en ional digi al compu ing sys ems.
Consequen ly, he e is no cen alized ime keepe ha
en o ces ac ions o happen in lock-s ep wi h each o he .
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |2
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
wi h STDP (Lina es-Ba anco and Se ano-
Go a edona, 2009b,a; Zama eño-Ramos e al.,
2011).
Al hough his s ill needs o be p o en expe -
imen ally and all p ac ical limi a ions a e ye
o be iden i ied, while mem is o s a e con inu-
ously being imp o ed and op imized o e many
labs wo ldwide, he po en ial o building e y
dense hyb id mem is i e-CMOS lea ning sys-
ems is he e. The esul ing implemen a ions
can be ex emely compac STDP-equipped sys-
ems, which con as wi h pu e CMOS-based
a emp s ha ei he ha e esul ed in physical
STDP synapses consuming signi ican chip eal-
es a e (Fie es e al., 2008)o complexcom-
pu a ional wo k a ounds in mo e algo i hmic
solu ions (Ras e al., 2010; Da ies e al., 2012).
In his pape we quickly e iew he basic p in-
ciples behind exploi ing mem is ance o asyn-
ch onous STDP and ex end he o iginal indings
o o he ypes o STDP. In he nex sec ion
we quickly e iew he mem is o concep as
well as some o he pos ula ed physical mech-
anisms esponsible o i s ope a ion. A e his,
sec ion 3summa izes STDP and some a ia-
ion o i , as well as addi i e, mul iplica i e and
quad a ic STDP. Sec ions 4and 5 e iew how
o combine mem is o s wi h speci ic CMOS
neu ons o esul in di e en ypes o STDP.
Sec ion 6men ions an applica ion in he con-
ex o a i icial ision, and sec ion 7p o ides
conclusions.
2. MEMRISTORS
Mem is ance was pos ula ed in 1971 by Chua
(1971) as he ou h missing canonical ci cui
elemen h ough his amous symme y a gu-
men , illus a ed in Figu e 1. Acco ding o ci -
cui heo e ical undamen als, he e a e ou
basic elec ical quan i ies (Chua e al., 1987): (1)
ol age di e ence be ween wo e minals “ ,” (2)
cu en lowing h ough in o a de ice e minal
“i,” (3) cha ge lowing h ough a de ice e mi-
nal o in eg al o cu en q=i(τ)dτ,and(4)
lux o in eg al o ol age φ= (τ)dτ.A wo-
e minal de ice is said o be canonical (Chua
e al., 1987) i ei he wo o he ou basic elec i-
cal quan i ies a e ela ed by a s a ic5 ela ionship,
as shown in Figu e 1. A esis o has a s a ic ela-
ionship be ween e minal ol age and de ice
cu en i,asshowninFigu e 1B. A capaci o
shows a s a ic ela ionship be ween cha ge qand
ol age ,asshowninFigu e 1C.Aninduc o
has a s a ic ela ionship be ween i s cu en i
and lux φ,asshowninFigu e 1D.These h ee
de ices ha e been e y well known since he
o igins o Elec onics and Elec ici y. Howe e ,
he e a e o he possibili ies o combining he
5By “s a ic” we mean i is no al e ed by changes o he
abo e elec ical quan i ies, o by hei his o y, in eg als,
de i a i es, e c. These “s a ic” cu es can, howe e , be
ime- a ying i he change is caused by an ex e nal agen .
Fo example, a mo o d i en po en iome e would ha e a
“s a ic” i/ cu e ha is ime a ying.
FIGURE 1 | Fou a iables o ci cui heo y linked by six ma hema ical
ela ions consis ing o he unc ional ela ionships o he ou passi e
ci cui elemen s, Fa adays law o induc ion and he de ini ion o elec ic
cu en . (A) Chua’s symme y a gumen and (B–E) desc ip ions o he ou
canonical wo- e minal de ices. (B) A esis o is de ined by a s a ic
ela ionship be ween a de ice’s ol age and cu en . (C) A capaci o is
de ined by a s a ic ela ionship be ween a de ice’s cha ge and ol age.
(D) An induc o is de ined by a s a ic ela ionship be ween a de ice’s cu en
and lux. (E) And a mem is o is de ined by a s a ic ela ionship be ween a
de ice’s cha ge and lux.
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |3
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
ou basic elec ical quan i ies: (q,i),( ,φ),and
(q,φ). Igno ing he combina ions o a quan-
i y wi h i s own ime de i a i e lea es us wi h
one single addi ional possibili y: (q,φ).This
easoning led Chua o pos ula e he exis ence
o a ou h basic wo- e minal elemen , which
he called he Mem is o .Mem is o s beha e
as esis ances in which he esis ance changes
h ough some o he basic elec ical quan i-
ies, and is somehow memo ized. The mem is-
o would show a s a ic ela ionship be ween
cha ge qand lux φ,asshowninFigu e 1E.I
he q s. φ ela ionship is linea , he mem is-
o degene a es in o a linea esis o . Al hough
none o he so- a epo ed mem is o s can be
desc ibed by a s a ic cons i u i e ela ionship in
he (q,φ)plane (and hus, s ic ly speaking, he
1971 ou h canonical elemen is s ill missing),
hey all all wi hin Chua’s 1976 gene aliza ion
o Mem is i e Sys ems (Chua and Kang, 1976).
F om he e on we will use he e m mem is o
o Chua’s 1976 de ini ion o mem is i e sys em.
Consequen ly, he simple concep o mem is-
ance as de ined in Figu e 1D can be ex ended o
e e o any de ice exhibi ing esis i e beha io
(i s i/ cu es c oss he o igin) whose esis ance
can change h ough some o he ou basic elec-
ical quan i ies (o a combina ion o hem, o
hei ime de i a i es o in eg als, e c.), while
a he same ime exhibi ing memo y o ha
esis ance. In ha case, mo e elabo a e ma h-
ema ical desc ip ions a e equi ed (Chua and
Kang, 1976).
Mem is ance has ecen ly been demon-
s a ed (wi h ex ao dina y impac among
he esea ch communi y) in nanoscale wo-
e minal de ices, such as ce ain i anium-
dioxide (S uko e al., 2008; Bo ghe i e al.,
2009; P od omakis e al., 2011, 2012a)and
amo phous Silicon (Jo e al., 2009) c oss-
poin swi ches. Howe e , mem is i e de ices
we e epo ed ea lie by o he g oups (A gall,
1968; P od omakis e al., 2012b). Mem is ance
a ises na u ally in nanoscale de ices because
small ol ages can yield eno mous elec ic ields
ha p oduce he mo ion o cha ged a omic o
molecula species, changing s uc u al p ope -
ies o a de ice (such as i s doping p o ile)
while i ope a es. I s unc ional cha ac e is ic
has been a pinched hys e esis loop in he i–
domain (Figu es 2C,D); a signa u e ha has
been obse ed in a ious dissipa i e de ices
(P od omakis e al., 2012b). Pa icula ly nowa-
days a ious eme ging esis i e andom-access
memo y (ReRAM) nano-de ices (Chua, 2011),
wi h one scaling ex eme being he a omic
swi ch (Te abe e al., 2005), a e classi ied as
being mem is o s, and show a ibu es ha
esemble biological synapses (Ohno, 2011)p o-
iding exci ing p ospec s o demons a ing
neu omo phic applica ions (A izienis e al.,
2012). Hys e esis is ypically no iced in sys-
ems/de ices ha possess ce ain ine ia, causing
he alue o a physical p ope y o lag behind
changes in he mechanism causing i ; mani-
es ing memo y (Pe shin and Di Ven a, 2011).
Pa icula ly in he case o nanoscale mem is o s,
his ine ia has been asc ibed o Joule hea -
ing (Fu sina e al., 2009), he elec ochemical
mig a ion o oxygen ions (Nian e al., 2007)
and acancies (Yang e al., 2008), he low-
e ing o Scho ky ba ie heigh s by apped
cha ge ca ie s a in e acial s a es (Hu e al.,
2010), he phase-change (Wu ig and Yamada,
2007), he o ma ion/ up u e o conduc i e il-
amen s (Kwon e al., 2010), Yang e al. (2012)
in a de ice’s co e, o e en o some ex en a
combina ion o he a o emen ioned swi ching
mechanisms.
Clea ly, he impac o mem is o s is o e-
seen o be ealized h ough hei nanome ic
dimensions (see Figu e 2B which is a c oss sec-
ion o one o he s uc u es in Figu e 2A),
hei capaci y o s o e mul iple bi s o a con-
inuum o in o ma ion pe elemen (Figu e 2E)
and he minuscule ene gy equi ed o w i e
dis inc s a es, esul ing in high spa ial- and
high s o age-densi y well beyond he cu -
en s a e-o - he-a (Go o eanu e al., 2011).
None heless, he ac ha he unc ional p op-
e ies o such elemen s a e associa ed wi h
a e-limi ing ( equency-dependen ) elec o- o
he mo-dynamic changes ha a e con ingen on
bo h he p esen as well as he pas en i onmen ,
p esen s us wi h oppo uni ies in exploi ing
hem as no el compu a ion elemen s.
By de ini ion, mem is o s can be ei he
ol age/ lux d i en o cu en /cha ge d i en.
Depending on he pola i y o he se and ese
po en ials equi ed o change esis i e s a es
(RS), he de ices can be classi ied as unipola
(URS) o bipola (BRS) (Schindle e al., 2007)
and consequen ly, hei ci cui symbol mus
indica e somehow hei pola i y, as depic ed in
Figu e 3A. Vol age/ lux d i en mem is o s can
be desc ibed by (Chua and Kang, 1976)
iMR =G(w, MR, ) MR (1)
˙w= (w, MR, )(2)
while cu en /cha ge d i en mem is o s would
be desc ibed as (Chua and Kang, 1976)
MR =R(w,iMR, )iMR (3)
˙w= (w,iMR, )(4)
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |4
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
FIGURE 2 | Solid-s a e TiO2-based mem is o s ab ica ed a Impe ial
College London. (A) Mic opho og aph o a mem is o c oss-ba a ay,
wi h a close-up SEM illus a ion o a single cell appea ing in he inse o
(A).(B) CHEMI-STEM map o a lamella c oss-sec ion o one o he
de ices shown in (A): blue deno es P ( op and bo om elec odes) while
g een and ed co espond o Ti and O2species (P od omakis e al.,
2012a). (C) Simula ed and measu ed pinched hys e esis I-V cha ac e is ics
(absolu e mem is o cu en |I| s. signed mem is o ol age V)
(P od omakis e al., 2011) in log scale o (D) linea scale, and (E)
mul i-s a e p og amming o a TiO2-based mem is o : ead pulses a e
posi i e and small ampli ude (1V) ha do no al e he esis ance
(mem is ance) o he mem is o , while successi e se pulses ha e
nega i e high ampli ude (3V) and do p og essi ely al e he esis ance
(mem is ance) o he mem is o .
He e w ep esen s some s uc u al p ope y
pa ame e o he mem is o . Fo example, in
he 2008 HP pape (S uko e al., 2008) he
ope a ion o he epo ed mem is o was pos-
ula ed as desc ibed by he mo ing wall model
depic ed in Figu e 3B. In his simpli ied model a
mem is o o heigh L, sandwiched be ween wo
elec odes, has a low esis ance egion o heigh
wand a high esis ance egion o heigh L−w.
The mem is o is conside ed o be di ided in o
wo egions. Bo h egions a e sepa a ed by a
bounda y wall a posi ion w,whichmo esup
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |5

Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
FIGURE 3 | (A) Mem is o asymme ic symbols. (B) Illus a ion o
mo ing wall model desc ibing mem is o ope a ion as wo a iable
esis o s in se ies. (C) Illus a ion o ilamen o ma ion/annihila ion
model desc ibing mem is o ope a ion as wo a iable esis ances in
pa allel. (D) Expe imen ally measu ed STDP unc ion ξ(T)on
biological synapses (da a om Bi and Poo, 1998, 2001). (E) Ideal
STDP upda e unc ion used in compu a ional models o STDP synap ic
lea ning. (F) An i-STDP lea ning unc ion o inhibi o y STDP synapses.
(G) Shape o mem is o weigh upda e unc ion ( MR),(H)
spike-shape wa e o m.
and down wi h he amoun o cha ge ha has
lown h ough he mem is o (in he case o
being cu en /cha ge d i en) o he accumu-
la ed lux (in case o being ol age/ lux d i en).
The mem is o would beha e as wo a iable
esis o s in se ies. The o al e ec i e esis ance
o he mem is o would be desc ibed by
R=RON
w
L+ROFF 1−w
L(5)
This mo ing wall model can app oxima e phe-
nomena like mig a ion o oxygen ions (Nian
e al., 2007) and acancies (Yang e al., 2008), he
lowe ing o Scho ky ba ie heigh s by apped
cha ge ca ie s a in e acial s a es (Hu e al.,
2010), and he phase-change in some PCM
(phase change ma e ials) de ices (Wu ig and
Yamada, 2007).
Howe e , esis i e swi ching e ec s in
dielec ic-based de ices ha e no mally been
assumed o be caused by conduc ing ilamen
o ma ion ac oss he elec odes, al hough
he unde s anding and modeling o hese
phenomena emains con o e sial. As a ma -
e o ac , some esea che s a e obse ing
he o ma ion and annihila ion o nanoscale
wid h conduc ing ilamen s in mem is o s
(Kwon e al., 2010; Yang e al., 2012). P ecise
modeling o his phenomenon is s ill unde
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |6
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
esea ch (Shihong e al., 2012). Howe e , le
us he e p opose he ollowing e y simpli ied
iew o app oxima e his physical mechanism.
Figu e 3C illus a es schema ically a mem is o
wi h se e al conduc ing ilamen s be ween
he wo elec odes. The numbe o ilamen s
o hei c oss-sec ional a ea would inc ease
o dec ease wi h mem is o ope a ion. Le us
call now w he o al c oss sec ional a ea o
he e ec i e conduc ing ilamen s a a gi en
ins an in ime, and S he o al c oss sec ion
a ea o he mem is o . The ilamen s p esen
high conduc i i y (low esis i i y), while he
bulk p esen s much lowe conduc i i y (high
esis i i y). All o med pa allel ilamen s beha e
as one e ec i e esis ance o low esis ance,
while he es o hebulkbeha esasano he
highe esis i i y esis o . The e o e, now he
mem is o beha es as wo a iable esis o s in
pa allel. Consequen ly, i s o al conduc ance
(in e se o esis ance) could be desc ibed as
G=GON
w
S+GOFF 1−w
S(6)
whe e GON is he conduc ance pe e ec i e c oss
sec ion a ea o he ilamen s, and GOFF is he
conduc ance pe e ec i e c oss sec ion a ea o
he ilamen -less bulk ma e ial. Pa ame e w
would change om 0 o wmax, he maximum
possible e ec i e c oss sec ion a ea o o al con-
duc ing ilamen s(wmax ≤S).
This changing c oss sec ion desc ip ion
no only app oxima es ilamen o ma-
ion/annihila ion phenomena, bu also some
o he g adual c oss sec ion a ea a ia ions
obse ed in some phase-change o e oelec ic-
domains-based ma e ials (Chan hbouala e al.,
2012).
As we will highligh la e in sec ions 4and
A i icial lea ning synapses
A i icially manu ac u ed de ice ha
beha es simila o a biological synapse,
e.g., i ’s communica ion s eng h (o
synap ic weigh ) changes as he de ice
is used acco ding o some lea ning ule.
Nanoscale a i icial synapse
This is an a i icial synapse made using
some de ice whose dimensions a e
below he mic on (10−6m).
Tunable STDP
STDP lea ning ule whose
ma hema ical desc ip ion can be made
o change in ime.
5, whe he a mem is o is be e desc ibed by
he mo ing wall model o he ilamen o -
ma ion/annihila ion model, impac s se e ely on
he esul ing ype o STDP lea ning mecha-
nism. The la e yields an addi i e ype o STDP,
while he o me esul s in a quad a ic ype
STDP. No e ha a mem is o can be ei he
ol age/ lux o cu en /cha ge d i en, indepen-
den ly o whe he i is a “wall” o a “ ilamen ”
mem is o .
3. SPIKE-TIMING-DEPENDENT-PLASTICITY
STDP is he abili y o na u al o a i icial
synapses o change hei s eng h acco ding o
he p ecise iming o indi idual p e- and/o
pos -synap ic spikes (Ge s ne e al., 1993, 1996;
Ma k am e al., 1997; Bi and Poo, 1998, 2001;
Zhang e al., 1998; Feldman, 2000; Mu and
Poo, 2006; Cassenae and Lau en , 2007; Jacob
e al., 2007; Young, 2007; Finelli e al., 2008;
Masquelie e al., 2008, 2009). A nice o e iew
o STDP and i s his o y can be ound else-
whe e (Sjös öm and Ge s ne , 2010). STDP
lea ning in biology is inhe en ly asynch onous
and on-line, meaning ha synap ic inc emen-
al upda e occu s while neu ons and synapses
ansmi spikes and pe o m compu a ions. This
con as s o mo e adi ional lea ning ules,
like backp opaga ion (Rojas, 1996), whe e i s
neu ons and synapses pe o m signal agg ega-
ion and neu al s a e upda e (we call his he e
“pe o ming phase”) and hen synap ic upda es
a e compu ed and applied (we call his he e
“weigh upda e phase”) al e na ing hese wo
phases du ing aining. E en ea ly p oposals o
mem is o -based STDP lea ning implemen a-
ions used a i icial ime-mul iplexing o al e -
na e con inuously and synch onously be ween
“pe o ming” and “weigh upda e” phases
(Snide , 2008), hus equi ing global sys em-
wide synch oniza ion. This can become a se e e
handicap when scaling up sys ems o a bi a y
size. He e we show a ully asynch onous imple-
men a ion o mem is o -based STDP whe e
“pe o ming” and “weigh upda e” phases hap-
pen simul aneously in a na u al manne , as
in biology (Lina es-Ba anco and Se ano-
Go a edona, 2009b,a; Zama eño-Ramos e al.,
2011), whe e he e is no need o any global syn-
ch oniza ion. O he esea che s ha e p oposed
a ia ions a ound hese ideas (Bichle e al.,
2012a; Kuzum e al., 2012).
Figu e 3D shows he change o synap ic
s eng h (in pe cen ) measu ed expe imen ally
om biological synapses as unc ion o ela-
i e iming T= pos − p e be ween he a i al
ime p e o a p e-synap ic spike and he ime pos
o gene a ion o a pos -synap ic spike. Al hough
he da a shows s ochas ici y, we can in e
an unde lying in e pola ed unc ion ξ(T)as
shown in Figu e 3E.
ξ(T)=a+e−T/τ+i T>0
−a−eT/τ−i T<0(7)
Fo a causal p e o pos spike iming ela-
ion (T>0) he s eng h o he synapse
is inc eased, while o an an i-causal ela ion
(T<0) i is dec eased. In he case o synapses
wi h nega i e synap ic s eng h (as in some a i-
icial ealiza ions), he e e sed e sion shown in
Figu e 3F can be used. Mic ochip CMOS ci cui
implemen a ions o STDP ules ha ollow he
desc ip ion o Equa ion (7) ha e been epo ed
(Indi e i e al., 2006), which esul in abou 30
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |7
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
ansis o s pe plas ic synapse, hus demons a -
ing he e y high cos o hei ha dwa e ealiza-
ion. Le us call his double-spike STDP,since he
weigh will be upda ed a e he a i al o he
second spike (ei he p e- o pos -synap ic).
Al e na i e a ia ions o STDP ha e been
p oposed ha do no equi e he in e en ion o
bo h p e- and pos -synap ic spikes (B ade e al.,
2007), esul ing in sligh ly less complex ci cui
implemen a ions (Mi a e al., 2009). Le us call
his single-spike STDP,since heweigh willbe
upda ed a e he a i al o p e-synap ic spikes
only.Thissingle-spikeSTDP uleupda es he
synap ic weigh depending on he alue o wo
local neu al soma s a e a iables. The i s one is
he memb ane ol age V( )and he second one
is an auxilia y s a e a iable C( )p opo ional
o he neu on’s i ing a e and equi alen o
he biological neu on’s Calcium concen a ion,
which has he ollowing dynamics
˙
C=−
C( )
τC
+JC
i
δ( − i)(8)
whe e JC ep esen s he con ibu ion o one
single pos -synap ic spike and he ime con-
s an τCis compa able o he STDP lea ning
window T. The synap ic weigh a iable ξis
upda ed only when a p e-synap ic spike occu s
a ime p e. The synap ic s eng h is inc eased o
dec eased by ixed size s eps |a±|depending on
he ins an aneous alues o V( p e)and C( p e)
wi h espec o a gi en se o global h esholds
{θ ,θl
up,θh
up,θl
down,θh
down},as:
ξ( p e)=⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
a+i V( p e)>θ and
θl
up <C( p e)<θh
up
−a−i V( p e)<θ and
θl
down <C( p e)<θh
down
(9)
Addi ionally, in his model he synap ic s eng h
d i s slowly owa d i s uppe o lowe bound
depending on whe he i is abo e o below an
in e media e h eshold.
Bo h ypes o STDP ules, double-spike and
single-spike, a e e y expensi e o implemen in
con en ional CMOS mic ochips (Indi e i e al.,
2006; Fie es e al., 2008; Khan e al., 2008; Mi a
e al., 2009). Howe e , as we will see in he nex
sec ion, bo h can be implemen ed wi h jus one
mem is o pe synapse i app op ia e pe iphe al
signal condi ioning neu ons a e used in hyb id
CMOS/mem is o ealiza ions.
Hyb id nano/CMOS neu al sys em
A i icial neu al ne wo k sys em buil
using con en ional mic ochip
echnology (CMOS) combined wi h
p esen ly eme ging nanoscale de ices.
Independen ly on whe he STDP is ei he
double-spike o single-spike, i is said o be
ei he addi i e, mul iplica i e o quad a ic i i
addi ionally depends o no on he ac ual synap-
ic s eng h. I he STDP upda e is independen
o he ac ual synap ic s eng h, i is said o be
addi i e. Addi i e STDP equi es he weigh al-
ues o be bounded o an in e al because weigh s
will s abilize a one o hei bounda y alues
( an Rossum e al., 2000; Rubin e al., 2001).
I he synap ic upda e is p opo ional o ac ual
synap ic s eng h, i is called mul iplica i e STDP
and weigh s may s abilize o alues in e me-
dia e o hei bounda ies ( an Rossum e al.,
2000; Rubin e al., 2001; Gü ig e al., 2003).
I he synap ic weigh upda e is p opo ional
o he squa e o ac ual synap ic s eng h, we
call i quad a ic STDP (Zama eño-Ramos e al.,
2011).
4. MEMRISTORS AND CMOS NEURONS FOR
DOUBLE-SPIKE STDP
The mo e adi ional double-spike STDP lea n-
ing ule [as modeled by Equa ion (7)] can, in
heo y, be implemen ed by (Zama eño-Ramos
e al., 2011) (a) using a pa icula ype o
ol age/ lux d i en mem is o (Jo e al., 2010)
whose ope a ion migh be app oxima ed by
Equa ion (2)wi h(seeFigu e 3G)
( MR)=⎧
⎨
⎩
Iosign( MR)e| MR|/ o−e h/ o
i | MR|> h
0o he wise (10)
and bounded synap ic s eng h w∈
[wmin,wmax], while (b) p o iding app o-
p ia ely shaped p e- and pos -synap ic spikes
a ailable a bo h synapse (mem is o ) elec-
odes (Zama eño-Ramos e al., 2011). Fo
example, conside a pai o iden ical p e- and
pos -synap ic spikes wi h a shape esembling
ha o biological spikes, wi h an on-se du a ion
| +
ail|and a ail o du a ion | −
ail|,asshownin
Figu e 3H,
spk( )=⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
A+
mp e /τ+−e− +
ail/τ+
1−e− +
ail/τ+i − +
ail < <0
−A−
mp e− /τ−−e− −
ail/τ−
1−e− −
ail/τ−i 0 < < −
ail
0o he wise
(11)
Unde hese ci cums ances, mem is o ol age is
MR( , )=αposspk( )−αp espk( + )and
om Equa ions (2,10) synap ic s eng h upda e
can be compu ed as
w(T)= ( MR( ,T))d =ξ(T)
(12)
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |8
Se ano-Go a edona e al. STDP and STDP a ia ions wi h mem is o s
which has been shown o esul in he same
shape illus a ed in Figu e 3E (Zama eño-
Ramos e al., 2011). Fu he mo e, by eshaping
hespikewa e o monecan ine uneo com-
ple ely al e he STDP lea ning unc ion ξ( ),
as illus a ed in Figu e 4 (Lina es-Ba anco
and Se ano-Go a edona, 2009a). This way, by
building neu ons wi h a gi en deg ee o shape
p og ammabili y, i is possible o change he
STDP lea ning unc ion a will, depending on
he applica ion, o make i e ol e in ime as
lea ning p og esses.
Figu e 5A shows a way o in e connec ing
mem is o s and CMOS neu ons o STDP
lea ning. T iangles ep esen he neu on soma,
being he la side i s inpu (dend i es) and he
sha p side he ou pu (axon). Da k ec angles
a e mem is o s, ep esen ing each one synap ic
junc ion. Each neu on con ols he ol age
a i s inpu (Vpos in Figu e 5B)andou pu
(Vp e in Figu e 5B) nodes. When he neu on
is no spiking i o ces a cons an ol age a
bo h nodes, while collec ing h ough i s inpu
node he sum o inpu synap ic spike cu en s
coming om he mem is o s, which con ibu e
o changing he neu on in e nal s a e. When he
neu on spikes, i se s a one-spike wa e o m a
bo h inpu and ou pu nodes. This way, hey
send hei ou pu spikes o wa d as p e-synap ic
spikes o he des ina ion synap ic mem is-
o s, bu also backwa d o p eceding synap ic
mem is o s as pos -synap ic spikes. Zama eño
e al. showed ex ensi e simula ions on hese
concep s, and how one can change om STDP
o an i-STDP by swi ching pola i ies o spikes
o mem is o s (Zama eño-Ramos e al., 2011).
FIGURE 4 | Illus a ion o in luence o ac ion po en ial shapes on he
esul ing STDP mem is o weigh upda e unc ion ξ(T). Mem is o
uppe and lowe h esholds a e no malized o ampli udes ±1.0. F om (A1,A2)
o (E1,E2) he same spike wa e o m a els o wa d and backwa d. In (F1,F2)
he o wa d and backwa d wa e o ms a e he same bu ha e opposi e
pola i y. In (G1,G2) o (H1,H2) he o wa d and backwa d wa e o ms a e
di e en . In (G1,G2), he posi i e pulse o he backwa d wa e o m exceeds
ampli ude +1.0, hus p oducing nega i e STDP upda e whene e he e is a
pos -synap ic spike alone (G2); o he wise i p e- and pos -synap ic spikes
happen wi hin a gi en ime window, he e will be posi i e STDP upda e.
F on ie s in Neu oscience www. on ie sin.o g Feb ua y 2013 | Volume 7 | A icle 2 |9