A Hybrid CMOS-Memristor Neuromorphic Synapse

IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 1 A Hyb id CMOS-mem is o Neu omo phic Synapse Mos a a Rahimi Azghadi, Membe , IEEE, Be nabe Lina es-Ba anco, Fellow, IEEE, De ek Abbo , Fellow, IEEE, Philip H.W. Leong, Senio Membe , IEEE Abs ac —Al hough da a p ocessing echnology con inues o ad ance a an as onishing a e, compu e s wi h b ain-like p o- cessing capabili ies s ill elude us. I is en isioned ha such compu e s may be achie ed by he usion o neu oscience and nano-elec onics o ealize a b ain-inspi ed pla o m. This pape p oposes a high-pe o mance nano-scale Complemen a y Me al Oxide Semiconduc o (CMOS)-mem is i e ci cui , which mimics a numbe o essen ial lea ning p ope ies o biological synapses. The p oposed synap ic ci cui ha is composed o mem is o s and CMOS ansis o s, al e s i s mem is ance in esponse o iming di e ences among i s p e- and pos -synap ic ac ion po en ials, gi ing ise o a amily o Spike Timing Dependen Plas ici y (STDP). The p esen ed design ad ances p eceding mem is i e synapse designs wi h ega ds o he abili y o eplica e essen ial beha iou s cha ac e ised in a numbe o elec ophysiological expe imen s pe o med in he animal b ain, which in ol e highe o de spike in e ac ions. Fu he mo e, he p oposed hyb id de ice CMOS a ea is es ima ed as 600 µm2in a 0.35 µm p ocess— his ep esen s a ac o o en educ ion in a ea wi h espec o p io CMOS a . The new design is in eg a ed wi h silicon neu ons in a c ossba a ay s uc u e amenable o la ge-scale neu omo phic a chi ec u es and may pa e he way o u u e neu omo phic sys ems wi h spike iming-dependen lea ning ea u es. These sys ems a e eme ging o deploymen in a ious applica ions anging om basic neu oscience esea ch, o pa e n ecogni ion, o B ain-Machine-In e aces. Index Te ms—Neu omo phic, Synap ic Plas ici y, Lea ning, Mem is o , C ossba , STDP, T iple , Quad uple . I. INTRODUCTION MEMRISTORS, due o hei special ea u es including non- ola ili y, nanoscale dimensions, low powe con- sump ion, and he abili y o be p og ammed while ope a - ing [1], ha e a ac ed a en ion o implemen ing an in-si u a chi ec u e [2], [3], [4]. These eme ging nanoscale de ices can implemen and mimic he synap ic plas ici y cha ac e - is ics o well-known lea ning algo i hms such as pai -based STDP and Spike Ra e-Dependen Plas ici y (SRDP) [5], [6], [7], [8]. A emp s ha e also been made o mimic expe imen al ou comes o highe o de spike-based synap ic plas ici y ules such as he supp essi e STDP ule o F oemke and Dan [9] o Local Co ela ion Plas ici y (LCP) ules o ep oduce highe o de synap ic plas ici y in mem is o s [10], [11]. In o de o ad ance ou unde s anding o he undamen al p ope ies M. Rahimi Azghadi was wi h he School o Elec ical and In o ma ion Engi- nee ing, The Uni e si y o Sydney, NSW 2006, Aus alia. He is cu en ly wi h he College o Science and Enginee ing o James Cook Uni e si y, Towns ille, QLD 4814, Aus alia (e-mail: [email p o ec ed]). B. Lina es-Ba anco is wi h he Mic oelec onics Ins i u e o Se ille, Se ille 41092, Spain (e-mail: [email p o ec ed]). D. Abbo is wi h he School o Elec ical and Elec onic Enginee ing o he Uni e si y o Adelaide, Aus alia (e-mail: [email p o ec ed]). P. Leong is wi h he School o Elec ical and In o ma ion En- ginee ing, The Uni e si y o Sydney, NSW 2006, Aus alia (e-mail: [email protected]). o synapses and hei ole in la ge-scale lea ning, he e is s ill a need o implemen a e sa ile mem is i e synapse ha is capable o ai h ully ep oducing a la ge egime o expe imen al da a ha akes in o accoun con en ional STDP [12], equency-dependen STDP [13], iple [14], [15] and quad uple [15], [16] plas ici y expe imen s. In a ecen s udy, Wei e al. eplica ed he ou come o a a ie y o synap ic plas ici y expe imen s including STDP, equency-dependen STDP, iple , and quad uple spike in e ac ions, using a TiO2 mem is o [17]. This pape p oposes a new hyb id CMOS-mem is i e ci cui ha aims o emula e all he a o emen ioned expe imen al da a, wi h minimal e o s close o hose epo ed in a phenomeno- logical model o T iple STDP (TSTDP) ule p esen ed in [15]. Simila o many p e ious s udies ha de ised mem is i e synap ic de ices/ci cui s wi h STDP, SRDP, o o he synap ic p ope ies, ou aim is a ci cui ha implemen s he TSTDP lea ning algo i hm o [15]. To he bes o ou knowledge, his has no been p e iously achie ed using mem is o s. The p oposed TSTDP mem is i e ci cui ad ances he synap ic ca- pabili ies o p e ious designs o be mo e biologically ealis ic, and p omo es ou unde s anding o synap ic al e a ion mech- anisms, belie ed o play a key ole in lea ning and memo y. Fu he mo e, he p oposed design signi ican ly dec eases he silicon eal es a e equi ed o implemen ing and u ilizing a a ie y o lea ning ules. Spiking neu al ne wo ks wi h mem is i e synapses inco po- a ing he p oposed compac and biologically plausible iple lea ning ci cui s, will be an impo an con ibu ion o he neu oscience esea ch, whe e a mo e ai h ul synap ic plas- ici y ule, compa ed o adi ional STDP, can be implemen ed and simula ed in a la ge-scale ne wo k. An in e es ing ea u e o mem is i e synapses ha dis inguishes hem om hei adi ional pu e Complemen a y Me al Oxide Semiconduc o (CMOS) coun e pa s is he easibili y o a anging hem in a dense c ossba s uc u e [1] in eg a ed wi h CMOS ci cui y. We also show how he p oposed CMOS-mem is i e ci cui can be used in his ashion, o acili a e la ge-scale in eg a ion. In o de o p omo e ep oducible esea ch, Ma lab and Cadence iles o gene a e he expe imen al da a and ep oduce he esul s in his pape a e made publicly a ailable h ough Gi hub.1 II. MEMRISTIVE SYNAPSE WITH SPIKE TIMING DEPENDENT PLASTICITY (STDP) Spike Timing Dependen Plas ici y (STDP) is a well- known synap ic plas ici y ule ha modi ies he synap ic weigh acco ding o he exac iming ela ionship o p e- 1h ps://gi hub.com/Mos a aRahimiAzghadi/Mem is i eSynapse IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 2 p e pos Fig. 1. Synap ic weigh changes, a he ime o each spike, as a unc ion o he iming di e ence be ween p e- and pos -synap ic spikes, hei empo al o de , and hei synap ic ampli ude pa ame e s, i.e. A+and A−. He e, he po en ia ion ime cons an (τ+), is assumed smalle han dep ession ime cons an (τ−), hence o he same ∆ s be ween p e and pos spikes, di e en weigh changes a e induced, e en i A+=A−. He e, ‘o’ deno es he exponen ially decaying po en ia ion po en ial, while ‘ ’ ep esen s dep ession po en ial. and pos -synap ic spikes and b ings abou Long Te m Po- en ia ion (LTP) o Long Te m Dep ession (LTD) [15]. In some elec ophysiological expe imen s pe o med in cul u ed hippocampal neu ons in 1998, he hypo hesized dependence o he synap ic e icacy o he spike iming was expe imen ally con i med [12]. Consequen ly, compu a ional neu oscien is s de eloped a model o app oxima e he indings o he expe - imen [18]. This model is oday known as pai -based STDP (PSTDP) and is usually ep esen ed as ∆w=(∆w+=A+e(−∆ τ+)i ∆ > 0 ∆w−=−A−e(∆ τ−)i ∆ ≤0, (1) whe e ∆ = pos − p e is he iming di e ence be ween a single pai o p e- and pos -synap ic spikes. As demons a ed in Fig. 1, he amoun o po en ia ion/dep ession will be de e - mined as a unc ion o he iming di e ence be ween p e- and pos -synap ic spikes, hei empo al o de , and hei ele an ampli ude pa ame e s (A+and A−). Since he epo o he i s mem is o , a ious a emp s ha e been made o de ise a i icial mem is i e synapses wi h PSTDP cha ac e is ics [19], [6], [20], [21]. In almos all o hese implemen a ions, he p og ammable non- ola ile mem- is ance ( esis ance o conduc ance) o he de ice is conside ed o play he ole o he synap ic weigh , and ol age spikes a e applied o he wo e minals o he mem is o o al e i s mem is ance. Howe e , he de ice physics, models and a ibu es, spike shape, and he me hod spike applied o elici mem is ance changes di e [22], [23]. In his pape , we ha e u ilized simila spikes and mem is i e de ice model o [20], o de elop a new synap ic ci cui o highe o de iming- and a e-based synap ic plas ici y. We discuss he u ilized model and he app oach we ha e aken o implemen ou new de ice in he ollowing. A. Mem is o model Fo his pape we ha e chosen a simple ol age/ lux d i en mem is o model such as he one p oposed in [21], and u ilized in [20]. The I-V cha ac e is ics o his mem is o , which is claimed o be physically implemen ed in [19] can be w i en as: iMR =g(w, MR) MR (2) dw d = (w, MR),(3) whe e iMR and MR a e he cu en passing h ough and he ol age ac oss he de ice, wdeno es a mem is o physical s a e a iable, and g ep esen s he nonlinea conduc ance o he de ice. Acco ding o [21], his mem is o is ol age/ lux d i en, because i s s uc u al pa ame e depends on MR. Conside ing his model o a mem is i e de ice, one should de ine he unc ion , so ha accoun o he mem is i e beha iou obse ed in physically implemen ed de ices. He e we u ilize a simple unc ion simila o he one employed in [20]. This unc ion is w i en as ( MR) = (I0sign( MR)[e | MR| 0−e h 0]i | MR|> h 0o he wise, (4) whe e I0and oa e some physical pa ame e s o he de ice and h is i s h eshold, beyond which he conduc ance o he de ice changes exponen ially. This beha iou al model o a mem is i e de ice can be illus a ed as shown in Fig. 2(a). No e o he wo h esholds and he exponen ial g ow h o he conduc ance. These a e he ea u es ha we exploi o de ise a mem is i e synapse wi h STDP. Fig. 2(b-c) demons a e he cu en - ol age and esis ance cha ac e is ics o he u ilized de ice, which is simula ed us- ing he mem is o mac omodel used in his pape and was p esen ed in [20]. This mac omodel depic s a h esholding be- ha iou simila o a comme cially a ailable ion-based physical mem is o [24] wi h a cu en - ol age cha ac e is ic as shown in Fig. 2(d). III. MEMRISTIVE SYNAPSE WITH TRIPLET STDP In 2002, F oemke and Dan p esen ed a modi ied STDP ule, ha akes in o accoun a supp essi e mechanism among spikes. This mechanism was hypo hesized o accoun o non- linea i ies obse ed in iple STDP expe imen s, whe e he PSTDP ailed [9]. In 2006, iple STDP ule was p oposed by P is e and Ge s ne [15] o accoun o a la ge se o highe o de STDP expe imen al da a. Recen ly Cai e al. [10], ha e de eloped a synap ic ci cui , u ilizing mem is o s wi h adap i e h eshold, o implemen he supp essi e STDP ule o F oemke-Dan [9]. They ha e shown ha using hei p oposed mem is i e synapse, he iple STDP beha iou o he supp essi e STDP model can be ep oduced. Howe e , hey did no explo e he s eng h o hei de eloped synapse in ep oducing o he synap ic plas ici y expe imen al da a, such as quad uple and pai ing equency expe imen s. In his pape , we ocus on implemen ing he iple ule o P is e and Ge s ne using mem is o s. A. T iple STDP The iple ule ex ends he con en ional o m o STDP ule (shown in Eq. 1) and in oduces ex a po en ia ion/dep ession con ibu ions o bo h p e- and pos -synap ic spikes. In he IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 3 −1.5 −1−0.5 0 0.5 1 1.5 −150 −100 −50 0 50 100 VMem [V] IMem [nA] −1.5 −1−0.5 0 0.5 1 1.5 20 30 40 50 60 70 80 90 VMem [V] RMem [MΩ] (a) (b) (c) (d) Fig. 2. (a) The symbol ep esen s a pola ized mem is o and he g aph demons a es a non-linea unc ion (Eq. 4), acco ding o which he s a e a iable o he mem is o changes, which leads o al e a ions in i s conduc ance acco ding o Eq. 2 and 3. (b) Cu en -Vol age cha ac e is ic o he u ilized mem is o . (c) Dependence o mem is o ime a ying esis ance wi h espec o mem is o ol age. Bo h (b) and (c) a e simula ed in Cadence using he mac o-model p oposed in [20]. (d) Th esholding and compliance beha iou o a comme cially a ailable ion-based physical mem is o , which has simila ea u es o ou simula ed mem is o . Image is ex ac ed om he use manual o neu o-bi de ice [24]. iple model, he pos spike, in addi ion o i s exponen ially decaying pai ing dep ession po en ial, 1, shown in Fig. 3, igge s an ex a po en ia ion po en ial, o2, o in e ac ion wi h upcoming pos spike(s). Simila ly, he p e spike also gi es ise o an ex a dep ession po en ial, 2, o in e ac wi h nex p e spikes, besides i s usual pai ing po en ia ion po en ial ace, o1. These ex a iple po en ials ha a e shown in Fig. 3, may di e in ime cons an s and ampli udes, compa ed o con en ional STDP po en ials. As shown in Fig. 3, a he ime o he i s p e spike, p e1, a dep ession happens due o he p e ious pos spike ha has le a dep ession ace, 1. Nex , a he ime o he second pos spike, pos2, wo po en ia ions ake place. The i s is due o he p e-pos pai ing, and he po en ia ion ace, o1, ha he i s p e spike le . The second po en ia ion hough, is a esul o a iple in e ac ion (pos -p e- pos ) among he i s and second pos and he i s p e spikes. This po en ia ion depends on he wo po en ia ion aces, one le by he i s p e spike, o1, and he second one igge ed by he second pos spike, o2. This second ace is he di e en ial poin o he s anda d STDP ule, as i in oduces in e ac ions among spikes o he same p e o pos neu on, and may lead o ex a po en ia ion/dep ession. This iple STDP in e ac ion can be ep esen ed as ∆w( ) = A+ 1o1( ) + A+ 2o1( )o2( −)i = pos −A− 1 1( )−A− 2 1( ) 2( −)i = p e, (5) whe e o1and o2a e po en ia ion po en ials igge ed by p e and pos spikes, espec i ely. In addi ion, 1and 2a e dep ession po en ials elici ed by he a i al o pos and p e spikes, espec i ely. Pa ame e s A+ 1,A+ 2,A− 1and A− 2a e cons an ampli ude pa ame e s ha de e mine he con ibu ion s eng h o each spike in po en ia ion/dep ession. He e, is a small posi i e cons an which ensu es ha he weigh upda e uses he co ec alues occu ing jus be o e he p e- o pos - synap ic spike o in e es . Simila o he pai -based STDP, he iple ule can also be ma hema ically ep esen ed as ∆w=   A+ 1e(−∆ 1 τ+)+A+ 2e(−∆ 1 τ+)e(−∆ 2 τy)i = pos −A− 1e(∆ 1 τ−)−A− 2e(∆ 1 τ−)e(−∆ 3 τx)i = p e, (6) O 1 dep po 2 2 po 1 O2O2 O1 1 1 2 2 2 dep Synap ic Weigh A 11 - ( ) p e1 Ao11 + ( ) pos2 A2 + +o( -ε) pos2 2 o1( ) pos2 - - A 11 - ( ) p e2 A2 ( -ε) p e2 2 - - 1( ) p e2 po 1 dep1 dep2 p e pos Fig. 3. Synap ic weigh changes, a he ime o each spike, as a unc ion o he iming di e ence be ween p e- and pos -synap ic spikes, hei empo al o de , and hei synap ic ampli ude pa ame e s, i.e. A+ 1,A− 1,A+ 2and A− 2. whe e ∆ 1= pos (n) − p e(m),∆ 2= pos (n) − pos (n−1) − and ∆ 3= p e(m) − p e(m−1) −, a e he ime di e ences be ween combina ions o p e- and pos -synap ic spikes, and τ−,τ+,τxand τya e ime cons an s ela ing o he po en ia- ion/dep ession po en ials o 1,o1, 2, and o2, espec i ely. P is e and Ge s ne [15] ha e shown ha he ull TSTDP ule o Eq. 6 can be simpli ied, wi hou he pe o mance o he model in ep oducing he expe imen s being comp omised, o a minimal ule ha does no include a iple dep ession e m, 2. The e o e, he iple ule o Eq. 6 will be minimized o a minimal TSTDP ule as ∆w=   A+ 1e(−∆ 1 τ+)+A+ 2e(−∆ 1 τ+)e(−∆ 2 τy)i = pos −A− 1e(∆ 1 τ−)i = p e, (7) No e ha in all he esul s p esen ed in his pape , he minimal iple STDP is used. B. Rela ing mem is o model o iple STDP Fo implemen ing he iple STDP ule, we used he com- bina ion o wo mem is o s and by applying he supe posi ion p inciple, we can sum he weigh changes o all spike in e - ac ions applied o hese wo mem is o s, o ob ain he inal weigh change. Hence, conside ing Eq. 7, le us assume ha mem is ance (synap ic weigh ) changes as ollows dw d = (w, ∆ pai ( )) + (w, ∆ iple ( )),(8) IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 4 whe e ∆ pai ( ) = pos − p e,(9) in esponse o a p e-pos o pos -p e pai o spikes, is applied o he wo e minals o he i s mem is o shown in Fig. 4(a), and ∆ iple ( ) = iple (po ) ( )− iple (dep) ( ),(10) whe e iple (po ) ( ) = [ pos (n−1) ( −)· p e(m) ( )]+,(11) iple (dep) ( )=[ p e(m−1) ( −)· pos(n) ( )]+,(12) a e espec i ely esponses o pos -p e-pos and p e-pos -p e spike combina ions, applied o he wo e minals o he second mem is o . He e, [x]+is a ec i ie unc ion ep esen ed as [x]+=xi x > 0 0o he wise.(13) I he minimal TSTDP ule is conside ed, i.e. iple (dep) = 0, Eq. 10 is simpli ied o ∆ iple ( ) = iple (po ) ( ).(14) I we in eg a e Eq. 8, we can ind he weigh changes ac oss mem is o s o a ious se o p e- and pos -synap ic ol ages (spikes) applied o he mem is o s as ollows ∆w(∆ 1,∆ 2) = Z ∆ 1 (∆ pai ( ))d +Z ∆ 2 (∆ iple ( ))d . (15) Conside ing Eq. 15, in a pos -p e-pos iple case o spikes, he in eg a ion will be ∆w(∆ 1,∆ 2) = p e Z pos 1 (∆ pai ( ))d + pos 2 Z p e (∆ pai ( ))d + (pos 2−) Z pos 1 (∆ iple ( ))d . (16) The h ee pa s o Eq. 16 a e demons a ed in Fig. 4(b), whe e he i s in eg al is o e a pe iod o 5 ms be ween pos 1-p e, which esul ed in a dec ease in mem is ance o he i s mem is o in Fig. 4(a), i.e. a synap ic dep ession, which is demons a ed as a nega i e alue in o ange in he ou h g aph. The second in eg a ion is o e a pe iod o 15 ms, i.e. be ween he p e and pos 2 spikes and esul ed in a posi i e alue, shown in g een in he ou h g aph, ep esen ing an inc ease in he mem is ance o he i s mem is o . These wo nega i e and posi i e alues a e in ela ion o he pai -based STDP model. Howe e , acco ding o he minimal iple STDP, o mula ed in Eq. 7, he pos 1-pos 2 spikes in he p esence o a p e spike can esul in po en ia ion. This po en ia ion shown in he bo om g aph o Fig. 4(b)), is demons a ed as an inc ease in he mem is ance o he second mem is o in Fig. 4(a), and Fig. 4. (a) The p oposed bi-mem is o hyb id synapse. This synapse is composed o wo mem is o s and a mul iplie / ec i ie ci cui shown as a c ossed squa e. (b) The h ee op g aphs demons a e he spikes ol ages applied o he wo e minals o he mem is o s, o a pos -p e-pos iple wi h -5 ms and 15 ms delays among spikes. The ou h g aph demons a es he ol age changes ac oss he i s mem is o , and he a eas beyond he mem is o h eshold, which can lead o inc ease/dec ease in he mem is ance. In addi ion, he bo om g aph demons a es an inc ease in he mem is ance o he second mem is o , which is in esul o he ec i ied mul iplica ion o he iple ace o he pos s and he po en ia ion ace o he p e (see second e m o he i s equa ion in Eq. 5). (c) The sum o p edic ed mem is ance changes o e he wo mem is o s, in esul o a pos -p e-pos spike iple , wi h a ious imings among he spikes is shown along wi h he da a measu ed in expe imen s p esen ed in [16]. The u ilized STDP pa ame e s o he esul shown in his igu e a e as ollows: τ+= 16.8ms and τ−= 33.7ms a e se simila o he me hod used in [15]. A+ 1= 1.04,A− 1= 0.51,A+ 2= 3.39,τy= 198 ms, and 0= 2.08 a e op imized, and | h|= 1.04. is in esul o an in eg a ion o e he pos 1-pos 2 spikes pe iod as shown in Eq. 16. No e ha , due o he lack o a second p e spike in his iple , he second e m o he second equa ion, in he equa ion a ay shown in Eq. 6 is ze o, and he e o e, no u he dep ession will be elici ed. This is also he case when a minimal TSTDP model is conside ed. In o de o e i y he unc ionali y o he p oposed iple mem is i e de ice, i was used o eplica e an expe imen al da a se gene a ed using pos -p e-pos iple spikes in [16]. Fig. 4(c) demons a es a e y close ma ch be ween he mem- is ance changes ob ained using he p oposed de ice, and hose IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 5 measu ed in he iple expe imen s [15], [16]. This ma ch was ob ained by op imizing he STDP and mem is i e pa ame e s o each he leas e o . IV. EXPERIMENTAL RESULTS So a we only conside ed synap ic weigh changes o one pai o iple o spikes using he p oposed CMOS-mem is i e synapse. Howe e , an ex ensi e se o simula ions should be ca ied ou o ep oducing he ou comes o a a ie y o essen ial expe imen al da a, which has been he subjec o esea ch in bo h neu omo phic [25], [26] and compu a ional neu oscience esea ch [27]. In his sec ion, we epo ou ind- ings and demons a e he limi a ions o he PSTDP mem is i e synapse o [20] in ep oducing a numbe o expe imen s. We hen show how ou p oposed synapse can closely eplica e he ou comes o a numbe o p e ious expe imen s, using a single se o STDP pa ame e s. A. Expe imen al p o ocols Ce ain s anda d expe imen al p o ocols a e p edominan ly ollowed in he a ea o elec ophysiological expe imen s o s udy synap ic plas ici y [9], [12], [13], [16]. The same p o ocols should he e o e be employed while e i ying he pe o mance o he de ised compu a ional models [9], [14], [15] o neu omo phic de ices [10], [25], [28] in app oxi- ma ing/ eplica ing he expe imen al da a obse ed in biolog- ical synapses. He e we ha e ollowed simila p o ocols o hose deployed in synap ic plas ici y expe imen s o examine he unc ionali y and pe o mance o ou p oposed CMOS- mem is i e synapse, and o compa e i wi h i s con en ional STDP coun e pa s. The u ilized p o ocols a e Pai -based STDP, equency-dependen STDP, iple -based STDP, ex a iple STDP, and quad uple , which a e de ined in ou p e ious s udies [25] and in he TSTDP modelling pape [15]. B. Da a i ing app oach and expe imen al scena ios In o de o es he e icacy o a synap ic model/de ice, one can de ine an e o unc ion ha ep esen s he di e - ence among he weigh changes p edic ed by a candida e model/de ice, and hose measu ed in elec ophisiological ex- pe imen s. A sui able e o unc ion, is he No malised Mean Squa e E o (NMSE) unc ion p oposed and u ilised in [15], NMSE = 1 p p X i=1 ∆wi exp −∆wi model σi!2 ,(17) whe e ∆wi exp,∆wi model and σia e he mean weigh change ob ained om biological expe imen s, he weigh change ob- ained om he model o ci cui unde conside a ion, and he s anda d e o mean o ∆wi exp o a gi en da a poin i, espec i ely. He e, p ep esen s he numbe o da a poin s in he da a se unde conside a ion. In all expe imen s pe o med in his pape , we u ilized he MATLAB buil -in minsea ch, an uncons ained non-linea minimiza ion unc ion, o minimize he NMSE o he synap ic de ice unde conside a ion. Fo ins ance, o he p oposed bi- mem is o hyb id synapse, in Fig. 4, i e pa ame e s including ou o he iple STDP ule embedded in he spike shapes (A+ 1,A− 1,A+ 2,τy) and one ela ing o he mem is o unc ion, 0, we e op imized. We p esen esul s ob ained om a ious expe imen s, in which hese pa ame e s along wi h some o he pa ame e s a e op imized o each he bes NMSE in di e en scena ios. Two di e en scena ios can be conside ed o e i y he unc ionali y and pe o mance o pai -based and iple -based mem is i e ci cui s in ep oducing he ou comes o expe i- men s using he a o emen ioned p o ocols. Unde i s sce- na io, simila o he expe imen s in [15], PSTDP ime con- s an s, i.e. τ+and τ−a e kep ixed and equal o 16.8 ms and 33.7 ms espec i ely, while o he pa ame e s a e op imized. Unde scena io wo, hese pa ame e s a e op imized along wi h o he pa ame e s o s udy he e ec o highe pa ame e lexibili y on synap ic plas ici y. C. F equency-dependen pai ing ( isual co ex) expe imen s Unde he i s scena io, pai -based STDP ails o mimic expe imen al da a, whe e synap ic weigh changes a e exam- ined agains he equency o pai s o spikes, ρ. The op imum NMSE is achie ed using he pai -based mem is i e synapse p esen ed in [20] is 8.19. The esul ing weigh p edic ion is shown in Fig. 5(a), which in e es ingly is simila o he weigh changes p edic ed by he PSTDP compu a ional model shown in Eq. 1, as epo ed in [15]. Scena io wo esul s in a lowe NMSE o 1.69 and an imp o ed ma ch o he expe imen al da a (see Fig. 5(b)). Howe e , he op imiza ion esul s in a e y long po en ia ion ime cons an , τ+= 110 ms, and a e y sho dep ession cons an o almos 1 ms. These ime cons an s lead o only po en ia ion when he epe i ion equency is high enough, i.e. ρ > 10 Hz, o he spikes o o e lap. Hence, we can conclude ha he pai -based mem is i e STDP synapse is no capable o ep oducing he ou come o equency- dependen pai ing expe imen s. This is in ag eemen wi h p esen ed esul s in [15]. On he o he hand, u he simu- la ions sugges ha ega dless o he op imiza ion o ime cons an s, he p oposed hyb id ci cui can closely app oxima e he beha iou obse ed in he expe imen s. These beha iou s, which esul ed in NMSE = 0.45 o he i s scena io, and NMSE = 0.34 o he second one, a e shown in Fig. 5(c) and (d), espec i ely. D. Pai , iple , and quad uple (hippocampal) expe imen s In he iple -based STDP s udy by P is e and Ge s ne [15], one se o pa ame e s and he minimal e sion o he iple STDP model we e u ilized, o minimize he NMSE o a se o expe imen al da a composed o 13 da a poin s, including pai s (2 da a poin s), iple s (8 da a poin s), and quad uple s (3 da a poin s). These da a poin s and hei espec i e e o ba s, which a e shown in black in ou igu es, ep esen s expe imen al da a ob ained om hippocampal cul u e as epo ed in [16]. Ou pe o med expe imen s using he PSTDP mem is i e synapse o [20] show ha his ci cui ails o accoun o he hippocampal cul u e da a se unde bo h scena ios. The esul s o scena io wo, a e shown in Fig. 6. As expec ed he PSTDP mem is i e synapse wi h op imized pa ame e s can IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 6 Fig. 5. (a) Pai -based STDP mem is i e synapse o [20] ails o mimic expe imen al da a o [13], unde scena io 1. (b) Simila o (a), only o scena io 2. (c-d) The p oposed iple -based STDP mem is i e synapse success ully mimics expe imen al da a, unde scena io 1 shown in (c) and scena io 2 p esen ed in (d). He e ρ ep esen s he equency o spike pai s wi h ime di e ences o 10 ms and -10 ms. success ully eplica e he STDP lea ning window. Howe e , in he case o quad uple expe imen (Fig. 6(c)), he PSTDP mem is i e synapse shows simila beha iou o he ailu e o PSTDP model as p esen ed in [15]. Beside hese, he PSTDP mem is i e synapse clea ly lacks he abili y o dis inguish be ween he p e-pos -p e and pos -p e-pos expe imen s as shown in Fig. 6(c)-(d). This is simply due o he accumula i e na u e o he PSTDP ule and i s mem is i e synapse, which sum he e ec o pos -p e and p e-pos spike pai s in a pos - p e-pos iple , and simila ly agg ega e he e ec o p e- pos and pos -p e pai s in a p e-pos -p e iple . The e o e, no di e ence be ween he wo iple s is expec ed as bo h o hem consis o a p e-pos along wi h a pos -p e spike pai . Howe e , he expe imen al da a, demons a ed in black, sugges s signi ican di e ence be ween he wo iple s. Fu - he mo e, ou simula ions also demons a e ha he pai -based mem is i e STDP synapse, using scena io 1, i.e. wi h ixed τ+ and τ−and while only he o he ou pa ame e s a e op imized, canno each an NMSE smalle han 12.25, and clea ly lacks he abili y o mimic he expe imen al da a. In con as o he PSTDP de ice, ou minimal TSTDP mem- is i e synapse shows a e y close ma ch o he expe imen al da a, and achie es a e y low NMSE o 0.87 unde scena io 2. This is much lowe han he PSTDP mem is i e synapse, whe e we eached an NMSE o 7.42 unde same scena io. Expe imen al esul s using he iple synapse demons a ed in Fig. 7(c–d) show how well his synap ic ci cui dis inguishes be ween wo di e en cases o iple da a. The mem is i e synapse, esul s in s ong po en ia ion in case o pos -p e- pos iple (Fig. 7(d)) as expec ed. This is due o he iple po en ia ion in e ac ion, which is absen in case o p e-pos -p e iple (Fig. 7(c)). Fig. 7(a) also demons a es he con en ional STDP lea ning window gene a ed by ou TSTDP ci cui , which closely ma ches he wo a ge ed PSTDP expe imen al da a. Finally, in case o quad uple expe imen s (Fig. 7(b)), Fig. 6. (a) Pai -based STDP mem is i e synapse o [20] ep oduces he STDP lea ning window, while i ails o gene a e (b) quad uple da a, and canno dis inguish be ween (c) p e-pos -p e, and (d) pos -p e-pos iple . he p oposed synapse closely i s he da a poin s and ollows simila beha iou o he da a ob ained using he minimal iple compu a ional model o P is e and Ge s ne [15]. Addi ionally, in case o scena io 1, i.e. when he pai ime cons an s τ+and τ−a e kep ixed, an NMSE o 3.61 was eached using ou p oposed iple ci cui , which is much lowe han he NMSE = 12.25, and NMSE = 7.42, ob ained using he pai -based de ice. Table I summa ises NMSEs and hei espec i e op imized pa ame e s o all he expe imen s and scena ios men ioned in p e ious subsec ions. In all cases, he iple mem is i e ci cui esul s in a be e NMSE compa ed o i s pai -based coun e pa o [20]. E. T iple expe imen s o F oemke-Dan [9] Apa om he iple expe imen s pe o med in p e ious subsec ion, whe e only p e-pos -p e and pos -p e-pos iple s we e conside ed, one may in es iga e he e ec o o he combina ions o h ee spikes. This is he expe imen , epo ed in [9], whe e six di e en combina ions o spike iple s a e s udied (see Fig. 8(a)). In e es ingly, ou p oposed iple de ice, is capable o ep oducing a close app oxima ion o he da a om he supp essi e STDP model o F oemke-Dan [9], o hese ex a iple expe imen s. Fig. 8(b) demons a es he ou come o ex a iple expe imen s using he p oposed iple mem is i e ci cui , unde he i s (Fig. 8(b1-b2)), and second (Fig. 8(b3-b4)) scena ios. In he i s scena io, he op imized pa ame e s o he iple case o hippocampal cul u e expe imen s [15] we e used, whe e he bes NMSE achie ed was 3.61 (see Table I). Pa (b1) in Fig. 8 depic s he a ie y o combina ions o 2 pos and 1 p e spikes, hei ime di e ences, ∆ 1= pos 1 − p e,∆ 2= pos 2 − p e, and hei esul ing weigh modi ica ion, ∆w, shown as a colo ba . Pa (b2) demons a es he weigh changes achie ed using he same se o pa ame e s in he iple ci cui , when 2 p e and 1 pos spikes a e combined, as shown in he igu e. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 7 TABLE I OPTIMIZED PARAMETERS AND NMSES FOR ALL EXPERIMENTS Scena io Exp STDP τ+(ms) τ−(ms) A+ 1A− 1τy(ms) A+ 2 h 1/ 0NMSE 1 Visual pai 16.8 33.7 0.12 0.076 NA NA 0.025 0.1 8.19 iple 16.8 33.7 0.042 0.027 135 6.85 0.005 0.68 0.45 Hippo pai 16.8 33.7 0.14 0.059 NA NA 0.098 0.15 12.25 iple 16.8 33.7 0.085 0.54 120 4.76 0.036 0.2 3.61 2 Visual pai 110 0.9 0.018 0.32 NA NA 0.024 1.07 1.69 iple 24 27 0.075 0.51 156 4.64 0.027 0.35 0.345 Hippo pai 27 20 0.06 0.061 NA NA 0.054 0.92 7.42 iple 19 16 0.035 0.036 43 2.03 0.024 1.35 0.87 Fig. 7. (a) P oposed iple -based STDP mem is i e synapse ep oduces he STDP lea ning window. (b) The p oposed TSTDP de ice p edic s simila weigh changes o he da a p esen ed in [15] o quad uple p o ocol. No e ha he e is no expe imen al da a a ailable a ound 0ms. (c)-(d) The p oposed synapse, co ec ly dis inguishes be ween (c) p e-pos -p e iple case, and (d) pos -p e-pos iple case. In o de o u he es he pe o mance o he p oposed iple mem is i e ci cui , we u ilized he op imized pa ame e s in case o scena io 2, whe e he achie ed minimal NMSE was 0.87. Figu e 8(b3-b4) p esen s he s eng h o he iple ci cui in closely app oxima ing he ou come o he iple expe imen s as shown in [9]. Al hough using di e en scena ios and op imized pa ame e se s, bo h pa s (b1-b2) and (b3-b4) in Fig. 8 p esen simila po en ia ion/dep ession cha ac e is ics o iple spike combi- na ions. Bo h hese pa s co ec ly mimic he weigh changes as obse ed in he iple expe imen s epo ed in [9], excep o he pos -p e-pos iple case. The eason o his di e ence has been explained in [15]. I is wo h no ing ha , o ob aining he esul s demons a ed in Fig. 8, he same pa ame e s ha we e u ilized o ep oduc- ing he hippocampal expe imen s a e applied. Fo ins ance, he esul s shown in Fig. 8(b) a e ob ained using he same pa ame e s, using which Fig. 7 weigh changes we e a ained. This ea u e u he es i ies o he s eng h o he p oposed iple de ice, which can ep oduce he ou come o quad uple , pai ing and a ious iple expe imen s including hose ha ha e no been explo ed in [15]. V. THE HYBRID SYNAPSE IN CROSSBAR ARRAY In he s uc u es p esen ed in Fig. 4, only one ins ance o he p oposed bi-mem is o hyb id synapse is demons a ed, wi hou conside ing he inclusion o such a synapse in a c ossba a ay s uc u e. In o de o u ilize he p oposed ci cui in c ossba a ays and employ i o simul aneous lea ning and compu a ion, he s uc u e mus be sligh ly modi ied. Figu e 9(a) shows a p e-synap ic neu on connec ed h ough a bi-mem is o hyb id synapse o a pos -synap ic neu on. He e, a modi ied CMOS neu on ci cui compa ed o ha o [20] has been u ilized. The di e ence be ween his new CMOS neu on and hose u ilized in he implemen a ion o PSTDP lea ning is ha , no only does his neu on gene a e pos spikes o in e ac wi h p e spikes, i also p oduces o he pos spikes, i.e. pos 1 spk, equi ed o iple lea ning. These spikes as shown in Eq. 11 should be mul iplied by he spikes coming om a e en p e-synap ic neu on, and hen he esul should be ec i ied and applied o he iple mem is o (R ip) as shown in Fig. 9(a). This igu e also shows wo swi ches ac oss he iple mem- is o . These swi ches, con olled by a signal om he pos - synap ic neu on, ensu e he co ec in eg a ion and lea ning in he mem is i e synapses. When in eg a ing spikes om he p e-synap ic neu on, he swi ches a e closed as shown in he igu e, and he e o e apply he p e spikes o he le sides o bo h mem is o s a he junc ion. On he pos -synap ic ( igh ) side o he mem is o s, a e e ence ol age is gene a ed by he neu on, ha shows no pos -synap ic ac i i y and a he same ime, ensu es no change in he mem is i e weigh s. This ope a ion can be in e p e ed as a weigh ead phase, whe e he p e spikes a e in eg a ed in o pos neu ons and exci e i p opo ional o he s eng h o hei espec i e mem is i e synapses. On he o he hand, when he pos -synap ic neu on, in esul o he in eg a ions, i es a spike, he swi ches u n o he second posi ion and he lea ning phase s a s. The weigh s o mem is i e synapses a e hen changed due o he exis ence o o e lapping p e- and pos -synap ic spikes and he iming di e ences be ween hem. In his case, due o a possible o e lap o a p e-synap ic spike and a iple pos -synap ic spike, he weigh o he second mem is o can be modi ied. No e ha , in his igu e, he minimal e sion o he TSTDP ule is implemen ed, i.e. he iple dep ession in e ac ions om p e-synap ic neu on a e neglec ed. This esul s in ha ing he le side o he mem is o connec ed o g ound du ing lea ning, as shown in he igu e. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 8 −25 −5 0 5 25 −25 −5 0 5 25 ∆ 2(ms) −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 ∆ 2(ms) ∆ 1(ms) −20 0 20 −30 −20 −10 0 10 20 30 ∆ 2(ms) −0.5 0 0.5 1 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 ∆ 2(ms) ∆ 1(ms) −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 ∆ 2(ms) ∆ 2(ms) ∆ 1(ms) −25 −5 0 5 25 −25 −5 0 5 25 ∆ 2(ms) ∆ 1(ms) −25 −5 0 5 25 −25 −5 0 5 25 50 100 200 (a) (1) (2) (3) (4) (b) (1) (2) (4) (3) −25 −5 0 5 25 −25 −5 0 5 25 ∆ 2(ms) ∆ 1(ms) Fig. 8. (a1-a2) Expe imen al iple da a o [9] o six di e en spike iple combina ions. (a3-a4) A supp essi e PSTDP model p oposed by F oemke and Dan app oxima e he expe imen al da a. (b1-b4) The p oposed iple -based STDP mem is i e synapse mimics he weigh modi ica ions da a and supp essi e PSTDP model o [9]. (b1-b2) show weigh changes p oduced using he op imized pa ame e s o he iple case o hippocampus expe imen s unde scena io 1, i.e. when NMSE = 3.61 (see Table I). (b3-b4) simila o (b1-b2), excep ha he pa ame e s used o gene a ing he weigh changes a e hose u ilized o each an NMSE o 0.87, i.e. he iple case o hippocampus expe imen s unde scena io 2 (see Table I). The con as be ween weigh changes in he pos -p e-pos case is due o he di e ence be ween he supp essi e PSTDP model o [9] and he TSTDP model o [15] ha is implemen ed in his pape . In (a), he colo ba shows no malized weigh changes ob ained om he expe imen s. Howe e , he colo ba in (b) demons a es he exac alues o weigh changes ob ained using he p oposed ci cui . The ci cui s uc u e shown in Fig. 9(a), which includes a mul iplie / ec i ie ci cui and a numbe o swi ches, was simula ed in Cadence Spec e. The mul iplie is a CMOS Gilbe cell ha along wi h a compa a o and wo pass ga es pe o m he equi ed mul iplica ion/ ec i ica ion. In addi ion, ou o he pass ga es we e used o p ope ly con ol he weigh ead and lea ning (weigh change) phases. The u ilized mem is- o is he one employed in he expe imen s pe o med in [20]. Resul s using he implemen ed hyb id ci cui a e demons a ed in Fig. 9(b). The p oposed s uc u e demons a ed in Fig. 9(a) is scalable. Figu e 10 depic s a 3-by-3 c ossba a ay ha inco po a es CMOS neu ons and CMOS-mem is o synapses. This igu e sugges s ha he p oposed TSTDP bi-mem is o synapses, analogous o hei o me single mem is o PSTDP coun- e pa s [20], can be in eg a ed wi h CMOS neu ons and implemen la ge scale neu al a ays. In he neu al a ay p esen ed in Fig. 10, each pos -synap ic neu on is d i en by h ee p e-synap ic neu ons connec ed o i h ough h ee bi-mem is o hyb id synapses. He e, he second p e-synap ic neu on is assumed silen , hence i is eplaced by a ol age sou ce o he alue o he pos -synap ic neu on spiking h eshold, VREF. The o he wo p e-synap ic neu ons gene a e egula spike ains wi h a ious in e spike in e als. In addi ion, mem is o s in he h ee ows o he a ay a e gi en a ious ini ial weigh s, which esul s in di e ence in spiking ac i i ies o hei espec i e pos -synap ic neu ons. Cadence simula ion esul s ha demons a e changes in synap ic weigh s ac oss all mem is o s in he 3-by-3 c oss- ba a ay o Fig. 10 a e shown in Fig. 11. In his igu e, he i s ow depic s weigh changes co esponding o he synapses in he i s column o he a ay, i.e. ela ed o he i s p e-synap ic neu on. The second ow shows ha no change akes place on he mem is i e synapses in he second column. This is due o he ac ha he p e-synap ic neu on associa ed wi h his column is silen and p oduces no spike. The hi d ow mani es s weigh changes occu ing ac oss he synapses d i en by he hi d p e-synap ic neu on. He e, a ious weigh change p o iles a e due o di e en ini ial weigh s se on he synapses, and because o he di e en imings among pos - synap ic spikes gene a ed by he pos neu on in each ow. As expec ed, only po en ia ion occu s o he iple mem is o s, while bo h po en ia ion and dep ession a e obse ed on pai mem is o s o each hyb id synapse, due o a ious p e-pos o pos -p e spike combina ions. VI. DISCUSSION AND CONCLUSION Implemen ing a ea e icien , low-powe , and la ge-scale neu al-inspi ed lea ning a chi ec u es can be acili a ed using mem is o s [23], [29]. Nanoscale dimensions, in insic non- ola ili y, and ul a low powe consump ion [30] combine o make mem is o s pe ec candida es o implemen synapses in neu omo phic a chi ec u es. The lea ning pe o mance o hese a chi ec u es is s ongly go e ned by he plas ici y mechanisms hei synapses implemen [31], [32]. The e o e, ca e ul con- side a ion mus be aken when synap ic plas ici y mechanism o he a ge ed neu al pla o m is being chosen. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 9 bias comp bias mul pos p e pos 1 pos 1 ec ec ec S1 S1 S1 S1 S1 ip R p e pos S1 S1 + - VREF Pos spk Pos 1 spk S1 PRE ip R pai R pos 1 pos POST Sun9May91916:59:3092016 P e9(V) Pos 9(V) Pos 1 (V) Rpai (MΩ) R ip (MΩ) 012345 ime(s) 1.0 0.5 0.0 -0.5 1.0 0.5 0.0 -0.5 -1.0 0.0 -0.5 -1.0 25.0 35.0 45.0 55.0 65.0 30.0 50.0 70.0 (b) (a) Fig. 9. Ci cui s uc u e and Cadence simula ion esul s o a p e-pos neu on combina ion. (a) A p e-synap ic neu on connec ed h ough a bi-mem is o hyb id synapse o a pos -synap ic neu on, which p oduces wo spikes (pos and pos 1) wi h di e en p ope ies. In he synapse s uc u e, he mul iplie - ec i ie ci cui is shown by a squa e box con aining a c oss. This ci cui along wi h he swi ching ci cui y needed o iple in e ac ion a e also shown he e. (b) Ci cui simula ion esul s gene a ed using Cadence Spec e o a ain o p e-synap ic spikes. The pos -synap ic neu on p oduces spikes depending on when he p e-synap ic spikes ha e been in eg a ed adequa ely o pass i s h eshold VREF. He e simila p e- and pos -synap ic spike shapes o hose u ilized in [20] ha e been used. The s a o each p e o pos -synap ic spike is composed o a pulse o he wid h o 1 ms, while he ail o he spikes ha e di e en leng hs as ollows: p e spike ail = 80 ms, pos spike ail = 130 ms, and pos 1 spike ail = 700 ms. In o de o accoun o he pa ame e o Eq. 7, pos 1 was delayed by 1 ms. In e ms o synap ic mechanisms, many s udies ha e ex- plo ed he implemen a ion o he simple ye nai e pai -based STDP ule using mem is i e de ices [19], [5], [6], [20], [21], [22]. Only a ew s udies epo implemen a ions o o he mo e powe ul synap ic plas ici y mechanisms such as supp essi e STDP [10]. These mechanisms ha ha e ad anced synap ic plas ici y (lea ning) abili ies compa ed o he PSTDP ule, can imp o e he pe o mance o he de eloped neu omo phic a chi ec u es in lea ning and compu a ion. In o de o each highe lea ning capabili ies in u u e neu al a chi ec u es, his pape p oposes a no el CMOS-mem is i e design o a highe o de STDP ule, namely iple STDP, which has ad an ages o e i s p e ious CMOS [25], [33], [34] as well as mem is i e [5], [6], [10], [20], [22] coun e pa s and signi ican ly imp o es lea ning capabili ies o neu omo phic synapses. The p oposed synap ic ci cui is composed o wo mem is o s along wi h se e al CMOS ansis o s o accoun o he non-linea i ies o he iple ule p oposed by P is e and Ge s ne [15]. Al hough his hyb id CMOS-mem is i e ci cui , compa ed o i s mem is i e PSTDP coun e pa s [6], [20], has highe complexi y in e ms o implemen a ion, i o e s signi ican ly imp o ed lea ning pe o mance. This highe pe - o mance is achie ed by adding a second ( iple ) mem is o , as well as a CMOS mul iplie / ec i ie ci cui . Many p e ious CMOS STDP synapse ci cui s occupy a la ge silicon a ea, e en i he synap ic weigh s o age is no conside ed. This could be imp o ed by using a mem is i e design such as he p oposed ci cui in his pape . Fo in- s ance, he p esen ed PSTDP synapse in [33] occupies an a ea o 145 ×31 µm2in a 0.8 µm CMOS p ocess, and he PSTDP weigh upda e design p oposed in [34] akes up 131.3×139.7µm2in a 0.6 µm CMOS p ocess. In addi ion, a p e ious TSTDP ci cui implemen ed by ou g oup has an a ea o 165 ×60 µm2in a 0.35 µm CMOS p ocess, om which o e 75 pe cen is occupied by i e la ge capaci o s [35]. No e ha hese a eas a e only ela ed o he weigh upda e ci cui ies