Pattern Classification and NNet applications with memristive crossbar circuits. Fabien ALIBART D. Strukov s group, ECE-UCSB Now at IEMN-CNRS, France
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1 Paern Classificaion and NNe applicaions wih memrisive crossbar circuis Fabien ALIBART D. Srukov s group, ECE-UCSB Now a IEMN-CNRS, France
2 Ouline Inroducion: Neural Nework wih memrisive devices Engineering and swiching dynamics High precision analog uning Nne Circuis MAC operaion Hopfield A/D converer Paern classifier Conclusion
3 Inroducion: Why ANNe New needs for compuing Recogniion, Mining, Synhesis (Inel) Von Neumann boleneck Increase of Faul (nanoscale engineering) SEMICONDUCTOR TECHNOLOGY CHALLENGES Sauraion of clock frequency + Energy consumpion Shif oward a new paradigm for compuaion BIO-INSPIRED COMPUTING o mach he brain performances (low power consumpion, faul oleran, performances for RMS)
4 Inroducion: NNET basic principle synapse Biological neural nework OUTPUT Bio-inspired sysem: in he brain, we learn by creaing (weighing) synapic connecions beween neurons from differen experiences. Afer, we can reac o unknown siuaions which are similar o he learning ones. INPUT The memory is in he processing uni (Direc soluion o Von Neumann boleneck!)
5 Inroducion: NNET roadmap 1 11 neurons / 1 15 synapses OxRAM + CMOS neuron Memrisive Xbar + CMOS
6 Curren (A) Memrisive TiO2 devices 1E-3 Incremenal rese Incremenal se Single sweep 1E-4 1E-5 1E-6 S A V RESET: R =R ON SET: R =R OFF 1 1E Volage (V) -Non-linear I-V -Analog non-volaile memory (any sae beween R on and Roff is accessible and sable) - smooh RESET ransiion - sharp SET ransiion - plaeau of non disurbing volage pulses Pulse volage (V) Main challenge: how o deal wih dispersion E-8 1E-6 1E-4.1 Time (s) R/R
7 Pourcenage of working devices Curren (A) Curren (A) Engineering 2 nm No prousion (5 devices) 17 nm prousion (1 devices) nm TiO 2-x 25 nm Au / 15 nm P op elecrode e-beam paerned P prorusion 1E-3 1E-4 1E-5 1E-6 1E-3 1E-4 1E-5 1E-6 5 nm Ti / 25 nm P boom elecrode 1E-7 1E-7 1E-8 2 nm 1E Volage (V) -1 1 Volage (V) 1 8 Engineering improve yield and decrease dispersion (beer conrol of forming) no prousion 17 nm prousion
8 V Tune Rese Read Swiching V Tune Read Se 6uA 3uA 1uA mV 3 parameer for swiching: -Volage -Time -Iniial sae 2mV uA 3uA 1uA.6.8 Pulse volage x x1-6 Cumulaive ime cumulaive ime (s) 1.x1-6 2.x Pulse volage -.6
9 V Tune Rese Read Swiching V Tune Read Se 6uA 3uA 1uA mV 3 parameers for swiching: -Volage -Time -Iniial sae 2mV uA 3uA 1uA.6.8 Pulse volage x x1-6 Cumulaive ime cumulaive ime (s) 1.x1-6 2.x Pulse volage mV (A) Bu sill a large dispersion!! mV (A) Volage (V) x1-6 4.x1-6 6.x1-6 8.x1-6 1.x1-5 Cumulaive ime (s) Volage (V) x1-7 1.x x1-6 2.x1-6 Cumulaive ime (s)
10 V Tune Rese Read Swiching V Tune Read Se.6.8 Pulse volage uA 3uA 1uA 1.x x1-6 Cumulaive ime 2mV Resriced analysis (2 parameers): -Volage -Iniial sae 2mV uA 3uA 1uA cumulaive ime (s) 1.x1-6 2.x Pulse volage S = une wrie read Conducance, G INITIAL (ms) Pulse volage (V) Parial conclusion: engineering is no enough o deal wih dispersion G AFTER /G INITIAL Read only available Self- limied swiching for boh SET and RESET ransiions
11 Resisance ( Curren (ma) G I(.2V)/.2 V S = S A V Algorihm Objecive: une he device o a desired sae by pulses of volage The perfec picure: Swiching dynamic Saisics Volage (V) -V swich +V swich Device modeling 1 Which pulse for a given sae? Tuning of he device/evaluaion Feedback conrol A more simple picure: sweep V or 1 V P =-1V V P =-1.1V V P =-1.2V V P =-1.3V Number of pulses (N+1) DILEMA Using Volage as he parameer: poenially fas bu low precision Using as he parameer: good accuracy bu may required infinie ime In addiion, we need o deal wih dispersion!
12 -2mV (A) Resisance sae Algorihm arge ime 1E-4 6 A 3 A 15 A 1E-5 Decrease Weigh Increase Weigh Sand-by (Read only) Time (s)
13 (A) -2mV ( A) Algorihm 1E-4 1E-5 volage Decrease se Weigh ime Increase Weigh Sand-by read (Read only) rese Pulse Number 12 A 6 A 3 A 7 A Pulse Number 15 A 1% accuracy equivalen o 8-bi Inermediae sae are non-volaile Can be improved wih beer modeling (more elaboraed feedback) Accuracy is limied by noise (evidence of RTS)
14 Inpu1 (V) Inpu2(V) Programming Programming Programming Programming Programming Oupu (V) Circui: MAC operaion 2 1 Inpu1 Inpu2 2K Oupu CMOS opamp R 2 =3333ohm R 2 =6666ohm R 2 =13333ohm R 2 =13333ohm R 2 =13333ohm R 1 =3333ohm R 1 =3333ohm R 1 =3333ohm R 1 =6666ohm R 1 =13333ohm 5 1 Time (s)
15 Circui: Hopfield Nework Basically an associaive memory: Energy funcion Suiable also for opimizaion problem, speech recogniion An example: Analog (inpu) o digial (oupu) conversion
16 Vinpu Circui: Hopfield Nework TiO2 memrisive devices
17 Paern classificaion v 1 v 2 v 3 v 4 Principle of a percepron: R 1 R 2 ou R 3 R 4. Vi/Ri ou The percepron ask is o realize classificaion: Considering a se of daa {(V 1,,V n )}, if his ensemble of daa is composed of wo separable group A and B, i is possible o define a se of (R 1,,R n ) ha verifies: V i /R i > hreshold if (V 1 V n ) is A (i.e. ou=1) V i /R i < hreshold if (V 1 V n ) is B (i.e. ou=) {V ib } Se of daas v n R n {V ia } The se of weigh is deermined by opimizaion procedure on real daas, or raining daas (No analyical soluion). This sage of programming is called learning (he sysem is rained o reac properly by adjusing he weighs). The performances are hen evaluaed on a esing se of daas (operaion of he sysem)
18 Seminal work Paern classificaion memisor
19 Paern classificaion bias x x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 pre-synapic neurons (inpus) Inpu se of paerns X Desired oupu: d = +1 Inpu se of paerns T Desired oupu: d = -1 w + w - I + I - y Learning rule: possynapic neuron (oupu) w + w 1 + w 2 + w 3 + w 4 + w 5 + w 6 + w 7 + w 8 + w 9 + w - w - w - 2 w - 3 w - 4 w - 5 w - 6 w - 7 w - 8 w x x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 y + y - = memrisors
20 Paern classificaion: seup V Arbirary waveform generaor B153 Swiching marix (Agilen E525A) A Curren measuremen B153 (fas IV mode) Ground (GNDU, Agilen) Agilen B15 Wires implemening crossbar circui Chip packaged wire bonded memrisive devices
21 2mV Paern classificaion: Ex siu We wan u use our high precision algorihm o une he sae of each device sequencially The final weighs are calculaed on a sofware based precursor nework. Challenge: we need o impor he weigh ino he Xbar array (XTALK) High precision algorihm Soluion: half bias rick. S1 Wrie D1 D2 1E-4 9uA 6uA Sligh Xalk V D3 V D4 S2 read 1E-5 device1 device2 device3 device number of pulses # 3uA 15uA 5-bi accuracy sill available Vread V D1 D3 V D2 D4 V
22 2mV (A) Number of Paern # 2mV (A) Paern classificaion: Ex siu A B 1 Iniial X T 1-4 accuracy ~1% weigh afer raining w + uning w - 1 Accuracy ~ 4% 1-5 weigh affeced by half-selec problem Accuracy ~ 1% C Pulse number # 1 Accuracy ~ 2% 1-4 accuracy ~2% weigh afer raining w + uning w I + - I - (A) Pulse number # 3-bi accuracy is enough for his classificaion ask Can be improve by dela rule insead of percepron rule
23 Paern classificaion: In siu +Vswich v -Vswich pre-synapic volage v x =-1 x =+1 v 4-sep pulse sequence Training in parallel of all he devices pos-synapic volage v d =+1 d = A Inpu se of paerns T Desired oupu: d = -1 Inpu se of paerns X Desired oupu: d = +1 y+ m B x +Vswich -Vswich x1 x2 x3 x4 x5 x6 x7 x8 v x9 v v x y- x1 x4 x7 x2 x5 x8 x3 x6 x9 pre-synapic neurons D (inpus) +Vs -Vs w- w+ v bias I+ volage across memrisors I- y Learning rule: = possynapic neuron (oupu) +Vs -Vs
24 Number of paern # ( 2mV) Paern classificaion: In siu A B V raining =.9V V raining = 1V 1 Iniial X T epochs V raining =.9V epochs V raining =1V I + - I - (A) Training evens # Figure 4
25 Number of Paern # = 2mV Paern classificaion: In siu A V TRAINING B 1 INITIAL.9V 1V 1.1V 8 class inversion 1 T -1 X T -1 X +1 X -1 T V TRAINING 2.9V 1 X -1 T V 1.1V 1 X -1 T Training evens I + - I - (A) RECONFIGURABLE Figure S4
26 conclusion Physics of he memrisive devices o be coninued (modeling will improve algorihms) Memrisive Xbar is promising for larger scale NNET circui implemenaion (forming free devices is required) Heerogeneous CMOS/Xbar is he nex echnological challenge (implemenaion of CMOL concep)
27 Acknowledgmens Open posiion: 1 Posdoc a UCSB 1 Posdoc a IEMN Supervisor: Dmiri Srukov ADC work: Ligang Gao, Farnood Merrikh-Baya, Xinjie Guo Paern classificaion: Elham Zamanidoos Maerial science: Brian Hoskins
Dmitri Strukov. UC Santa Barbara
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