Unconventional computing with stochastic magnetic
tunnel junctionsAlice Mizrahi, Tifenn Hirtzlin, Matthew Daniels, Nicolas Locatelli, Akio Fukushima, Hitoshi Kubota, Shinji Yuasa,
Mark Stiles, Julie Grollier, Damien Querlioz
Lowering the energy consumption reduces the stability
2
Reference magnet
Tunnel barrier
Free magnet
thermal noise
ΔE P AP
Low Resistance High Resistance
Low ΔE
Small size
Low write energy
Unstable
Different energy barriers for different applications
3
Energy barrier
60 kBT
15 kBT
years
ms
μs
Memory for storage (MRAM)
Synaptic weight for continuously learning neural net
Stochastic regime6 kBT
Stochastic spiking neuron
Stochastic oscillator
Stochastic bitstream generator
A stochastic oscillator powered by thermal noise
4
AP
P
“1”
“0”
No external energy source
Two-state signal easy to convert to digital signal
Stochasticity well understood and controlled
5
Spin torque controls the stochasticity
Stochastic analog to digital conversion
dc current
Vo
ltag
e
-50 0 500
500
1000
Ra
te (
Hz)
Current (A)
APP
kBTI > 0
Stabilizes the antiparallel state
Stabilizes the parallel state
kBTI < 0
P AP 0.100 0.125 0.150
400
500
600
Resis
tan
ce (
)
Time (s)
0.100 0.125 0.150
400
500
600
700
Re
sis
tan
ce
(
)
Time (s)
0.100 0.125 0.150
400
500
600
Re
sis
tan
ce
(
)
Time (s)
6
1. Population coding with stochastic spiking neurons
2. Noise-induced synchronization of a stochastic oscillator
Encoding information in the spike rate of a stochastic neuron
7
Time
Vo
ltag
e
Rate coding✓ Robust to errors✓ Fast approximate results Rate varies with value of stimulus
Kumano et al., J. Neurophysiology 2010
Tuning curve
Direction 𝜃
Neuron
8
The stochastic magnetic tunnel junction emulates a stochastic spiking neuron
Switches ↔ spikesStimulus = current
-50 0 500
500
1000
Rate
(H
z)
Current (A)
Time
Vo
ltag
e
0.100 0.125 0.150
400
500
600
700
Resis
tan
ce (
)
Time (s)
θ
9
rates 𝑟𝑖
Neurons
Firi
ng
rate
Firi
ng
rate
Preferred direction
Preferred direction
𝑟 𝑖𝑟 𝑖
θ
θ
Each neuron processes a range of inputs (directions)
The direction can be inferred from the rates of the neurons
Robust coding of information by a population of neurons
10
𝐻 𝐼 =
𝑖=1
9
𝑤𝑖𝑟𝑖(𝐼eff𝑖)
𝐼eff𝑖 = 𝐼 − 𝐼bias
𝑖Shift the tuning curves
-400 -200 0 200 400
0.0
0.2
0.4
0.6
0.8
1.0
No
rma
lize
d R
ate
Current (µA)
-300 0 300
0.0
0.5
1.0
-300 0 300 -300 0 300
H(I
) (a
.u.)
Current (µA) Current (µA) Current (µA)
𝑟1𝑟2 𝑟3 𝑟4 𝑟5 𝑟6 𝑟7 𝑟8 𝑟9
Mizrahi et al., Nature Communications, 2018
Constructing non-linear transformation with a population of artificial neurons
11
𝑟𝑗OUT =
𝑖=1
𝑁
𝑤𝑖𝑗𝑟𝑖IN
Weights
Input
Output
𝑟1IN 𝑟𝑁IN
INInput rates
𝑟1OUT 𝑟𝑁OUT
OUTOutput rates
Input value I
Transformation F
Output value O = F(I)
Stochastic junctions as neurons (NIN)
Stochastic junctions as neurons (NOUT)
Stable junctions as binary encoded synaptic weights
(NIN x NOUT)
“Transfer of coded information from sensory to motor networks”
Salinas et Abbott, J. Neuroscience, 1995
An artificial neural net with magnetic tunnel junctions
12
Learning rule:Catch → do nothing
Miss → modify the weights
Simulations with experimentally verified modelΔEneuron = 6 kBT
The system is capable of learning a transformation
𝑟1IN 𝑟𝑁IN
INInput rates
𝑟1OUT 𝑟𝑁OUT
OUTOutput rates
Direction ϴ
0 00
13
CMOS overhead: • Switch detection & count• Calculation (rate and weights)• Learning rule
Neurons
Synaptic Weights
Area and energy consumption of our system (Work of T. Hirtzlin at C2N)
Operation7.8 nJ
12,000 μm2
CMOS-only neurons:Area > 20,000 μm2
Energy of operation > 20 nJ
Key asset = stochastic analog to digital conversion
The system consumes less energy and area than CMOS-only implementations
2 3 4 5 6 7 8 9 10 11 12
0.001
0.01
0.1
1
Error (%)
No
rma
lize
d p
ow
er
co
nsu
mp
tio
n
46 neurons
Increase energy barrier ΔEw
14
Using unreliable synapses lowers the power consumption
𝐼 ∝ ∆𝐸𝑤
𝑃𝑜𝑤𝑒𝑟 ∝ ∆𝐸𝑤2
Write power
Write current
(Sato et al., APL 2014)
2 3 4 5 6 7 8 9 10 11 12
0.001
0.01
0.1
1
10 neurons
20 neurons
100 neurons
Error (%)
No
rma
lize
d p
ow
er
co
nsu
mp
tio
n
46 neurons
15
Using unreliable synapses lowers the power consumption
𝐼 ∝ ∆𝐸𝑤
𝑃𝑜𝑤𝑒𝑟 ∝ ∆𝐸𝑤2
Write power
Write current
(Sato et al., APL 2014)
0.001
0.01
0.1
1
10
100
2 3 4 5 6 7 8 9 101112
10
12
14
16
18
20
100
46
20
10 neurons
OptimumNo
rma
lize
d p
ow
er
co
nsu
mp
tio
nN
um
be
r
of
ne
uro
ns
En
erg
y b
arr
ier
(k
BT
)
Error (%)
16
Using unreliable synapses lowers the power consumption
𝐼 ∝ ∆𝐸𝑤
𝑃𝑜𝑤𝑒𝑟 ∝ ∆𝐸𝑤2
Write power
Write current
(Sato et al., APL 2014)
0.001
0.01
0.1
1
10
100
2 3 4 5 6 7 8 9 101112
10
12
14
16
18
20
100
46
20
10 neurons
OptimumNo
rma
lize
d p
ow
er
co
nsu
mp
tio
nN
um
be
r
of
ne
uro
ns
En
erg
y b
arr
ier
(k
BT
)
Error (%)
17
Using unreliable synapses lowers the power consumption
Example:For 3% precision→ 54 neurons in each population (2916 weights)→ ΔEw = 12 kBT
𝐼 ∝ ∆𝐸𝑤
𝑃𝑜𝑤𝑒𝑟 ∝ ∆𝐸𝑤2
Write power
Write current
(Sato et al., APL 2014)
A low energy continuously learning neural net with magnetic tunnel junctions
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Mizrahi et al., Nature Communications, 2018 Mizrahi et al., J. Applied Physics, 2018
Fully stochastic magnetic tunnel junction as neuron
Slightly stochastic magnetic tunnel junction as synapse
Continuous learning
+ +
Artificial neural networkLow energy
Capable of learningResilient to variability & unreliability
Adaptable to changes
=
0.100 0.125 0.150
400
500
600
Re
sis
tan
ce
(
)
Time (s)
Key application: smart sensors
19
1. Population coding with stochastic spiking neurons
2. Noise-induced synchronization of a stochastic oscillator
Noise can induce low-power synchronization
20
Deterministic Vac > Vc
Vc
-Vc
Vac
R
R
Vc
-Vc
VacVc
-Vc
Vc
-Vc
Vc
-Vc
Vac
R
Subthreshold Vac < Vc
Optimal noise range
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
80
0 50 100 1500 50 100 150 0 50 100 150 200
1
-Vac
RP
Fre
que
ncy (
Hz)
Electrical noise (mV)
1
Fac
2
3
2 3RAP
+Vac
Re
sis
tance
sta
te
Time (ms)Time (ms)
Time (ms)
D
rive
vo
ltage
Noise controls frequency and phase locking
21
Vac = 63 mV while Vc = 235 mV @0K
ΔE = 22.5 kBTNatural frequency ≈ 0.1 Hz
Thermal noise (room temperature)
+Electrical noise (white
Gaussian)
Mizrahi et al., Scientific Reports, 2016
Sync
22
Fac = 50 Hz Vac = 82 mV
Natural frequency ≈ 0.1Hz
0 20 40 60 80 100
0
10
20
30
40
50
101
102
103
104
0
10
20
30
40
50
60
Ele
ctr
ical nois
e (
mV
)
Drive voltage (mV)
Ele
ctr
ical nois
e (
mV
)Drive frequency (Hz)
Model Experiments
SyncSync
Boundaries of synchronization
Synchronization is possible at broad ranges of amplitudes and frequencies
Low-energy synchronization for computing
23
Need to reinvent computing schemes for several coupled stochastic oscillators!
Mizrahi et al., Scientific Reports, 2016 ; Mizrahi et al., IEEE Transactions on Magnetism, 2015
How to use it for associative memory,
pattern classification etc.?
The stochastic magnetic tunnel junction is a promising building block
for low-power computing
24
Powered by thermal noiseDriven by small signalsAnalog to digital conversionStochasticity understood and controlled
EnduranceReliabilityCMOS compatibilityNew handles (spin-orbit etc.)
Stochastic spiking neuron
Stochastic oscillator for
synchronization
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