The brain, which uses redundancy and continuous learning to overcome the unreliability of its components, provides a promising path to building computing systems that are robust to the unreliability of their constituent nanodevices. In this work, we illustrate this path by a computing system based on population coding with magnetic tunnel junctions that implement both neurons and synaptic weights. We show that equipping such a system with continuous learning enables it to recover from the loss of neurons and makes it possible to use unreliable synaptic weights (i.e., low energy barrier magnetic memories). There is a trade-off between power consumption and precision because low energy barrier memories consume less energy than high barrier ones. For a given precision, there is an optimal number of neurons and an optimal energy barrier for the weights that leads to minimum power consumption.

1.
J. R.
Heath
,
P. J.
Kuekes
,
G. S.
Snider
, and
R. S.
Williams
,
Science
280
,
1716
(
1998
).
2.
A. A.
Faisal
,
L. P. J.
Selen
, and
D. M.
Wolpert
,
Nat. Rev. Neurosci.
9
,
292
(
2008
).
3.
R. A.
Mason
,
C. S.
Prat
, and
M. A.
Just
,
Cereb. Cortex
24
,
1474
(
2014
).
4.
A. P.
Georgopoulos
,
R. E.
Kettner
, and
A. B.
Schwartz
,
J. Neurosci.
8
,
2928
(
1988
).
5.
A.
Pouget
,
P.
Dayan
, and
R.
Zemel
,
Nat. Rev. Neurosci.
1
,
125
(
2000
).
6.
A.
Pouget
,
J. M.
Beck
,
W. J.
Ma
, and
P. E.
Latham
,
Nat. Neurosci.
16
,
1170
(
2013
).
7.
M. M.
Merzenich
,
W. M.
Jenkins
, and
S.
Levy-Reiner
, in The Adaptable Brain, edited by S. Levy-Reiner (Library of Congress, Washington, DC, 1999), Vol. II.
8.
A.
Pascual-Leone
,
A.
Amedi
,
F.
Fregni
, and
L. B.
Merabet
,
Annu. Rev. Neurosci.
28
,
377
(
2005
).
9.
S. B.
Hofer
,
T. D.
Mrsic-Flogel
,
T.
Bonhoeffer
, and
M.
Hübener
,
Curr. Opin. Neurobiol. Sens. Syst.
16
,
451
(
2006
).
10.
Y.
LeCun
,
Y.
Bengio
, and
G.
Hinton
,
Nature
521
,
436
(
2015
).
11.
A.
Alaghi
and
J. P.
Hayes
,
ACM Trans. Embedded Comput. Syst.
12
,
1
(
2013
).
12.
W. J.
Poppelbaum
,
C.
Afuso
, and
J. W.
Esch
, “Stochastic computing elements and systems,” Proceedings of the Fall Joint Computer Conference, Anaheim, CA, November 14–16, 1967 (ACM Press, 1967), pp. 635–644.
13.
B. R.
Gaines
, in Proceedings of the April 18-20, 1967, Spring Joint Computer Conference, AFIPS ’67 (Spring) (ACM, New York, NY, 1967), pp. 149–156.
14.
A.
Mizrahi
,
T.
Hirtzlin
,
A.
Fukushima
,
H.
Kubota
,
S.
Yuasa
,
J.
Grollier
, and
D.
Querlioz
,
Nat. Commun.
9
,
1533
(
2018
).
15.
E.
Salinas
and
L. F.
Abbott
,
J. Neurosci.
15
,
6461
(
1995
).
16.
S.
Yuasa
,
T.
Nagahama
,
A.
Fukushima
,
Y.
Suzuki
, and
K.
Ando
,
Nat. Mater.
3
,
868
(
2004
).
17.
S. S. P.
Parkin
,
C.
Kaiser
,
A.
Panchula
,
P. M.
Rice
,
B.
Hughes
,
M.
Samant
, and
S.-H.
Yang
,
Nat. Mater.
3
,
862
(
2004
).
18.
W.
Rippard
,
R.
Heindl
,
M.
Pufall
,
S.
Russek
, and
A.
Kos
,
Phys. Rev. B
84
,
064439
(
2011
).
19.
A.
Mizrahi
,
N.
Locatelli
,
R.
Matsumoto
,
A.
Fukushima
,
H.
Kubota
,
S.
Yuasa
,
V.
Cros
,
J.-V.
Kim
,
J.
Grollier
, and
D.
Querlioz
,
IEEE Trans. Magn.
51
,
1
(
2015
).
20.
D.
Apalkov
,
B.
Dieny
, and
J. M.
Slaughter
,
Proc. IEEE
104
,
1796
(
2016
).
21.
D.
Vodenicarevic
,
N.
Locatelli
,
A.
Mizrahi
,
J.
Friedman
,
A.
Vincent
,
M.
Romera
,
A.
Fukushima
,
K.
Yakushiji
,
H.
Kubota
,
S.
Yuasa
,
S.
Tiwari
,
J.
Grollier
, and
D.
Querlioz
,
Phys. Rev. Appl.
8
,
054045
(
2017
).
22.
J. C.
Slonczewski
,
Phys. Rev. B
71
,
024411
(
2005
).
23.
D.
Ralph
and
M.
Stiles
,
J. Magn. Magn. Mater.
320
,
1190
(
2008
).
24.
A.
Mizrahi
,
N.
Locatelli
,
R.
Lebrun
,
V.
Cros
,
A.
Fukushima
,
H.
Kubota
,
S.
Yuasa
,
D.
Querlioz
, and
J.
Grollier
,
Sci. Rep.
6
,
30535
(
2016
).
25.
B.
Sutton
,
K. Y.
Camsari
,
B.
Behin-Aein
, and
S.
Datta
,
Sci. Rep.
7
,
44370
(
2017
).
26.
C. M.
Liyanagedera
,
A.
Sengupta
,
A.
Jaiswal
, and
K.
Roy
,
Phys. Rev. Appl.
8
,
064017
(
2017
).
27.
K. Y.
Camsari
,
R.
Faria
,
B. M.
Sutton
, and
S.
Datta
,
Phys. Rev. X
7
,
031014
(
2017
).
28.
A.
Fukushima
,
T.
Seki
,
K.
Yakushiji
,
H.
Kubota
,
H.
Imamura
,
S.
Yuasa
, and
K.
Ando
,
Appl. Phys. Express
7
,
083001
(
2014
).
29.
W. H.
Choi
,
Y.
Lv
,
J.
Kim
,
A.
Deshpande
,
G.
Kang
,
J.-P.
Wang
, and
C. H.
Kim
, in 2014 IEEE International Electron Devices Meeting (IEEE, 2014), pp. 12.5.1–12.5.4.
30.
B.
Parks
,
M.
Bapna
,
J.
Igbokwe
,
H.
Almasi
,
W.
Wang
, and
S. A.
Majetich
,
AIP Adv.
8
,
055903
(
2017
).
31.
H.
Lee
,
F.
Ebrahimi
,
P. K.
Amiri
, and
K. L.
Wang
,
AIP Adv.
7
,
055934
(
2017
).
32.
N.
Rangarajan
,
A.
Parthasarathy
, and
S.
Rakheja
,
J. Appl. Phys.
121
,
223905
(
2017
).
33.
G.
Srinivasan
,
A.
Sengupta
, and
K.
Roy
,
Sci. Rep.
6
,
29545
(
2016
).
34.
A.
Sengupta
,
P.
Panda
,
P.
Wijesinghe
,
Y.
Kim
, and
K.
Roy
,
Sci. Rep.
6
,
30039
(
2016
).
35.
D.
Zhang
,
L.
Zeng
,
F.
Gong
,
T.
Gao
,
S.
Gao
,
Y.
Zhang
, and
W.
Zhao
, in 2015 15th Non-Volatile Memory Technology Symposium (NVMTS) (IEEE, 2015), pp. 1–4.
36.
37.
H.
Sato
,
E. C. I.
Enobio
,
M.
Yamanouchi
,
S.
Ikeda
,
S.
Fukami
,
S.
Kanai
,
F.
Matsukura
, and
H.
Ohno
,
Appl. Phys. Lett.
105
,
062403
(
2014
).
38.
K.
Palem
and
A.
Lingamneni
,
ACM Trans. Embedded Comput. Syst.
12
,
1
(
2013
).
39.
J.
Han
and
M.
Orshansky
, in 2013 18th IEEE European Test Symposium (ETS) (IEEE, 2013), pp. 1–6.
40.
P.
Korkmaz
,
B. E. S.
Akgul
, and
K. V.
Palem
,
IEEE Trans. Circuits Syst. I: Reg. Pap.
55
,
2249
(
2008
).
41.
S.
Ambrogio
,
P.
Narayanan
,
H.
Tsai
,
R. M.
Shelby
,
I.
Boybat
,
C. d.
Nolfo
,
S.
Sidler
,
M.
Giordano
,
M.
Bodini
,
N. C. P.
Farinha
,
B.
Killeen
,
C.
Cheng
,
Y.
Jaoudi
, and
G. W.
Burr
,
Nature
558
,
60
(
2018
).
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