In-memory computing with emerging memory devices - Daniele Ielmini Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano ...
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In-memory computing with emerging memory devices Daniele Ielmini Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano daniele.ielmini@polimi.it
From von Neumann to in-memory computing
2
In-memory computing
Von Neumann architecture • Resistive memory
• Volatile memory (DRAM) • Compute in situ
• Data movement • High parallelism
• Memory bottleneck
M A Zidan, et al. Nat. Electron. (2018)
Daniele Ielmini
Three types of in-memory computing
3
In-memory computing
Artificial Brain-inspired
neural Algebra
neural
networks accelerators networks
- Deep neural networks - Linear system solver - Unsupervised learning
- Convolutional neural networks - Matrix inversion - Reinforcement learning
- LSTM - Regression - Associative memories
- Supervised training - Eigenvector calculation - Spatiotemporal networks
- Backpropagation - Differential equations - Reservoir computing
Adapted from D. Ielmini and S. Ambrogio, Nanotechnology 31, 092001 (2019)
Daniele Ielmini
Memory devices for in-memory computing
4
PCM Flash Analog DRAM FEFET
RRAM SW
G G
VL
Top Electrode (TE) TE S S
D D
Dielectric layer Active chalcogenide S
D
Conductive filament volume
Bottom Electrode (BE) BE
ID ID ID
STT-MRAM FERAM SOT-MRAM ECRAM Memtransistor
TE G
ID S
D
Free layer TE S
S
D D
Tunnel layer Ferroelectric layer
Pinned layer G
BE
Ipol ID
D. Ielmini and G. Pedretti, Adv. Intell. Syst. 1, 2000040 (2020)
Daniele Ielmini
Analogue resistive memory
5
IC
set
Current [µA]
Ti G
HfO2
reset Carbon
Voltage [V]
• Analogue conductance controlled by a compliance current IC
• Good linearity below 0.5 V
Z. Sun, et al., PNAS 116, 4123 (2019)
Daniele Ielmini
Matrix-vector multiplication
6
• Multiplying a matrix A and a vector x
in a CPU requires individual
products aij*xj, and summation à
multiply/accumulate (MAC) process
• In a crossbar, the operation is
carried out physically by Kirchhoff’s
and Ohm’s law, in just one step
!" = $ &%" '%
%
D. Ielmini and H.-S. P. Wong, Nature Electronics 1, 333 (2018) Kirchhoff’s law Ohm’s law
Daniele Ielmini
1 – Forward propagation
7
In-memory MVM
S. Agarwal, et al., IJCNN 929 (2016)
Daniele Ielmini
2 – Error evaluation
8
Error
Supervised training =
pattern is submitted with
the corresponding label
à we know the correct
answer
Daniele Ielmini
3 – Weight update
9
In-memory outer-product
Error
Δ"#$ = &'# ($
S. Agarwal, et al., IJCNN 929 (2016)
Daniele Ielmini
Device non-linearity
10
G
• In general, physical devices are not linear in time and voltage D
S
• Record linearity for Li-based ECRAM (IBM, IEDM 2018)
ID
Daniele IelminiIn-memory convolutional neural networks (CNNs)
11
P. Yao, et al., 3D RRAM array
Nature 577, P. Lin, et al., Nat Electron 3, 225 (2020)
641 (2020)
Daniele IelminiInverting MVM
12
G
-
+
V + I = G·V
- -
+
-
+
Georg Ohm
G I1 V3
I2 V2
I - V= -G-1·I
+ I3 V1
Harold Black V = -A-1·I
Matrix-vector division is equivalent to solving Ax = b, with x = A-1b
Z. Sun, et al., PNAS 116, 4123 (2019)
Daniele IelminiO(1) complexity of inverse MVM
13
b c Digital
CG O(polyN)
QC
IMC Quantum
O(logN)
In-memory
O(1)
N
Z. Sun, et al., IEEE Trans. Electron
Devices 67, 2945 (2020)
Daniele IelminiIn-memory PageRank
14
2 Page No. Company
3
1 Amazon
6 2 Baidu
3 Facebook
7 4
4 Google
5 LinkedIn
1 8 6 PayPal
7 Quora
8 Twitter
5
9 9 YouTube
Z. Sun, et al., PNAS 116, 4123 (2019) Throughput [TOPS] Energy efficiency [TOPS/W]
In-memory 0.183 362
TPU 92 2.3
150X
Daniele IelminiSolving a Schrödinger equation
15
V (eV)
0
-1
-2 !Ψ = $Ψ,
-3 ℏ' * '
!=− +-
-4 2) * ' +
x (nm)
-2 -1 0 1 2
matrix A matrix B matrix C
Z. Sun, et al., PNAS 116, 4123 (2019)
Daniele IelminiVolatile RRAM
16
5 Ag 50
4 C 40
W
3 30
I [ A]
V [V]
!"
2 tret 20
1 10
0 0
-2 0 2 4 6 8
-4 W. Wang, et al., Nat. Commun., 10, 81 (2019) Z. Wang et al.,
Time [s] 10
Nat. Mater. 16 101 (2017)
• Volatile behavior due to Ag diffusion and filament disconnection in the µs-ms timescale
Daniele IelminiAnalogy with biological synapses
17
L-Glutamate (neurotransmitter)
Neurotransmitter
Receptor Individual ionic channels
Ca2+ EPSC
160 pA
100 ms
Na+/Ca2+ 4 pA 17
100 ms
EPSC
Ca2+
R. A. J. Lester and C. E. Jahr, J. Neurosci., 12, 635 (1992)
Electrical stimulus
Ag Ag
HfOx e- Individual RRAM device
C
SiO2 Ag e- tret 1 A
N = 5
W 100 ms N = 10
e- HfOx
N = 20
!" 2 A N devices N = 50
C 100 ms
W. Wang, et al., Adv. Intell. Syst. 2000224 (2020)
Daniele IelminiDirection selectivity in the human retina
18
Photoreceptor
A B
18
…
…
N
Bipolar cell IA IEPSC=IA-IB
SAC -
Excitation
…
Inhibition
…
N
IB
DS ganglion cell
°
A-B 120
° 90
60
°
100 %
97 %
150° 30 °
EPSC Peak [µA]
A-B B-A ° °
2 A 2 A 180 0
0 1 2 3 4
2.5 µA 100 ms 2.5 µA 100 ms
1 2 3 4
-150 ° -30 °
!
EPSC Peak [ A] -120
°
-60
°
°
-90
W. Wang, et al., Adv. Intell. Syst. 2000224 (2020)
Daniele IelminiConclusions
19
• In-memory computing by crosspoint operations:
• MVM (dot product) à DNN inference
• Outer product à DNN training
• MVM + feedback (inverse MVM) à linear algebra
• Device physics for brain-inspired neuromorphic computing (short-
term RRAM)
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