in-memory accelerators with memristors
DESCRIPTION
NVM. MEM. PU. In-memory Accelerators with Memristors. Yuval Cassuto Koby Crammer Avinoam Kolodny Technion – EE ICRI-CI Retreat May 8, 2013. 3-way Collaboration. K. Crammer. ML App. Y. Cassuto. Representations. A. Kolodny. Devices. The Data Deluge. Computing. Mobile, - PowerPoint PPT PresentationTRANSCRIPT
In-memory Accelerators with Memristors
Yuval CassutoKoby Crammer
Avinoam KolodnyTechnion – EEICRI-CI Retreat
May 8, 2013
PUMEMNVM
3-way Collaboration
A. Kolodny
Y. Cassuto
K. CrammerML App.
Devices
Representations
The Data Deluge
Mobile, Cloud
Computing
Non-Volatile Memories 101
functionality
density
PROM EPROM E2PROM
Memristors
Mass StorageNANDFlash
+ logic!
Non-Volatile Memories 101
functionality
density
PROM EPROM E2PROM
NANDFlash Main Memory
Memristors + logic!
Memristor Crossbar Arrays
Vg
RL
Vo
cijcij=0 high resistance low current sensedcij=1 low resistance high current sensed
Memristor Readout
Vg
RL
Vo
0 1
1
1
Desired PathSneak Path
1
1
cij=0 high resistance low current sensedcij=1 low resistance high current sensed
Sneak Paths
Two Solutions
1 1 1
1 1 1
0 00
0 00
1
1
0 0 0 0 0
0 0 0 0 001 0 0 0 0
00 0 0 0 0
Poor capacityHigh read power
Our Mixed Solution
YC, E. Yaakobi, S. Kvatinsky, ISIT 2013
b
Results Summary
YC, E. Yaakobi, S. Kvatinsky, ISIT 2013
1) Fixed partition 2) Sliding window
• Higher capacity • e.g. 0.465 vs. 0.423 for
b=7 • Column-by-column encoding,
optimal
In-memory Acceleration
• Motivation: transfer bottlenecks• Method: compute in memory,
transfer results• What to compute?
Similarity Inner Products11001100010
1
000011011011
010111010101
Hyp. 1 Hyp. 2
Trial
110011000101
000011000001
∑ =3
110011000101
010011000101
∑ =5
More similarLess similar
Inner Products in ML
• K-Nearest Neighbors– Distance (Euclidean or Hamming)
• Kernel Methods– Low-dim nonlinear → high-dim linear– -2 high dimension image for K
• Graph based ML
Memristor Inner Products (ideal)
Trial
Hyp. 111001100010
100001101101
1
R=∞GT=3/2R
R2R 2R 2R
Output = 3· Const Inner product
Ideal Inner Products
𝒙
𝒚
Hamming distance in 3 measurements:
1 2 3
Real Inner Products
𝒙
𝒚
Error terms
Evaluation• Can compute Hamming distance as if
ideal– 3 measurements– plus arithmetic
• Cannot compute inner product precisely in 1 measurement
Continued Research
Transform input vectors to maximize precision
• ML Theory: provable optimality (information-theoretic learning)
• ML Practice: optimize transformations within real ML algorithms
Multi-level Inner Products
R=∞
R1
R1+R2
R2
R3
R3+R12R3
+ +
Thank You!