In-memory Accelerators with Memristors Yuval Cassuto Koby Crammer Avinoam Kolodny Technion – EE...

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

cij

cij=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 Products

110011000101

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. 1

110011000101

000011011011

R=∞

GT=3/2R

R

2R 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!