Logarithmic Mult ltiplication for Convolutional Neural Networks - - PowerPoint PPT Presentation

A Cost-Efficient It Iterative Truncated Logarithmic Mult ltiplication for Convolutional Neural Networks

HyunJin in Kim im, , Min in Soo Kim im, , Alb Alberto A.

• A. Del

l Bar arrio, Nad ader Bag agherzadeh

Motivations

• Well

ll appli lied to inference of simple le neura ral l networks.

• But

t high igh comple lex convolu lutional l neural l netw tworks (C (CNNs) re require re high igh accura rate computation.

Approxim imate mult ultiplic icatio ion

• Ite

Itera rative stru tructure can enhance th the accura racy.

• Repeating basic

ic blocks add sign ignificant cost.

• Let

t us re reduce cost of f basic ic blocks wit ithout degra rading perfo rformance of f CNNs!!

Hig High accurate co computatio ion with low co cost

Summary of Proposed Design

• 3-
• Tru

Truncated ed Mit Mitche hell l mult ltip iplie ier wit with h n1-bit fra fractions

Fi First sta stage

• Trun

Truncated ed Mit Mitche hell l mult ltip iplie ier wit with h n2-bit fra fractions

Sec Second sta stage

• Tra

Transfer error error from from 1st

st sta

stage e to

• 2nd

nd stag

stage

Err Error te term ca calc lcula lation

• Su

Sum of

• f ou
• utputs of
• f 1st

st

and nd 2nd

nd sta

stages

Fi Final l

• u
• utput

Basics of Mitchell Algorithm (Multiplication)

• 4 -

Error Error dep depends ends o

• n s

n sum of um of fr frac actio tions. ns.

* * rerr err: : rel relati tive e erro error Ho How to w to app appro roxi xima mate te it? it?

Str tructure of Proposed Design

• 5-

1st

st Stag

tage Mitc itchell Mult ltip iplie ier 2nd

nd Sta

tage Mitc itchell Mult ltip iplier

Co Compensated er error in n tr truncatio ion Co Compensated er error in n tr truncatio ion

Ou Output put of

• f Erro

Error r Ter erm m Calcula Calculator

• r is

is tran ansfe sferr rred ed to n

• next

xt s stage e

* LOD: Leading One Detect

Err rror Term Calculator

• 6 -

1’s com complement plement

Summary of Err rror Analysis

• 7 -

11 11.1% .1% rerr errmax

max from

from error term using 1’s com complement.

• plement. (e.g

(e.g. A= . A=11 112, , B= B=11 112→A(2)=0, (2)=0, B(2)=0 B(2)=0 )

Comparison of Err rror and Cost

• 8 -

Bett tter re rerr rravg compared to to oth ther appro roximate mult ltipli liers rs Gre reat cost re reduction

• ver

r Booth mult ltipli lier when n=16 and n=32

Comparison of Accuracy on CNNs

• 9 -

When n1=6 and n2=2, th there re is is no sign ignificant accura racy dro rop in in CNN models ls, whic ich

• utperforms orig

riginal l Mit itchell ll mult ltipli lier. For r n1=8, to top-5 accura racy

• f

f ResNet-50 re reaches up to to 90.9%.

Conclusion

• 10

10 -

We e propose proposes the s the it iter erati tive e trunca truncate ted d lo logarithmic arithmic multi multipli plica cation, tion, and erro and error r & cost & cost and applica and applicati tion

• n of
• f CN

CNNs Ns are a are analyz nalyzed. ed.

• Can in

incre rease perf rform rmance wit ith small l cost in in applications of f appro roximate multipli lier r

Pr Proposed ite terativ ive tr truncated logarithmic ic mult ltiplication

• Th

The tru truncation and erro rror r te term rm calculation of f our r design do not t in incur substantial l im impact on in infe ference accuracy on CNN models ls

Ap Applic ication

• f
• f CNNs

A Cost-Efficient It Iterative Truncated Logarithmic Mult ltiplication for Convolutional Neural Networks

HyunJin in Kim im, , Min in Soo Kim im, , Alb Alberto A.

• A. Del

l Bar arrio, Nad ader Bag agherzadeh