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. Approxim imate • But t high igh comple lex convolu lutional l neural l netw tworks mult ultiplic icatio ion (CNNs) re (C require re high igh accura rate computation. • Ite Itera rative stru tructure can enhance th the accura racy. High Hig accurate • Repeating basic ic blocks add sign ignificant cost. computatio co ion • Let t us re reduce cost of f basic ic blocks wit ithout with low co cost degra rading perfo rformance of f CNNs!!
Summary of Proposed Design • Tru • Trun Truncated ed Mit Mitche hell l Truncated ed Mit Mitche hell l mult ltip iplie ier wit with h n 1 -bit mult ltip iplie ier wit with h n 2 -bit fra fractions fra fractions Sec Second Fi First sta stage stage sta Final Fi l Err Error te term output ou calc ca lcula lation • Su of 1 st st • Tra Sum of of ou outputs of Transfer error error from from nd sta st sta nd stag and nd 2 nd stages 1 st stage e to o 2 nd stage -3-
Basics of Mitchell Algorithm (Multiplication) Ho How to w to app appro roxi xima mate te it? it? * * rerr err : : rel relati tive e erro error Error Error dep depends ends o on s n sum of um of fr frac actio tions. ns. - 4 -
Str tructure of Proposed Design Output Ou put of of Erro Error r Ter erm m Calcula Calculator or is is tran ansfe sferr rred ed to n o next xt s stage e Co Compensated Co Compensated er error in n er error in n truncatio tr ion tr truncatio ion nd Sta st Stag 2 nd tage Mitc itchell Mult ltip iplier 1 st tage Mitc itchell Mult ltip iplie ier -5-
Err rror Term Calculator 1’s com complement plement * LOD: Leading One Detect - 6 -
Summary of Err rror Analysis 11 11.1% .1% rerr err max max from from error term using 1’s complement. com plement. (e.g (e.g. A= . A=11 11 2 , , B= B=11 11 2 → A(2)=0, (2)=0, B(2)=0 B(2)=0 ) - 7 -
Comparison of Err rror and Cost Bett tter re rerr rr avg compared to to oth ther appro roximate mult ltipli liers rs Gre reat cost re reduction over r Booth mult ltipli lier when n =16 and n =32 - 8 -
Comparison of Accuracy on CNNs When n 1 =6 and n 2 =2, th there re is is no sign ignificant accura racy dro rop in in CNN models ls, whic ich outperforms orig riginal l Mit itchell ll mult ltipli lier. For r n 1 =8, to top-5 accura racy of f ResNet-50 re reaches up to to 90.9%. - 9 -
Conclusion 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 on of of CN CNNs Ns are a are analyz nalyzed. ed. Proposed Pr ite terativ ive • Can in incre rease perf rform rmance wit ith small l cost in in truncated tr applications of f appro roximate multipli lier r logarithmic ic mult ltiplication • Th The tru truncation and erro rror r te term rm calculation of f our r Ap Applic ication design do not t in incur substantial l im impact on of of CNNs infe in ference accuracy on CNN models ls - 10 10 -
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
Recommend
More recommend
