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深層ニューラルネットワークにおける訓練高速化のための自動最適化
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Kazuhiro Serizawa
March 07, 2019
Research
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36
深層ニューラルネットワークにおける訓練高速化のための自動最適化
My slide at "第168回HPC研究会".
http://id.nii.ac.jp/1001/00194707/
Kazuhiro Serizawa
March 07, 2019
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Transcript
ਂχϡʔϥϧωοτϫʔΫ ʹ͓͚Δ܇࿅ߴԽͷͨΊͷ ࣗಈ࠷దԽ ۔༸ ݐ෦मݟ ஜେֶେֶӃγεςϜใֶݚڀՊ ஜେֶܭࢉՊֶݚڀηϯλʔ ۔༸ ݐ෦मݟਂχϡʔϥϧωοτϫʔΫʹ͓͚Δ܇࿅ߴԽͷͨ
Ίͷࣗಈ࠷దԽ ใॲཧֶձୈճ)1$ݚڀձใࠂ )1$ 7PM )1$ /P .BS !ੴࢁԹઘྤཨޫ
ൃද༰ w ݚڀഎܠ w ؔ࿈ݚڀʢϋΠύʔύϥϝʔλνϡʔχϯάɼࢄ%//ʣ w ༧උ࣮ݧ w ఏҊख๏ w
ఏҊख๏(16ར༻Λར༻ͨ͠࠷దԽ w ఏҊख๏܇࿅ॲཧ࣌ؒͷਪҠΛར༻ͨ͠࠷దԽ w ධՁ࣮ݧ w ݁ 2
ݚڀͷഎܠʢʣ w ۙɼਂχϡʔϥϧωοτϫʔΫʢҎԼ%//ʣΛ༻͍ ͨػցֶशͷར༻͕׆ൃԽ Ґ
Ґ Ґ ̐Ґ Ґ Ґ Ґ IUUQJNBHFOFUPSHDIBMMFOHFT-473$SFTVMUTIUNMΑΓҾ༻ #FUUFS *-473$ͷ ը૾ೝࣝ෦ͷUPQ Τϥʔ<> "MFY/FU ΈࠐΈχϡʔϥϧ ωοτϫʔΫ Λ࠾༻ 3
ݚڀͷഎܠʢʣ Ϟσϧͷઃܭ ϋΠύʔ ύϥϝʔλͷ ܾఆ ܇࿅ॲཧ ܇࿅ࡁΈ ϞσϧͷධՁ ࣌ؒʙؒ ϑΟʔυόοΫ
܇࿅࣌ؒͷظԽ ༻αʔϏεʹ͓͍ͯ ػձଛࣦͷՄೳੑ͕ݒ೦͞ΕΔ 4
w %//ͷ܇࿅࣌ؒॖͷͨΊͷΞϓϩʔν w (16ͷ࠾༻ w ϛχόον܇࿅ͷ࠾༻ w ࢄॲཧԽ w ઐ༻ϋʔυͷ࠾༻
w Ϟσϧѹॖ ݚڀͷഎܠʢʣ ຊݚڀͰѻ͏ྖҬ 5
ݚڀͷత w ϊʔυ(16ͷڥʹ͓͍ͯɼϛχόονͷύϥϝʔλͰ͋Δ ϛχόοναΠζΛɼ܇࿅࣌ؒΛ࠷খԽ͢ΔΑ͏ʹࣗಈͰ࠷ద Խ͢Δख๏ΛఏҊ͢Δ w ఏҊख๏ΛػցֶशϑϨʔϜϫʔΫ$IBJOFSʹ࣮͠ධՁΛߦ͏ 6
ؔ࿈ݚڀʢʣ w ࢄॲཧΛ༻͍ٖͯࣅతʹେنͳϛχόον܇࿅Λ࣮ݱ w ύϥϝʔλαʔόΛ༻͍ͨඇಉظࢄฒྻ܇࿅ <%FBOFUBM > w .1*ͷ"MM3FEVDFΛ༻͍ͨಉظࢄฒྻ܇࿅ <"LJCBFUBM
> େྔͷܭࢉϊʔυΛલఏͱͨ͠ख๏Ͱ͋Γɼϊʔυ୯ҐͰͷ࠷దԽ·Ͱ ߟྀ͍ͯ͠ͳ͍ ຊݚڀͰϊʔυ(16୯ҐͰͷ܇࿅Λ্ͤ͞ɼ ࢄ܇࿅ʹద༻ͯ͠ߴԽʹد༩Ͱ͖Δख๏ΛఏҊ͢Δ 7
ؔ࿈ݚڀʢʣ w ػցֶशϞσϧͷਫ਼Λ࠷େԽ͢ΔϋΠύʔύϥϝʔλ νϡʔχϯά w 3BOEPNTFBSDI ߏ1BS[FOਪఆثΛ༻ͨ͠ख๏ <#FSHTUSBFUBM > w
ϕΠζ࠷దԽΛ༻͍ͨख๏<4OPFLFUBM > ܇࿅Λ࠷େԽ͢ΔͨΊͷϋΠύʔύϥϝʔλνϡʔχϯάख๏ ͜Ε·ͰఏҊ͞Ε͍ͯͳ͍ ຊݚڀͰ܇࿅Λ࠷େԽ͢ΔͨΊͷϛχόον αΠζͷࣗಈ࠷దԽख๏Λݕ౼ 8
ϛχόον܇࿅ʹ͍ͭͯ ʢʣ ϛχόονΛ࠾༻ͤͣʹ܇࿅͢Δ߹ɼ ܇࿅σʔλͷ͕܇࿅ճʹ݁͢Δ ܇࿅σʔλ͕ ຕ ࠷Ͱ JUFSBUJPOͷ܇࿅͕ඞཁ 9
܇࿅σʔλ͕ ຕ JUFSBUJPO ͷ܇࿅͕ඞཁ ϛχόον͝ͱʹFNCBSSBTTJOHMZQBSBMMFMͳ σʔλฒྻԽ͕Մೳ ϛχόον܇࿅ʹ͍ͭͯ ʢʣ
ϛχόονԽʹΑΓ܇࿅ճͷݮ͕ՄೳʹͳΔ 10
ϛχόοναΠζΛ૿Ճͤ͞ଓ͚Δͱ(16ଆͷԋࢉίετ͕಄ ଧͪʹͳͬͯॲཧ࣌ؒͷݮޮՌ͕ࣦΘΕΔ͜ͱ͕ఆ͞ΕΔ ϛχόοναΠζ ϛχόοναΠζ ܇࿅࣌ͷ߹ܭԋࢉྔ<qPQ> ߹ܭ܇࿅ॲཧ࣌ؒ<TFD> ཧ্ͷ܇࿅ॲཧ࣌ؒͷਪҠ ʢը૾ຕ͋ͨΓͷॲཧ͕࣌ؒ Ұఆͷ߹ʣ ཧ্ͷԋࢉྔͷਪҠ
U U O O ϛχόον܇࿅ʹ͍ͭͯ ʢʣ 11 ҰൠతʹɼͳͲ͕ϛχόοναΠζͱͯ͠༻͞Ε͍ͯΔ͕ ϛχόοναΠζΛܾఆ͢Δ٬؍తͳࢦඪΒΕ͍ͯͳ͍
༧උ࣮ݧʢʣ w ϛχόοναΠζΛͷൣғͰม͑ͳ͕ΒΈࠐΈ χϡʔϥϧωοτϫʔΫʢ7((̍̒ʣΛ܇࿅ͯ͠ɺҎԼͷ ؔΛௐࠪ͢Δ w ϛχόοναΠζͱ܇࿅࣌ؒͷؔ w ϛχόοναΠζͱฏۉ(16ར༻ͷؔ ฏۉ(16ར༻܇࿅தʹOWQSPGͰඵִؒͰܭଌͨ͠ͷฏۉ
12
༧උ࣮ݧʢʣ ϛχόοναΠζΛ૿͢ը૾ຕ͋ͨΓͷ܇࿅͕࣌ؒॖ ϛχόοναΠζ͝ͱͷ܇࿅ॲཧ࣌ؒͷਪҠ ϛχόοναΠζ͕ Λ͑ͨͨΓͰมԽ͕ऩଋ ͠εέʔϧ͠ͳ͘ͳΔ 'BTUFS 13
༧උ࣮ݧʢʣ ϛχόοναΠζΛ૿͢ฏۉ(16ར༻্͕ঢ ϛχόοναΠζ͝ͱͷฏۉ(16ར༻ͷਪҠ ϛχόοναΠζ͕ Λ͑ͨͨΓͰ ฏۉ(ۙʹ౸ୡ 14
༧උ࣮ݧʢʣ ϛχόοναΠζΛաʹ૿͢ϞσϧͷੑೳʹѱӨڹ FQPDI ը૾ೝࣝਖ਼ղ #FUUFS ϛχόοναΠζ͝ͱͷϞσϧੑೳ
15
༧උ࣮ݧ͔Βߟ͑ΒΕΔԾઆ ϛχόοναΠζΛ૿͢ w ը૾ຕ͋ͨΓͷ܇࿅͕࣌ؒݮগ w ฏۉ(16ར༻্͕ঢ w ྆ऀͱҰఆͷαΠζͰऩଋ w աʹ૿͢ͱϞσϧੑೳʹѱӨڹ
ฏۉ(16ར༻ͷมԽ͕ऩଋ࢝͠ΊΔલޙͷ ϛχόοναΠζ͕܇࿅࣌ؒΛ࠷খԽ͢Δ ༧උ࣮ݧΑΓ 16 खಈͰϛχόοναΠζ͝ͱʹ(16ར༻Λܭଌ͠ͳ͕Β ϚχϡΞϧͰϛχόοναΠζΛௐ͢Δͷඇৗʹख͕͔͔ؒΔ
ఏҊख๏ w ҎԼ̎ͭͷख๏ΛఏҊ w ఏҊख๏ ฏۉ(16ར༻͕ࢦఆͨ͠ʹۙͮ͘Α͏ʹ ܇࿅Λߦ͍ͳ͕ΒϛχόοναΠζΛ ࣗಈͰ࠷దԽ w ఏҊख๏
܇࿅ॲཧ࣌ؒͷมԽ͕࠷খʹͳΔΑ͏ʹ܇࿅ Λߦ͍ͳ͕ΒϛχόοναΠζΛࣗಈͰ࠷దԽ 17
ఏҊख๏ʢʣ ᶃฏۉ(16ར༻͕ඪͷ ྫ͑ ʹ ۙͮ͘Α͏ʹϛχόοναΠζΛมԽͤ͞Δ ᶄϛχόοναΠζͷมԽ͕ ऩଋͨ͠Βͦ͜Λ࠷దͱͯ͠ ࠾༻͢Δ ඪͷฏۉ(16ར༻
ܭଌͨ͠ฏۉ(16ར༻ ͕ ࠷খʹͳΔΑ͏ʹ࠷దԽ 18
ఏҊख๏ʢʣ /ճ܇࿅Λߦ͏ ্Ґͷܭଌ͔Βฏۉ(16ར༻Λܭࢉ ඵ͝ͱͷ(16ར༻ ΛOWNMͰඇಉظͰܭଌ ϛχόοναΠζΛௐ ฏۉ(16ར༻͕ඪͷΑΓখ͍͞ ૿Ճݮ ϛχόοναΠζΛॳظԽ ϛχόοναΠζͷมԽ͕ऩଋͨ͠
'BMTF 5SVF ࠷దԽऴྃ ॲཧϑϩʔ 19
ఏҊख๏̎ʢʣ ᶃॳظϛχόοναΠζͷ ॲཧ࣌ؒΛϕʔεϥΠϯͱ͢Δ ᶄϕʔεϥΠϯ͔Βͷॲཧ࣌ؒͷվળ͕ ऩଋͨ͠Βͦͷ࣌ͷϛχόοναΠζΛ ɹ࠷దͱͯ͠࠾༻͢Δ ϕʔεϥΠϯ͔Βͷ܇࿅ॲཧ࣌ؒͷվળ͕มԽ͠ͳ͘ͳΔ·Ͱ ϛχόοναΠζΛ૿Ճͤ͞Δ 20
ఏҊख๏̎ʢʣ FQPDIͨΓͷ܇࿅ॲཧ࣌ؒ<TFD> JUFSBUJPOͨΓͷॲཧ࣌ؒ<TFD>Y FQPDIʹඞཁͳΠςϨʔγϣϯ σʔλαΠζϛχόοναΠζʣ 21 ϕʔεϥΠϯͷ܇࿅ॲཧ࣌ؒ ϛχόον͝ͱͷ܇࿅ॲཧ࣌ؒ ϕʔεϥΠϯͷ܇࿅ॲཧ࣌ؒ
FQPDIͨΓͷ܇࿅ॲཧ࣌ؒͷվળ
ఏҊख๏̎ʢʣ /ճ܇࿅Λߦ͍ɼॲཧ࣌ؒΛܭଌ FQPDI͋ͨΓͷ܇࿅ॲཧ࣌ؒվળΛࢉग़ ϛχόοναΠζΛ૿Ճ ϛχόοναΠζΛॳظԽ FQPDI͋ͨΓͷ܇࿅ॲཧ࣌ؒվળͷมԽ͕ऩଋͨ͠ʁ 'BMTF 5SVF ࠷దԽऴྃ ॲཧϑϩʔ
ॳճͷܭଌΛϕʔε ϥΠϯͱͯ͠อଘ 22
$IBJOFSΛ༻͍࣮ͨํ๏ .PEFMΛΠϯελϯεԽ NPEFM7(( 0QUJNJ[FSΛΠϯελϯεԽͯ͠.PEFMͱώϞ PQUJNJ[FS.PNFOUVN4(% NPEFM ςετσʔλΛϩʔυͯ͠*UFSBUPSΛΠϯελϯεԽ
JUFSBUPS4FSJBM*UFSBUPS HFU@DJGBS 6QEBUFSΛΠϯελϯεԽͯ͠JUFSBUPS PQUJNJ[FSͱώϞ VQEBUFS4UBOEBSE6QEBUFS JUFSBUPS PQUJNJ[FS 5SBJOFSΛΠϯελϯεԽͯ͠VQEBUFSͱώϞ USBJOFS5SBJOFS VQEBUFS ఏҊख๏Λ࣮ͨ͠&YUFOTJPOΛՃ USBJOFSFYUFOE .JOJCBUDI4J[F0QUJNJ[FS ܇࿅ϧʔϓΛ࣮ߦ USBJOFSSVO $IBJOFSΛ༻͍ͨ܇࿅ॲཧεΫϦϓτͷ࣮ྫͱओཁΫϥεͷॴ༗ؔ 23
ධՁ࣮ݧ֓ཁʢʣ w ఏҊख๏ Λ༻͍ͯҎԼͷ༰ΛධՁ͢Δ w ҙਤͨ͠ͱ͓Γʹ࠷దԽ͕ਐΈऩଋ͢Δ͔Ͳ͏͔ w ऩଋ݅ w ఏҊख๏ϛχόοναΠζͷมԽ͕Ҏ
w ఏҊख๏FQPDI͋ͨΓͷॲཧ࣌ؒվળ͕Ҏ 24
ධՁ࣮ݧ֓ཁʢʣ ༻͢ΔσʔληοτͱωοτϫʔΫͷΈ߹Θͤ σʔληοτʢը૾ղ૾<QJYFM>ʣ ωοτϫʔΫ $JGBSʢYʣ 7(( $JGBSʢYʣ 3FT/FU *NBHF/FULʢYʣ 7((
*NBHF/FULʢYʣ 3FT/FU 25
ධՁ࣮ݧ֓ཁʢʣ ධՁڥ TQFD $16 9FPO 3 $16&W!()[Y .FNPSZ (J# (16
/7*%*"5FTMB7(J# 04 $FOU04 1ZUIPO $IBJOFS B GPSL࣌ $6%" DV%// W 26
ఏҊख๏̍ʹ͓͚Δ $JGBSͷධՁ݁Ռ $JGBSͷ ฏۉ(16ར༻ऩଋͷ༷ࢠ 7(( 3FT/FU w ࠷దԽͷਐߦͱڞʹฏۉ(16ར༻͕૿Ճ w ϛχόοναΠζͱฏۉ(16ར༻ͱͷؒʹਖ਼ͷ૬ؔੑ͕ݟΒΕΔ
27 $JGBSͷϛχόοναΠζͱ ฏۉ(16ར༻ͷؔ 7(( 3FT/FU )JHIFS ࠷దԽਐḿ େ খ
*NBHF/FULͷ ฏۉ(16ར༻ऩଋͷ༷ࢠ 7(( 3FT/FU $JGBSͱಉ༷ͷ͕ݟΒΕΔ͕ܭଌ͞Εͨ(16ར༻ͷࢄ͕େ͖͍ ఏҊख๏̍ʹ͓͚Δ *NBHF/FULͷධՁ݁Ռ 28 7(( 3FT/FU
*NBHF/FULͷϛχόοναΠζͱ ฏۉ(16ར༻ͷؔ )JHIFS ࠷దԽਐḿ େ খ
ఏҊख๏̎ʹ͓͚Δ $JGBSͷධՁ݁Ռ $JGBSͷ܇࿅ॲཧ࣌ؒ վળऩଋͷ༷ࢠ #FUUFS 29 7(( 3FT/FU
$JGBSͷϛχόοναΠζͱ ܇࿅ॲཧ࣌ؒվળͷؔ w ࠷దԽͷਐߦͱڞʹFQPDIͨΓͷॲཧ࣌ؒվળ͕૿Ճ w ϛχόοναΠζͱվળͱͷؒʹਖ਼ͷ૬ؔੑ͕ݟΒΕΔ ࠷దԽਐḿ େ খ
ఏҊख๏̎ʹ͓͚Δ *NBHF/FULͷධՁ݁Ռ *NBHF/FULͷ܇࿅ॲཧ࣌ؒ վળऩଋͷ༷ࢠ $JGBSͷධՁ݁Ռͱ΄΅ಉͷΛ͕ࣔ͢ $JGBSΑΓվળ͕͍ 30 7((
3FT/FU *NBHF/FULͷϛχόοναΠζͱ ܇࿅ॲཧ࣌ؒվળͷؔ #FUUFS ࠷దԽਐḿ େ খ
ಘΒΕͨ࠷దΛ༻͍ͯ FQPDI܇࿅ͨ݁͠Ռ $JGBSͷܭଌ݁Ռ *NBHF/FULͷܭଌ݁Ռ #FUUFS ಘΒΕͨϛχόονͷ࠷దΛ༻͍ͯFQPDIͷ܇࿅Λߦ͍ ܇࿅࣌ؒΛܭଌͨ݁͠ՌɼͲͷέʔεʹ͓͍ͯϕʔεϥΠϯ͔Βվળ͕ݟΒΕͨ CBTF QSPQPTFE QSPQPTFE
CBTF QSPQPTFE QSPQPTFE #FUUFS 31
ධՁ݁Ռ·ͱΊ ධՁύλʔϯ ఏҊख๏ ఏҊख๏̎ ύλʔϯ ύλʔϯ
ύλʔϯ ύλʔϯ ࠷దͱͯ͠ಘΒΕͨϛχόοναΠζ ࠷దͱͯ͠ಘΒΕͨϛχόοναΠζΛൺֱ͢Δͱ ࠷దԽख๏ؒຖͰ͕ࠩݟΒΕͨ 32
$JGBSͰͷධՁ݁Ռ ʹ͓͚Δߟʢʣ ύλʔϯ ʢ$JGBSʣʹ͓͚Δ྆ख๏ͰಘΒΕͨ࠷దͱվળͷൺֱ 7(( 3FT/FU ఏҊख๏Ͱ ಘΒΕͨ࠷ద ఏҊख๏̎Ͱ ಘΒΕͨ࠷ద
#FUUFS $JGBSͰಘΒΕͨ࠷దఏҊख๏̎ख๏ͷํ͕࠷ద 33
$JGBSͰͷධՁ݁Ռ ʹ͓͚Δߟʢʣ #FUUFS 7(( 3FT/FU ఏҊख๏ ఏҊख๏ ฏۉ(16ར༻͕ۙ͘ʹͳͬͨҎ߱ ϛχόονʹΑΔॲཧ࣌ؒͷݮޮՌ͕֬ೝ͞ΕΔ FQPDIͨΓͷ܇࿅ॲཧ͕࣌ؒ
ϛχόοναΠζͷมԽʹൺྫ͢ Δ߹ͷཧۂઢ ఏҊख๏̎ 34 (16 ϛχόοναΠζ
ύλʔϯ̏ ̐ʢ*NBHF/FULʣʹ͓͚Δ྆ख๏ͰಘΒΕͨ࠷దͱվળͷൺֱ 7(( 3FT/FU #FUUFS *NBHF/FULͰಘΒΕͨ࠷ద྆खํؒͰେ͖ͳࠩݟΒΕͳ͍ ఏҊख๏ͰಘΒΕͨ࠷ద ఏҊख๏̎Ͱ ಘΒΕͨ࠷ద *NBHF/FULͰͷධՁ݁Ռ
ʹ͓͚Δߟʢʣ 35
*NBHF/FULͰͷධՁ݁Ռ ʹ͓͚Δߟʢʣ 7(( 3FT/FU #FUUFS ఏҊख๏ ఏҊख๏ (16ʹΑΔߴԽϛχόονʹΑΔॲཧݮޮՌͷ྆ํ͕ ͋·ΓޮՌతͰͳ͍ վળͷਪҠ͕ॳظ͔Βͷ
ϛχόοναΠζͷมԽʹൺྫ ͢Δ߹ͷվળਪҠ վળͷਪҠ͕ॳظ͔Βͷ ϛχόοναΠζͷมԽʹͷΈ ൺྫ͢Δ߹ͷཧۂઢ 36
ฏۉ(16ར༻ͷࢄʹ ؔ͢Δߟʢʣ $JGBS 7(( ύ$JGBS 3FT/FU *NBHF/FUL 7(( *NBHF/FUL 3FT/FU
w ฏۉ(16ར༻ͷࢄ*NBHF/FUL$JGBS w σʔληοτͷαΠζࠩʹΑͬͯ(16ͷར༻ঢ়گ͕ ҟͳΔՄೳੑ͕ߟ͑ΒΕΔ 37
*NBHF/FULΛ༻ͨ͠߹ɼJUFSBUJPO͝ͱʹ ඵ(16Χʔωϧ͕࣮ߦ͞Ε͍ͯͳ͍࣌ؒଳ͕ଘࡏ͢Δ ܇࿅ॲཧதʢJUFSBUJPOʣͷ(16ར༻ঢ়گΛώʔτϚοϓͱͯ͠ՄࢹԽͨ͠ਤ $JGBS *NBHF/FUL ܇࿅ॲཧதͷ(16Χʔωϧ࣮ߦঢ়گ ฏۉ(16ར༻ͷࢄʹ ؔ͢Δߟʢʣ 38 (16͕ར༻͞Ε͍ͯͳ͍࣌ؒଳ
ը૾ಡΈࠐΈ࣌ͷ%JTL*0ը૾͔Βߦྻͷมॲཧ͕ߦΘΕ͍ͯΔͱߟ͑ΒΕΔ
݁ w ຊݚڀͰɼ(16ར༻ͱ܇࿅ͷվળʹணͨ͠ϛχόονα Πζͷ࠷దԽख๏ΛఏҊͨ͠ w $JGBSΛ༻͍ͨ܇࿅ʹ͓͍ͯɼϛχόοναΠζͱൺֱͯ͠࠷ େͰFQPDIͨΓͷ܇࿅ॲཧ࣌ؒΛվળ͢Δϛχόονα ΠζΛࣗಈͰ୳ࡧ͢Δ͜ͱ͕Ͱ͖ͨ w *NBHF/FULΛ༻͍ͨ܇࿅ʹ͓͍ͯɼϛχόοναΠζͱൺֱͯ͠
࠷େͰFQPDIͨΓͷ܇࿅ॲཧ࣌ؒΛ࠷େվળ͢Δϛχ όοναΠζΛࣗಈͰ୳ࡧ͢Δ͜ͱ͕Ͱ͖ͨ w *NBHF/FULΛ༻͍ͨ܇࿅Ͱ܇࿅ॲཧͷ(16Λར༻͍ͯ͠Δ࣌ؒͷ ׂ߹͕$JGBSͱൺ͍ͯ͜ͱ͕֬ೝ͞Εͨ 39
ࠓޙͷ՝ w JUFSBUJPOؒͷ(16Χʔωϧ͕࣮ߦ͞Ε͍ͯͳ͍࣌ؒͷ ݮํ๏Λݕ౼͢Δ w ܇࿅σʔλϩʔυ࣌ͷ%JTL*0ͷߴԽ w ܇࿅σʔλͷมॲཧͳͲͷલॲཧͷӅṭ 40
ҎԼ༧උεϥΠυ 41
ఏҊख๏̎ͷ ධՁ݁Ռͷݕূ ධՁύλʔϯ ఏҊख๏̎ख๏Ͱਪଌ͞Εͨ࠷ద ʹ͓͚Δվળ<> ࣮ࡍʹܭଌ͞Εͨվળ<> ύλʔϯ ύλʔϯ
ύλʔϯ ύλʔϯ ಘΒΕͨϛχόονͷ࠷దΛ༻͍ͯFQPDIͷ܇࿅Λߦ͍ɼ ॳظ͔ΒͷվળΛܭଌͨ͠ͱ͜Ζɼਪଌͱܭଌ΄΅ಉΛࣔͨ͠ 42
ఏҊख๏ͷ ධՁ݁Ռͷݕূʢৄࡉʣ ධՁύλʔϯ ਪଌ͞Εͨվળ <> ܭଌ͞Εͨվળ <> ॳظͰͷܭଌ <TFD> ࠷దͰͷܭଌ
<TFD> ύλʔϯ ύλʔϯ ύλʔϯ ύλʔϯ ಘΒΕͨϛχόονͷ࠷దΛ༻͍ͯFQPDIͷ܇࿅Λߦ͍ ॲཧ࣌ؒͱॳظ͔ΒͷվળΛܭଌͨ͠ 43
ఏҊख๏ͱఏҊख๏ͷ ࠷దൺֱ ධՁύλʔϯ ॳظͰͷܭଌ<TFD> ఏҊख๏ͷ࠷దͰͷ ܭଌ<TFD> ఏҊख๏Ͱͷ࠷దͰ ͷܭଌ<TFD> ύλʔϯ
ύλʔϯ ύλʔϯ ύλʔϯ ಘΒΕͨϛχόονͷ࠷దΛ༻͍ͯFQPDIͷ܇࿅Λߦ͍ ॲཧ࣌ؒΛܭଌͨ͠ 44
ఏҊख๏ͷ ධՁ݁Ռͷݕূ σʔληοτ ωοτϫʔΫ ϕʔεϥΠϯ<TFD> ఏҊख๏ʹ͓͚Δ࣮ଌ <TFD> $JGBS 7((
3FT/FU *NBHF/FUL 7(( 3FT/FU ఏҊख๏ͰಘΒΕͨ࠷దΛ༻͍ͯFQPDIܭଌͨ݁͠Ռ 45
ఏҊख๏ͷ ධՁ݁Ռͷݕূ σʔληοτ ωοτϫʔΫ ϕʔεϥΠϯ<TFD> ఏҊख๏ʹ͓͚Δ࣮ଌ <TFD> $JGBS 7((
3FT/FU *NBHF/FUL 7(( 3FT/FU ఏҊख๏ͰಘΒΕͨ࠷దΛ༻͍ͯFQPDIܭଌͨ݁͠Ռ 46
$JGBS 7((ʹ͓͚Δ ϛχόοναΠζ͝ͱͷਫ਼ NBJOBDDVSBDZ FQPDI WBMJEBUJPOBDDVSBDZ FQPDI
47
$JGBS 3FT/FUʹ͓͚Δ ϛχόοναΠζ͝ͱͷਫ਼ NBJOBDDVSBDZ FQPDI WBMJEBUJPOBDDVSBDZ FQPDI
48
FQPDI͋ͨΓͷॲཧ࣌ؒվળ ͷཧۂઢͷܭࢉϩδοΫ 49
ධՁதͷܭଌྫ
DIFDL DIFDL DPOWFSHFODF DIFDL লུ DIFDL DPOWFSHFODF ఏҊख๏ ఏҊख๏̎ ϛχόον αΠζ ϛχόον αΠζ 50