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Pruning Basics on Multi Head Attention-based Models
Scatter Lab Inc.
May 18, 2020
Research
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Pruning Basics on Multi Head Attention-based Models
Scatter Lab Inc.
May 18, 2020
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Transcript
1SVOJOH#BTJDTPO .VUJ)FBE"UUFOUJPOCBTFE.PEFMT ഘथജ .-4PGUXBSF&OHJOFFS 1JOHQPOH
ݾର ݾର "SF4JYUFFO)FBET3FBMMZ#FUUFSUIBO0OF <.JDIFMFUBM> "OBMZ[JOH.VMUJ)FBE4FMG"UUFOUJPO 4QFDJBMJ[FE)FBET%PUIF)FBWZ-JGUJOH UIF3FTU$BO#F1SVOFE
<7PJUBFUBM> 3FEVDJOH5SBOTGPSNFS%FQUIPO%FNBOEXJUI4USVDUVSFE%SPQPVU <'BOFUBM> 2
"SF4JYUFFO)FBET 3FBMMZ#FUUFSUIBO0OF 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CTUSBDU • ୭Ӕ5SBOTGPSNFSCBTFE.PEFMٜীೱਸҊח.VMUJIFBE"UUFOUJPO • ৈ۞ѐ)FBEٜ۽णೠറ*OGFSFODF5JNFীࠗ࠙)FBEٜਸহগࠆ • ࢿמೞۅহ ݻѐ-BZFSٜইೠѐ۽ৈبҡଳও
"SF"MM"UUFOUJPO)FBET*NQPSUBOU • ѐঀ݅.BTLJOHೞחप ѐࡐҊ.BTLJOHೞחपਸ೯ೣ • فѐݽ؛ࢎਊ • 8.5 • 7BTXBOJFUBM-BSHF5SBOTGPSNFS
-BZFS )FBETQFS-BZFS • 0UUFUBM GBJSTFR 1SFUSBJOFE.PEFM newstest2013#-&64DPSF • ѐ"UUFOUJPO.FDIBOJTNࢎਊ &OD&OD &OD%FD %FD%FD • #&35 • %FWMJOFUBM -BZFS "UUFOUJPO)FBET • #BTF .VMUJ/-*.BUDIFE%BUBTFU'JOFUVOJOH೧ࢲࢎਊ "DDVSBDZӝળ࠺Ү • ѐ"UUFOUJPO.FDIBOJTNࢎਊ п-BZFS߹TFMGBUUFOUJPO 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
"SF"MM"UUFOUJPO)FBET*NQPSUBOU • ח • ౠ)FBEܳ.BTLJOHೞӝਤ೧೧чਸઑ೧ࢲपೣ • чਸࠗ۽ݏ୶ݶੌ߈ੋ.VMUJIFBE"UUFOUJPOҗэ ξh 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
"CMBUJOH0OF)FBE ਗࠄ4DPSFܳ೧ঋחࢶীࢲࠗ࠙"UUFOUJPO)FBEٜࢤۚоמ೮ 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
"CMBUJOH0OF)FBE ୨ѐয়ѐ݅4UBUJTUJDBMMZ4JHOJGJDBOU೮ बযӒѐח4DPSFоৢۋ 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
"CMBUJOH0OF)FBE "UUFTUUJNF NPTUIFBETBSFSFEVOEBOU HJWFOUIFSFTUPGUIFNPEFM 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
"CMBUJOH"MM)FBETCVU0OF 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
• पઁ۽о*NQPSUBOUೠ)FBEೞա݅ਵ۽࠙ೠࢿמա৳ • $SPTTUBTL&WBMVBUJPOীࢲب࠺तೠѾҗܳࠁ • ҭҊޖੋѾҗ • 1BSBNFUFS ࠙݅ࢎਊ೧ࢲࢿמࠁઓؽ
• ೞ݅ݻѐ-BZFSীࢲח.VMUJIFBEоਃ೮ • &ODPEFS%FDPEFS"UUFOUJPOীࢲೞաो؊פڄয "CMBUJOH"MM)FBETCVU0OF 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT • Әөղਊౠ5FTU4FUীઓػഋకपѾҗ • ܲ%BUBTFUীೠੌ߈ചооמೠо • )FBEо6OJWFSTBMMZ*NQPSUBOUೠഋక۽ઓೞחо •
৮ઑੋೡਸೞח0VUPGEPNBJO5FTU4VJUF۽ппपೣ • 8.5ী.5/5&OHMJTIUP'SFODI5FTU4FU • #&35ী./-*.JTNBUDIFE%BUBTFU7BMJEBUJPO4FU "SF*NQPSUBOU)FBETUIF4BNF"DSPTT%BUBTFUT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "SF*NQPSUBOU)FBETUIF4BNF"DSPTT%BUBTFUT ୶࠺तೠਤ࠙ನ ೠ%PNBJOীࢲਃೠ)FBEо ܲ%PNBJOীࢲب6OJWFSTBMMZਃ೮
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT • Әөח-BZFS݃ٮ۽ٮ۽प೮ • ೠߣীৈ۞-BZFSীࢲ)FBEܳ.BTLJOHೞחप೯ • )FBE*NQPSUBODF4DPSFܳ҅೧ࢲӒчਵ۽)FBEܳ۳ • )FBEܳೞաঀহগоݶࢲࢿמਸஏೣ *UFSBUJWF1SVOJOHPG"UUFOUJPO)FBET
)FBE*NQPSUBODF4DPSF ౠ)FBEо-PTTীೱਸՙחبܳӝળਵ۽҅
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT &GGFDUPG1SVOJOHPO#-&6"DDVSBDZ ਵ۽ࠌਸٸ*OEJWJEVBM0SBDMFࠁ؊જࢿמਸࠁ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT &GGFDUPG1SVOJOHPO&GGJDJFODZ 1SVOFE.PEFM*OGFSFODF4QFFEо#BUDI4J[Fоழࣻ۾ࡈۄ .FNPSZDPOTUSBJOUFE4FUUJOHীࢲ%FQMPZNFOUীӝৈ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT • ইө)FBEܳೠѐ݅Ҏۋਸٸцझۣѱࢿמ%SPQغח$BTFо • যڃ҃ী۞ೠഅ࢚ੌযաחप • )FBE*NQPSUBODF4DPSFীٮۄ)FBEܳपҗڙэੜۄն • 8.5о"UUFOUJPOߑधী೧ࢲппࣻ೯ೞҊ࠺Үೣ 8IFO"SF.PSF)FBET*NQPSUBOU
5IF$BTFPG.BDIJOF5SBOTMBUJPO
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 8IFO"SF.PSF)FBET*NQPSUBOU 5IF$BTFPG.BDIJOF5SBOTMBUJPO ਬդ&OD%FDߑध݅_ҳрীࢲәѺೞѱ#-&64DPSFоڄয
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT • 5SBJOJOHҗীࢲ)FBE*NQPSUBODFоযڌѱחঌӝਤೠपਸ೯ • 1SVOJOHਸ೯ೡٸ4DPSFоযڌѱڄযחܳп&QPDIীࢲஏೣ • _1SVOJOH೮ਸٸпп#-&6оযڌѱ߸ചೞחܳ3FQPSU • о݅ٚߡ8.5ݽ؛ਸण೧ࠆ •
-BZFS п-BZFSѐ)FBE • *84-5%BUBTFUࢎਊ %ZOBNJDTPG)FBE*NQPSUBODFEVSJOH5SBJOJOH
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT %ZOBNJDTPG)FBE*NQPSUBODFEVSJOH5SBJOJOH _&QPDIदীࢲח1SVOJOHبীٮۄࢿמ-JOFBSೞѱхࣗ ਃೠ)FBEחള۲ୡӝ റחইפҊઑӘաࢲ ীѾؽ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT • .VMUJIFBE"UUFOUJPOۿਵ۽അࢿڪযա݅ ࢎਊೞঋחחࢎपਸߊѼ • ࢿמਸѱೞदఃঋਵݶࢲ)FBEܳࣻহচࣻਸࠁ • .5࠙ঠীࢲ &ODPEFS%FDPEFSݽ؛.VMUJIFBEী݆ઓೣਸߊѼೣ •
п)FBE࢚ਃࢿള۲ୡӝীҙؽ $PODMVTJPO
"OBMZ[JOH.VMUJ)FBE4FMG"UUFOUJPO 4QFDJBMJ[FE)FBET%PUIF)FBWZ-JGUJOH UIF3FTU$BO#F1SVOFE 1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CTUSBDU • .VMUJIFBE"UUFOUJPOীࢲп)FBEਃࢿҗೡী೧োҳ • ਃೠ)FBEח$POTJTUFOUೞҊ-JOHVJTUJDBMMZJOUFSQSFUBCMFೠౠࢿਸשਸߊѼ • 4UPDIBTUJD(BUF৬ QFOBMUZܳਊೠ%JGGFSFOUJBCMF3FMBYBUJPOਸࢎਊೞৈ 1SVOJOH೮Ҋ
ਃೠ)FBEٜоաী1SVOJOHؽ • ࠗ࠙)FBEܳহগҊبࢿמਸࠁઓೣਸࠁ • &OHMJTIUP3VTTJBO8.5%BUBTFUࢎਊ • )FBEѐѐզܻҊ#-&6ࣚ೧ࠆ L0
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT *EFOUJGZJOH*NQPSUBOU)FBET • 5SBOTMBUJPOѾҗীৈ۞ߧਤ۽ೱਸחѐ߹)FBEٜীೠ࠙ࢳ • )FBE$POGJEFODFܳ • &044ZNCPMਸઁ৻ೠࠗ࠙.BYJNVN"UUFOUJPO8FJHIU • $POGJEFOUೠ)FBEח"UUFOUJPOࠗ࠙ਸౠ5PLFOী֍חࢿೱਸש
• 5SBOTMBUJPOীೱਸ݆Ѫ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT -BZFSXJTF3FMFWBODF1SPQBHBUJPO -31 • %JOHFUBM ীࢲઁदؽ • 8FJHIU3BUJPܳഝਊೞৈ/FUXPSL࢚ౠ/FVSPOٜࢎ 3FMBUJWF$POUSJCVUJPOਸ҅ೞחߑߨ •
.PEFMী೧ஏػ୭࢚ਤ5PQ-PHJUীп)FBEо݃աҙৈೞחоܳ ҅ೞחؘী.FUIPEܳࢎਊೡѪਸઁदೣ • чਸӝળਵ۽ਃبܳಣо
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT -BZFSXJTF3FMFWBODF1SPQBHBUJPO -31
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT -BZFSXJTF3FMFWBODF1SPQBHBUJPO -31 -31ח_ѐ)FBE݅ਃೞחѾҗܳն $POGJEFODF৬-31חࢲ۽࠺तೠন࢚чਸࠁ ߣ૩-BZFSীࢲ݅-31о$POGJEFODF৬ܰѱಣоܳೞחਬח
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT $IBSBDUFSJ[JOH)FBET • -31ী೧֫ࣻܳ߉)FBEٜਸઑࢎೠѾҗо۽࠙ܨؽ • 1PTJUJPOBM • ੋೠ5PLFOਸоܻఃח)FBE • 4ZOUBDUJD
• ౠ4ZOUBDUJD3FMBUJPOਸоח5PLFOਸоܻఃח)FBE • 3BSF8PSE • -FBTU'SFRVFOU5PLFOਸоܻఃח)FBE
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 1PTJUJPOBM)FBET • ࢚ഛܫ۽नҗੋೠ5PLFOਸоܻఃח)FBEٜ • .BYJNVN"UUFOUJPO8FJHIU ߣ૩5PLFOীࠗৈؽ • -31߂$POGJEFODFীࢲ֫чਸࠗ࠙җэࠗ࠙ীߓؽ •
8FJHIUоౠ5PLFOীନ൧ب۽ъبо֫҃о݆ও ࠁۄ࢝ࠗ࠙
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 4ZOUBDUJD)FBET • 5SBOTMBUJPO5BTL೯&ODPEFSо4ZOUBDUJD4USVDUVSFܳणೠחоࢸਸઁद • ౠ)FBEо4ZOUBDUJDೠоח5PLFOਸоܻఆѪэ • ࠙ࢳѾҗо%FQFOEFODZ3FMBUJPOਸഛੋೣ • /PNJOBM4VCKFDU
OTVCK %JSFDU0CKFDU EPCK "EKFDUJWBM.PEJGJFS BNPE "EWFSCJBM.PEJGJFS BEWNPE ୡ۾࢝ࠗ࠙
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 4ZOUBDUJD)FBETn.FUIPEPMPHZ • $PSF/-1 .BOOJOHFUBM ܳࢎਊ೧ࢲ%FQFOEFODZ4USVDUVSFܳ݅ٞ • "UUFOUJPO8FJHIUਸ୶ೠറਤ%FQFOEFODZ4USVDUVSF৬࠺Ү • খীࢲݺदೠޙߨਃࣗܳоܻఃח%FQFOEFODZо٘۞աחܳഛੋೞҊर
• ౠ%FQFOEFODZ3FMBUJPOౠ%JSFDUJPOਸоܻఃח҃ীೠ"DDVSBDZܳ҅ • "DDVSBDZоইېౠޙߨਃࣗীೠ1PTJUJPOBM3FMBUJPOࠁ࢚֫ਸ҃4ZOUBDUJDೞҊ пޙߨਃࣗ߹۽1PTJUJPOBM3FMBUJPOਸ࠺Үೣ ਤ҃ೱࢿژೠэоחѪਸഛੋೣ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 4ZOUBDUJD)FBETn3FTVMU • 4ZOUBDUJD3FMBUJPOਸఐೞח)FBE"DDVSBDZо Ӓۧঋ҃ࠁ֫ও • &ODPEFSо4ZOUBDUJD%JTBNCJHVBUJPOਸࣻ೯ೠח оࢸਸّ߉ஜೞחѾҗ۽೧ࢳೡࣻ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3BSF8PSET • ݽٚݽ؛ীࢲ -BZFSೠ)FBEоҭ*NQPSUBODFо֫חѾҗܳഛੋ೮ • ઑࢎѾҗ -FBTU'SFRVFOUೠ5PLFOਸоܻఃחѪਵ۽ࠁ • חо؏١ೠ5PLFOਸ
חо؏١ೠف5PLFOೞաܳоܻௌ ട࢝ࠗ࠙
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 1SVOJOH"UUFOUJPO)FBET • .VMUJIFBE"UUFOUJPOਸҕधਵ۽߄Է • • חп)FBE݃ܰѱࠗৈغח(BUF • *OQVU4FOUFODF৬ח*OEFQFOEFOUೣ
• п)FBEܳ%PXO8FJHIUJOHೞחѱইפҊই%JTBCMFदఃҊर • ী 3FHVMBSJ[BUJPOਸਊ • .VMUJ)FBE(Q, K, V) = $PODBUi (gi ⋅ )FBEi )WO gi gi L0 L0 (g1 , …, gi ) = h ∑ i=1 (1 − [[gi = 0]])
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 1SVOJOH"UUFOUJPO)FBET • Ӓ۞ա 3FHVMBUJPO࠙ࠛоמೞ۽ 4UPDIBTUJD3FMBYBUJPOਸࢎਊೣ • ܳ3BOEPN7BSJBCMF۽فҊ)FBETQFDJGJD%JTUSJCVUJPOীٮۄة݀ਵ۽ೣ • )BSE$PODSFUF%JTUSJCVUJPOਸࢎਊೣ
$PODSFUF#JOBSZߡ L0 gi LC (ϕ) = h ∑ i=1 (1 − P(gi = 0|ϕi )) L(θ, ϕ) = Lxent (θ, ϕ) + λLC (ϕ) -/PSN3FMBYBUJPO L0 (g1 , …, gi ) = h ∑ i=1 (1 − [[gi = 0]]) ୭ઙ-PTTೣࣻ 5SBOTMBUJPO.PEFM$SPTT&OUSPQZ 3FHVMBSJ[BUJPO$PFGGJDJFOU թਸ)FBEіࣻઑ Lxent λ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 2VBOUJUBUJWF3FTVMUT#-&64DPSF )FBEѐթӝҊ #-&64DPSFхࣗ )FBEѐթӝҊ #-&64DPSFхࣗ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT )FBET*NQPSUBODF • .PEFM&ODPEFS4FMG"UUFOUJPOਸઁੌ ݢ1SVOJOHೞח҃ೱ • %FDPEFS4FMG"UUFOUJPO %PNBJOীٮۄܴ • 8.5-POH4FOUFODFחਃب֫
• 0QFO4VCUJUMFT4IPSU4FOUFODFח ਃبծ • &ODPEFS%FDPEFS"UUFOUJPO 5SBOTMBUJPOীࣻ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT )FBET*NQPSUBODF • %FDPEFS&ODPEFS"UUFOUJPO ծױ҅-BZFSীࢲ؊ਬؽ • %FDPEFS4FMG"UUFOUJPO ֫ױ҅-BZFSীࢲ؊ਬؽ 5SBOTGPSNFS-BZFSח ծױ҅ীࢲ-BOHVBHF.PEFMJOHਸೞҊ
֫ױ҅ীࢲ4PVSDF4FOUFODF$POEJUJPOJOHਸೣ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT $PODMVTJPO • -BZFSXJTF3FMFWBODF1SPQBHBUJPOਸࢎਊ೧ࢲ)FBEਃࢿਸಣо • 5SBOTMBUJPO5BTLীࢲ)FBEٜ4VCTFU݅ਃೞחࢎपҙؽ • ਃ)FBEח೧ࢳоמೠౠӝמਸೠחѪਸߊѼ • ਃೞঋ)FBEٜ1SVOJOHغযঠೠחѐ֛ਸӝୡ۽1SVOJOH.FUIPEܳઁद
• &ODPEFS4FMG"UUFOUJPOਸਤदೠࠗ࠙)FBEٜࢿמࣚ೧Ѣহহচࣻਸࠁ
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1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CTUSBDU • -BZFS%SPQਸࣗѐೣ • 5SBJOJOH3FHVMBSJ[BUJPO&GGFDUܳоೞҊ *OGFSFODF5JNFীബਵ۽1SVOJOH • ֎ਕীࢲ'JOFUVOJOHҗহೞա4VCOFUXPSLܳࢶఖ೮ਸٸ ࢿמ%SPQহ୶ۿоמೠҳઑܳࠁ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT -BZFS%SPQ • Өѱऺੋ5SBOTGPSNFSܳ3FHVMBSJ[FೞҊ 5SBJOJOHਸউചदఇ • নೠ#FODINBSLীࢲ405"1FSGPSNBODFܳਬೞب۾ೣ • ೞա1SFUSBJOFE.PEFMীࢲౠӨܳоҊബਯੋݽ؛ਸ୶ೣ •
5FTU5JNFীزਵ۽ܖয • 'JOFUVOJOHҗਃೞঋ • %SPQPVUҗ࠺तೠࣻળए*NQMFNFOUBUJPOդبܳо
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CTUSBDU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3BOEPNMZ%SPQQJOH4USVDUVSFTBU5SBJOJOH5JNF • п8FJHIUоة݀ਵ۽߬ܰ־࠙ನ ী೧Ѿػ%SPQ3BUFܳٮܴ • .\ ^উীࢲ3BOEPNMZ4BNQMFػ.BTL.FUSJYੌٸ
8FJHIU.BUSJYח p > 0 Wd = M ⊙ W
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3BOEPN4USVDUVSFE%SPQPVU • эҊਬҳઑܳо$PNQPOFOUীౠ8FJHIUٜ(SPVQਸഋࢿೞҊ Ӓ(SPVQীٮۄࢲп$PNQPOFOUܳ.BTLJOHೣ • )FBEա''/.FUSJDFT -BZFS৬э0WFSMBQQJOHೞחҳઑ۽غযח ݽٚ8FJHIUীਊೡࣻ
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 1SVOJOHBU*OGFSFODF5JNFn4FMFDUJOH-BZFSTUP1SVOF • 1SVOJOHೡ-BZFSܳҊܰחо4USBUFHZ • &WFSZ0UIFS • 3BUF оযਸٸ %FQUI
ী೧ࢲܳ1SVOJOHೣ • оҙҊ#BMBODFE/FUXPSLٜܳ݅ࣻחߑߨ ݽٚ҃ীੜزೣ • 4FBSDIPO7BMJE • -BZFSٜৈ۞$PNCJOBUJPOਸ҅ೞҊ7BMJEBUJPO4FUਵ۽ппѨૐೣ • 4USBJHIUGPSXBSEೞ݅ো࠺ऱҊ7BMJEBUJPO4FUী0WFSGJUUJOHೡࣻ • %BUB%SJWFO1SVOJOH • п-BZFS%SPQ3BUF ܳणೞݴ -BZFSٜ"WFSBHF3BUFܳ ৬эѱೣ • -BZFS"DUJWBUJPOਵ۽ ܳणೞҊ4PGUNBYܳ҅ೞחഋక • *OGFSFODJOH5JNFী4PGUNBY0VUQVU5PQLܳࡳইࢲ೧-BZFSٜਸࢎਊೣ p d pd p pd d ≡ 0(mod⌊ 1 p ⌋)
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 1SVOJOHBU*OGFSFODF5JNFn4FUUJOHUIFESPQSBUFGPSPQUJNBMQSVOJOH • (SPVQ ѐҊ 'JYFE%SPQ3BUJP оਸٸ (SPVQٜಣӐіࣻח ۽ ѐ(SPVQਸ1SVOJOHೠҊೞݶ
0QUJNBM%SPQ3BUF ח • ֫1SVOJOH3BUFח.PEFMীࢲ؊աࢿמਸࠁ • -BZFS%SPQীࢲח ܳࢎਊ೮ਵա .PEFMীࢲח ܳӂೣ N p N(1 − p) r p* p* = 1 − r N p = 0.2 p = 0.5
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3FTVMU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3FTVMU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3FTVMU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3FTVMU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT 3FTVMU
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CMBUJPO4UVEJFT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT "CMBUJPO4UVEJFT
1SVOJOH#BTJDTPO.VMUJ)FBE"UUFOUJPOCBTFE.PEFMT $PODMVTJPO • 4USVDUVSFE%SPQPVU3FHVMBSJ[BUJPOীب݆ؽ • ؋࠙ী1SVOJOHदী/FUXPSLо؊3PCVTUೡࣻ • যڃ%FQUI۽1SVOJOHೞ؊ۄبযוب&GGJDJFOUೞب۾ࣁೣ • Ө/FUXPSLܳणदఆٸب-BZFS%SPQ4UBCJMJUZীبਸ݆
хࢎפ✌ ഘथജ .-4PGUXBSF&OHJOFFS 1JOHQPOH &NBJMTFVOHIXBO!TDBUUFSMBCDPLS
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