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ஜ೾େֶେֶӃਤॻؗ৘ใϝσΟΞݚڀՊम࢜೥ ຊ઒఩࠸ 1 %-)BDLT࣮૷ൃද )FTTJBOCBTFE"OBMZTZTPG-BSHF#BUDI5SBJOJOHBOE 3PCVTUOFTTUP"EWFSTBSJBMT

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2 ͸͡Ίʹ

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ॻࢽ৘ใ w λΠτϧ)FTTJBOCBTFE"OBMZTZTPG-BSHF#BUDI5SBJOJOHBOE 3PCVTUOFTTUP"EWFSTBSJBMT w ஶऀ;IFXFJ:BP "NJS(IPMBNJ 2J-FJ ,VSU,FVU[FS .JDIBFM8.BIPOFZ w BS9JWIUUQTBSYJWPSHBCT w ձٞ/FVS*14` 3

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ΞδΣϯμ w ࿦จ֓ཁ w എܠ w ϔοηߦྻ w )FTTJBOCBTFE"OBMZTJTͱ͸ w TIBSQNJOJNVNWTqBUNJOJNVN w ࣮ݧ w ࣮ݧઃఆ w ࣮૷ w ߟ࡯ 4

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֓ཁ w χϡʔϥϧωοτͷֶशʹ͓͍ͯόοναΠζΛେ͖͘͢Δͱਫ਼౓͕Լ͕Δ͕ɼ ͦͷݪҼղ໌͸͞Ε͍ͯͳ͍ w ͜ͷ໰୊ʹରͯ͠ϔοηߦྻͷݻ༗஋Λར༻͢Δ͜ͱͰɼύϥϝʔλ্ۭؒͰͷ ଛࣦؔ਺ͷہॴతͳߏ଄͕Ͳ͏ͳ͍ͬͯΔ͔Λ෼ੳ w ·ͨऩଋઌͷϔοηߦྻͷݻ༗஋෼෍͕େ͖͍ύϥϝʔλ͸ɼఢରతྫ୊ ʢ"&Tʣʹରͯ͠΋ऑ͍ʢʹϩόετੑ͕௿͍ʣ͜ͱΛ࣮ݧతʹࣔͨ͠ 5

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ࠓճͷओ࣠ w ͜ͷ໰୊ʹରͯ͠ϔοηߦྻͷݻ༗஋Λར༻͢Δ͜ͱͰɼύϥϝʔλ্ۭؒͰͷ ଛࣦؔ਺ͷہॴతͳߏ଄͕Ͳ͏ͳ͍ͬͯΔ͔Λ෼ੳ 6

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7 എܠ

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ϔοηߦྻ w ଛࣦؔ਺ʹ͓͚Δೋ֊ඍ෼શମͰߏ੒͞ΕΔߦྻ w ݻ༗஋ͷූ߸ɾେ͖͞ʹΑͬͯہॴೋ࣍ۙࣅͨ͠ͱ͖ͷܗঢ়͕Θ͔Δ w χϡʔϥϧωοτͰ͸ޯ഑ಉ༷ ޡࠩٯ఻೻๏ͰٻΊΔ͜ͱ͕Մೳʢ13.-ষʣ 8 ݻ༗஋͕શͯਖ਼ɿۃখ஋ ݻ༗஋͕શͯෛɿۃେ஋ ݻ༗஋ʹਖ਼ෛͲͪΒ΋͋ΔɿҌ఺ ݻ༗஋ʹؚ͕·ΕΔɿ൑அෆೳʢϓϥτʔʁʣ IUUQXXXUIPUIDIJMESFODPNDIBQUFSCDGGFG

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)FTTJBOCBTFE"OBMZTJTͱ͸ w χϡʔϥϧωοτʹ͓͚ΔֶशͷڍಈΛϔοηߦྻͷݻ༗஋Λ༻͍ͯ෼ੳ͢Δख๏ w ݹ͘͸-V$VO ʹΑͬͯݴٴ w 9 ֶशޙͷଛࣦؔ਺ʹ͓͚Δϔοηߦྻͷݻ༗஋෼෍ ʢ)FTTJBOTQFDUSVNʣ ΄ͱΜͲͷݻ༗஋͸ʹ͍ۙ஋ΛऔΔ͕ɼҰ෦ͷඇৗʹେ͖ͳ ݻ༗஋͕ଘࡏ͢Δ ֶशޙͷύϥϝʔλۭؒͰ͸ɼ΄ͱΜͲͷ࣍ݩͰฏୱͳ஍ܗɼ গ਺ͷ࣍ݩ͕ٸफ़ʹۂ͕͍ͬͯΔ IUUQZBOOMFDVODPNFYECQVCMJTQEGMFDVOCQEG

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TIBSQNJOJNVNWTqBUNJOJNVN • sharp minimumΑΓ΋flat minimumͷํ͕൚Խੑೳ͕ߴ͍ʢHochreiter+ 1997ʣ • 10 ύϥϝʔλͷઁಈʹରͯ͠ϩόετ

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:BP ͷओு • sharp minimumΑΓ΋flat minimumͷํ͕൚Խੑೳ͕ߴ͍ʢHochreiter+ 1997ʣ • 11 ϔοηߦྻͷݻ༗஋͕খ͍͞ όοναΠζ͕খ͍࣌͞ʹ౸ୡ ϔοηߦྻͷݻ༗஋͕େ͖͍ όοναΠζ͕େ͖͍࣌ʹ౸ୡ

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12 ࣮ݧ

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࣮ݧઃఆ w σʔληοτ$*'"3 w Ϟσϧ࿦จ಺ͷ$ w ࿦จͷ࣮ݧೖྗʹؔ͢Δϔοηߦྻͷݻ༗஋෼ੳ w ࠓճͷ࣮ݧॏΈʹؔ͢Δϔοηߦྻͷݻ༗஋෼ੳ w શͯͷॏΈύϥϝʔλʹؔ͢Δϔοηߦྻ͸ڊେ w ͦ͜Ͱࠓճ͸࠷ऴ૚ͷॏΈʹؔ͢ΔϔοηߦྻͷΈར༻ʢޡࠩٯ఻೻๏ͷܭࢉ͕࠷΋ܰྔʣ w όοναΠζ   Ͱ࣮ݧ w .PNFOUVN4(%MS NPNFOUVN FQPDI 13

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࣮ݧઃఆʢ:BP ʣ 14 1 2 i-1 i k-1 k ɾɾɾ X Y ଛࣦؔ਺ ೖྗͰͷ ϔοηߦྻ ݻ༗஋ ɾɾɾ ɾɾɾ

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࣮ݧઃఆʢࠓճʣ 15 1 2 i-1 i k-1 k ɾɾɾ X Y ଛࣦؔ਺ ࠷ऴ૚Ͱͷ ϔοηߦྻ ݻ༗஋ ɾɾɾ ɾɾɾ

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ஶऀ࣮૷ w IUUQTHJUIVCDPNBNJSHIPMBNJ)FTTJBO'MPX w 5FOTPSqPXͰ͸ͳ͘1ZUPSDI 16

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݁Ռʢ:BP ʣ 17

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࣮૷ w ϔοηߦྻ͸UGIFTTJBOTͰ؆୯ʹऔಘՄೳ w ϕΫτϧͷTIBQFͰग़ྗ͞ΕΔͷͰߦྻͷTIBQFʹ௚͢ 18

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࣮૷ w ݻ༗஋ͷܭࢉ w TDJQZMJOBMHFJHIͰ্ҐL݅ͷݻ༗஋ɾݻ༗ϕΫτϧͷΈΛൈ͖ग़͢͜ͱ͕Մೳ 19

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࣮૷ w ՄࢹԽͷͨΊʹऩଋઌͷύϥϝʔλ෇ۙͰͷMPTTΛܭࢉ͢Δ w ऩଋઌͰ࠷ऴ૚ͷॏΈϕΫτϧʹݻ༗ϕΫτϧΛ଍ͯͦ͜͠ͰͷMPTTΛٻΊͯɼҾ͍ͯऩଋઌʹ ໭͢Λ܁Γฦ͢ʢ໭࣌͢ʹ਺஋ޡ͕ࠩൃੜͯ͠͠·͏͕ՄࢹԽʹ͸ͦ͜·ͰӨڹ͠ͳ͍ʜ͸ ͣʣ 20

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࣮૷ w ιʔείʔυ͸(JUIVCʹ্͛·ͨ͠ w IUUQTHJUIVCDPNNULX5)FTTJBOCBTFEBOBMZTJTUFOTPSqPX 21

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࣮ݧ݁Ռ 22 όοναΠζ͕େ͖͘ͳΔ΄ͲTIBSQNJOJNVN

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·ͱΊ w ॏΈʹؔ͢ΔϔοηߦྻͰ΋όοναΠζʹΑΔӨڹ͸େ͖͍ w খ͍͞όοναΠζ͸ॏΈͷઁಈʹରͯ͠ϩόετͳύϥϝʔλʹ౸ୡ͢Δ 23

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ؔ࿈࿦จϦετ w )PDISFJUFS 'MBUNJOJNB /FVSBM$PNQVUBUJPO  IUUQ XXXCJPJOGKLVBUQVCMJDBUJPOTPMEFSQEG w -V$VO &⒏DJFOU#BDLQSPQ /FVSBMOFUXPSLT5SJDLTPGUIFUSBEF   IUUQZBOOMFDVODPNFYECQVCMJTQEGMFDVOCQEG w ,FTLBS 0O-BSHF#BUDI5SBJOJOHGPS%FFQ-FBSOJOH(FOFSBMJ[BUJPO(BQ BOE4IBSQ.JOJNB  *$-3 IUUQTBSYJWPSHBCT w 4BHVO &NQJSJDBM"OBMZTJTPGUIF)FTTJBOPG0WFS1BSBNFUSJ[FE/FVSBM /FUXPSLT  *$-3 IUUQTBSYJWPSHBCT 24