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人知工能入門
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DaichiWarasuga
June 24, 2025
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人知工能入門
DaichiWarasuga
June 24, 2025
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Transcript
*44%BJDIJ ਓೳ ೖߨ࠲ "SUJ fi DJBM*OUFMJHFOUF$PSTF A
INDEX ʮχϡʔϥϧωοτϫʔΫʯͱʁ ʮ"*Λֶशͤ͞Δʯͱʁ ݴޠͷѻ͍ํͱʁ ࠓ͢༰
χϡʔϥϧωοτϫʔΫ ۚͷΑ͏ʹݱΛۙࣅ͢Δ ʮχϡʔϥϧωοτϫʔΫʯͱ
χϡʔϥϧωοτϫʔΫͱʁ ਆܦࡉ๔ʢχϡʔϩϯʣ͔ΒͳΔΛͨ͠ख๏ Ͱχϡʔϩϯͱʁ
χϡʔϥϧωοτϫʔΫͱʁ ਆܦࡉ๔ʢχϡʔϩϯʣ͔ΒͳΔΛͨ͠ख๏ Ͱχϡʔϩϯͱʁ ᶃܹΛड͚Δ
χϡʔϥϧωοτϫʔΫͱʁ ਆܦࡉ๔ʢχϡʔϩϯʣ͔ΒͳΔΛͨ͠ख๏ Ͱχϡʔϩϯͱʁ ᶄใΛ౷߹͢Δ
χϡʔϥϧωοτϫʔΫͱʁ ਆܦࡉ๔ʢχϡʔϩϯʣ͔ΒͳΔΛͨ͠ख๏ Ͱχϡʔϩϯͱʁ ᶅୡ͢Δ͠ͳ͍Λܾఆ
χϡʔϥϧωοτϫʔΫͱʁ ਆܦࡉ๔ʢχϡʔϩϯʣ͔ΒͳΔΛͨ͠ख๏ Ͱχϡʔϩϯͱʁ ᶆใΛୡ
ʹdԯݸͷχϡʔϩϯ dԯ w୯७ͳߏͰͨ͘͞Μܨ͕Εڧྗ wಉ༷ʹɺ//୯७ͳॲཧͷू·Γ
ਓޱχϡʔϩϯ ͜ΜͳͷΛߟ͑·͢ x1 x2 xm + Act ;
b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ ग़ྗ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳͷ
ਓޱχϡʔϩϯ ͜ΜͳͷΛߟ͑·͢ x1 x2 xm + Act ;
b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳͷ
ਓޱχϡʔϩϯ ͜ΜͳͷΛߟ͑·͢ x1 x2 xm + Act ;
b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳͷ ᶄೖྗΛ౷߹
ਓޱχϡʔϩϯ ͜ΜͳͷΛߟ͑·͢ x1 x2 xm + Act ;
b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳͷ ᶄೖྗΛ౷߹ ᶅൃՐ͢Δ͔ΛܾΊΔ
ਓޱχϡʔϩϯ ͜ΜͳͷΛߟ͑·͢ x1 x2 xm + Act ;
b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳͷ ᶄೖྗΛ౷߹ ᶅൃՐ͢Δ͔ΛܾΊΔ ᶆ࣍ͷχϡʔϩϯ
ਓޱχϡʔϩϯ ˣʮχϡʔϥϧωοτϫʔΫͱݴ͑ʯͷਤ w͜ΕਓޱχϡʔϩϯΛͨ͘͞ΜूΊͨਤ wͱࣅͯΔʜ ΑͶʜ wશମෳࡶոح͗ͯ͢ཧղෆೳ Ұͭͷχϡʔϩϯʹ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ ॏΈɺύϥϝʔλͱ͍͏ ग़ྗ
࣍ͷχϡʔϩϯͷೖྗͱݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) x z +Act b(1) w(1) w(2) b(2)
࠷୯७ͳ//ΛࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ ॏΈɺύϥϝʔλͱ͍͏ ग़ྗ
࣍ͷχϡʔϩϯͷೖྗͱݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) x z +Act b(1) w(1) w(2) b(2)
׆ੑԽ͍ؔͬͺ͍͋Δ 3F-6 -FBLZ3F-6 4XJTI (&-6 1.εςοϓؔ(step) 2.߃ؔ(identity) 3.Bent Identityؔ
4.hardShrinkؔ 5.softShrinkؔ 6.Thresholdؔ 7.γάϞΠυؔ(sigmoid) 8.hardSigmoidؔ 9.logSigmoidؔ 10.tanhؔ 11.tanhShrinkؔ 12.hardtanhؔ 13.ReLUؔ 14.ReLU6ؔ 18.leaky-ReLUؔ 19.ELUؔ 20.SELUؔ 21.CELUؔ 22.ιϑτϚοΫεؔ(softmax) 23.softminؔ 24.logSoftmaxؔ 25.softplusؔ 26.softsignؔ 27.Swishؔ 28.hardSwishؔ 29.ACONؔ 30.Mishؔ 31.tanhExpؔ ˞࣌
׆ੑԽؔͷׂ ReLU(x) = max(0,x) "DUJWBUF x = 0 ཁ͢Δʹ
׆ੑԽؔɺ ೖྗΛ͏͔ࣺͯΔ͔ΛܾΊ͍ͯΔ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ ॏΈɺύϥϝʔλͱ͍͏ ग़ྗ
࣍ͷχϡʔϩϯͷೖྗͱݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) z(x) = 1 ⋅ Act(1 ⋅ x + 0) + 0 ม͕ଟ͍ͱ͍͠ˠ୯७Խͯ͠৭ʑࢼ͢
࠷୯७ͳ//ΛࣜͰॻ͘ͱ z(x) = 1 ⋅ Act(w(1) ⋅ x +
0) + 0 w(1) = − 2 w(1) = 2 w(1) = 0 ͖ͱંΕΔαΠυΛܾఆ͢Δύϥϝʔλ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ z(x) = 1 ⋅ Act(1 ⋅ x +
b(1)) + 0 b(1) = − 2 b(1) = 2 b(1) = 0 ԣҠಈΛܾఆ͢Δύϥϝʔλ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ z(x) = w(2) ⋅ Act(1 ⋅ x +
0) + 0 w(2) = − 2 w(2) = 2 w(2) = 0 ંΕΔ͖Λܾఆ͢Δύϥϝʔλ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ z(x) = 1 ⋅ Act(1 ⋅ x +
0) + b(2) b(2) = − 2 b(2) = 2 b(2) = 0 ॎҠಈΛܾఆ͢Δύϥϝʔλ
࠷୯७ͳ//ΛࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ ॏΈɺύϥϝʔλͱ͍͏ ग़ྗ
࣍ͷχϡʔϩϯͷೖྗͱݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) ͋ΒΏΔzΧυzΛදݱͰ͖Δ z(x)
χϡʔϩϯΛԿݸ͔ܨ͛Δͱʜ w͍ΖΜͳҐஔʹΧυ͕Ͱ͖Δ w͜ΕΒΛ͠߹ΘͤΔͱχϡʔϩϯͷ͚ͩંΕΔ
χϡʔϥϧωοτϫʔΫ ۚͷΑ͏ʹݱΛۙࣅ͢Δ
INDEX ʮχϡʔϥϧωοτϫʔΫʯͱʁ ʮ"*Λֶशͤ͞Δʯͱʁ ݴޠͷѻ͍ํͱʁ ࠓ͢༰
ֶशͱ σʔλ͔ΒؔͷܗΛ ܾΊΔ͜ͱ ʮ"*Λֶशͤ͞Δʯͱʁ
ֶशલͬͯͲ͏ͳ͍ͬͯΔͷʁ ໌ͷఱؾ<."4,>Ͱ͢ ֶशલ ֶशޙ ͱΓ͋͑ͣύϥϝʔλʹཚΛׂΓ͍ͯͯΔ ͜ͷ··ͰϥϯμϜંΕઢੜث ۮ વ ্
Ґ ͳ ͩ ͚ cl-tohoku/bert-base-japanese-v3
ֶशͷత ֶशͱ ϥϯμϜͳύϥϝʔλΛzྑ͍ײ͡zʹௐ͢Δ͜ͱ ຊߨ࠲Ͱͷଛࣦؔ λεΫʹର͢Δੑೳ͕ ྑ͚Εɺখ͍͞Λฦ͢ ѱ͚Εɺେ͖͍Λฦ͢ ཁ͢Δʹʮਖ਼ղͱ༧ଌͷࠩʯ ٯ͋ΔΑ
FHڧԽֶशͷใुؔ zྑ͍ײ͡zͱʁ ଛࣦؔΛ࠷খԽ͢Δ͜ͱ
ଛࣦؔͷΠϝʔδ ଛࣦਖ਼ղͱϞσϧͷ༧ଌͷࠩ ฏۉೋଛࣦ ଛ ࣦ େ Loss =
∑ i (y(xi ) − ti) 2 ଛࣦσʔλ ʹґଘ͢Δ (xi , ti ) ଛ ࣦ খ
࣮ࡍʹଛࣦΛখͯ͘͞͠ΈΔ Loss(w) = ∑ i (wxi − ti )2
= ∑ i (x2 i w2 − 2xi ti w + t2 i ) = (∑ i x2 i ) w2 − 2 (∑ i xi ti) w + (∑ i t2 i ) ࠷؆୯ͳϞσϧ ୯ճؼ Ͱߟ͑Δ yw (x) = wx Loss(w) = ∑ i (yw (xi ) − ti )2 Ϟσϧɿ ଛࣦؔɿ ͜ͷͱ͖ଛࣦؔ ͨͩͷXʹ͍ͭͯͷ ೋ࣍ؔʹͳΔ
࣮ࡍʹଛࣦΛখͯ͘͞͠ΈΔ ֬ೝ λεΫʹର͢ΔੑೳΛ্͍͛ͨ ˠଛࣦΛখ͍ͨ͘͞͠ ˠଛࣦ͕খ͘͞ͳΔ࣌ͷύϥϝʔλΛٻΊ͍ͨʂ w = ̂ w ʮೋ࣍ؔͷ࠷খʯߴߍҰͷൣғ
%FFQͳ//ෳࡶͳଛࣦؔͰʁ ը૾ग़యIUUQTBSYJWPSHBCT //
%FFQͳ//ෳࡶͳଛࣦؔͰʁ y = fw (x) H(p, q) = −
∑ x p(x)log(q(x)) Ϟσϧɿ ଛࣦؔɿ$SPTTFOUSPQZ-PTT ˞ྨͰΑ͘ΘΕΔఆ൪ͷଛࣦؔ ݫີʹ࠷খղΛٻΊΔ͜ͱෆՄೳʜ ͜ͷͱ͖ͷଛࣦؔͷܗʁ
ύϥϝʔλΛֶशͤ͞Δ͔͠ͳ͍ dస͕ΔϏʔۄͷΑ͏ʹd ʮ"*Λֶशͤ͞Δʯͱʁ
·ֶͣशલͬͯͲ͏ͳͷʁ ͱΓ͋͑ͣύϥϝʔλʹཚΛׂΓ͍ͯͯΔ w(0)
·ֶͣशલͬͯͲ͏ͳͷʁ ͱΓ͋͑ͣύϥϝʔλʹཚΛׂΓ͍ͯͯΔ w(0) ଛࣦؔࣗମΘ͔ΒΜ Ͳ͏ͨ͠ΒଛࣦΛ࠷খԽ͢ΔύϥϝʔλΛݟ͚ͭΒΕΔʁ
ޯ߱Լ๏cΠϝʔδ ہॴతʹଛࣦ͕ݮগ͢ΔํʹύϥϝʔλΛߋ৽͢Δ w(0) ˡ ֦ େ ޯ߱Լ๏ ϞσϧʹσʔλΛೖྗͯ͠ଛࣦΛٻΊΔ
ͦͷଛࣦͷޯΛٻΊΔ ଛࣦؔΛඍͯ͠ಘΔ ύϥϝʔλΛޯํߋ৽͢Δ
ޯ߱Լ๏cΠϝʔδ ہॴతʹଛࣦ͕ݮগ͢ΔํʹύϥϝʔλΛߋ৽͢Δ w(0) ˡ ֦ େ w(1) = w(0) −
η∇w ℒ(w(0)) w(2) = w(1) − η∇w ℒ(w(1)) w(3) = w(2) − η∇w ℒ(w(2)) ⋮ w(s+1) = w(s) − η∇w ℒ(w(s)) ͜ͷล·ͰҠಈ Ͱ͖ͨΒخ͍͠ͳ ߋ৽ͷ෯ଛࣦʹґଘ
ֶशͷҙຯ ߋ৽෯σʔλʹґଘ͢Δ ߋ৽෯ଛࣦʹґଘ͢Δ ଛࣦσʔλʹґଘ͍ͯͨ͠ w(s+1) = w(s) − ηΔw L(w(s))
લड़ͷ௨Γ L(w; x, t)
INDEX ʮχϡʔϥϧωοτϫʔΫʯͱʁ ʮ"*Λֶशͤ͞Δʯͱʁ ݴޠͷѻ͍ํͱʁ ࠓ͢༰
ྔԽ͠ͳ͍ͱ࢝·Βͳ͍ ݴޠͷѻ͍ํͱ
ཧϞσϧ͔͠ೖྗͰ͖ͳ͍ ଟ͘ͷσʔλͰه͞Ε͍ͯΔ ͡Ό͋ݴޠʁ wܗࣜͱͯ͠ه߸ྻ wUIFʹɺZPVʹͱΛׂΓৼΔ͔͠ͳ͍ ؾ ؾԹɺ߱ਫྔͳͲ Ի ৼ෯ͱप
ը૾ ޫͷࡾݪ৭ͷׂ߹
ԽͷҰྫcૄͳϕΫτϧ ࠓΕɻ໌Ӎɻ
ԽͷҰྫcૄͳϕΫτϧ ࠓΕɻ໌Ӎɻ ࠓΕɻ໌Ӎɻ 5PLFOJ[F
ԽͷҰྫcૄͳϕΫτϧ ࠓΕɻ໌Ӎɻ ࠓΕɻ໌Ӎɻ \ɻ ࠓ Ε Ӎ ษڧ
ΧϑΣ େ୩ ʜ^ 5PLFOJ[F $PVOU
ԽͷҰྫcૄͳϕΫτϧ ࠓΕɻ໌Ӎɻ ࠓΕɻ໌Ӎɻ \ɻ ࠓ Ε Ӎ ษڧ
ΧϑΣ େ୩ ʜ^ < ʜ> ༰ʹΑͬͯ༻ޠมԽ͢ΔͷͰ͓͓·͔ͳҙຯଊ͑ΒΕΔ ྫεϙʔπࢴͱܦࡁࢽ 5PLFOJ[F $PVOU 7FDUPSJ[F େ͕ૄ
ૄͳϕΫτϧͷऑ wࢲੁෲେஐͰ͢ɻ wԶੁෲେஐͰ͢ɻ ࣅ͍ͯΔ͠ಉ͡ҙຯ
ૄͳϕΫτϧͷऑ wࢲੁෲେஐͰ͢ɻ wԶੁෲେஐͰ͢ɻ ࣅ͍ͯΔ͠ಉ͡ҙຯ wࢲੁෲେஐͰ͢ɻ w܅ੁෲେஐͰ͢ɻ ࣅ͍ͯΔ͚Ͳҧ͏ҙຯ
ૄͳϕΫτϧͷऑ wࢲੁෲେஐͰ͢ɻ wԶੁෲେஐͰ͢ɻ ࣅ͍ͯΔ͠ಉ͡ҙຯ wࢲੁෲେஐͰ͢ɻ w܅ੁෲେஐͰ͢ɻ ࣅ͍ͯΔ͚Ͳҧ͏ҙຯ \ࢲɺԶɺ܅^ ه߸ͱͯ͠ΈΔͱˠͦΕͧΕҟͳΔ
ݴ༿ͱͯ͠ΈΔͱˠࢲ Զ ܅ ≒ ≠ ୯ޠͷҙຯΛ ଊ͑ΒΕ͍ͯͳ͍
ີͳϕΫτϧcҙຯͷ߹ ֤୯ޠΛ্ۭؒͷ ϕΫτϧ ͱͯ͠ߟ͑Δˠ͠ࢉʹΑΓ߹ΛදݱՄೳʂʂ 2,JOHNBO XPNBO
ີͳϕΫτϧcҙຯͷ߹ ֤୯ޠΛ্ۭؒͷ ϕΫτϧ ͱͯ͠ߟ͑Δˠ͠ࢉʹΑΓ߹ΛදݱՄೳʂʂ 2,JOHNBO XPNBO "2VFFO
ີͳϕΫτϧcҙຯͷ߹ ֤୯ޠΛ্ۭؒͷ ϕΫτϧ ͱͯ͠ߟ͑Δˠ͠ࢉʹΑΓ߹ΛදݱՄೳʂʂ 2*UBMJBO DBST 2+BQBOFT fi
MN
ີͳϕΫτϧcҙຯͷ߹ ֤୯ޠΛ্ۭؒͷ ϕΫτϧ ͱͯ͠ߟ͑Δˠ͠ࢉʹΑΓ߹ΛදݱՄೳʂʂ 2*UBMJBO DBST 2+BQBOFT fi
MN
ີͳϕΫτϧcҙຯͷ߹ ֤୯ޠΛ্ۭؒͷ ϕΫτϧ ͱͯ͠ߟ͑Δˠ͠ࢉʹΑΓ߹ΛදݱՄೳʂʂ 2*UBMJBO DBST 2+BQBOFT fi
MN
ີͳϕΫτϧcҙຯͷྨࣅੑ
ີͳϕΫτϧcҙຯͷྨࣅੑ ͜ͷਤֶश͞ΕͨϕΫτϧ
ີͳϕΫτϧcҙຯͷྨࣅੑ ͜ͷਤֶश͞ΕͨϕΫτϧ Ͳ͏ͬͯҙຯΛֶशͨ͠ʁ
ີͳϕΫτϧcҙຯͷྨࣅੑ ͜ͷਤֶश͞ΕͨϕΫτϧ Ͳ͏ͬͯҙຯΛֶशͨ͠ʁ ͦͦҙຯͱԿ͔ʁ
ݴ༿ͷҙຯ ͦΕࣗͰͳ͘༻Ͱܾ·Δ ݴޠͷѻ͍ํͱ
Ծઆʹ͓͚Δҙຯ 2<."4,>ʹԿ͕ೖΔ͔ʁ wࢲຖ൩<."4,>ΛΈΔͷ͕͖Ͱ͢ɻ w͜ͷ<."4,>࠷৽ܕͳͷͰߴՁͰ͢ɻ w<."4,>ͷϦϞίϯΛݟ͚ͭΒΕͳ͍ɻ wࢲͨͪɺࢼ߹؍ઓ͢ΔͨΊʹ<."4,>Λങͬͨɻ
Ծઆʹ͓͚Δҙຯ 2<."4,>ʹԿ͕ೖΔ͔ʁ wࢲຖ൩<."4,>ΛΈΔͷ͕͖Ͱ͢ɻ w͜ͷ<."4,>࠷৽ܕͳͷͰߴՁͰ͢ɻ w<."4,>ͷϦϞίϯΛݟ͚ͭΒΕͳ͍ɻ wࢲͨͪɺࢼ߹؍ઓ͢ΔͨΊʹ<."4,>Λങͬͨɻ શ෦ʹڞ௨͢Δͱͨ͠Β<ςϨϏ>
Ծઆʹ͓͚Δҙຯ 2<."4,>ʹԿ͕ೖΔ͔ʁ wࢲຖ൩<."4,>ΛΈΔͷ͕͖Ͱ͢ɻ w͜ͷ<."4,>࠷৽ܕͳͷͰߴՁͰ͢ɻ w<."4,>ͷϦϞίϯΛݟ͚ͭΒΕͳ͍ɻ wࢲͨͪɺࢼ߹؍ઓ͢ΔͨΊʹ<."4,>Λങͬͨɻ શ෦ʹڞ௨͢Δͱͨ͠Β<ςϨϏ> ୯ޠͷҙຯɺपғͷ୯ޠʹΑͬͯܗ͞ΕΔ <ςϨϏ>ͷҙຯ<ςϨϏ>͕Ͳ͏ΘΕ͔ͨͰܾ·Δɻ ͜ΕΛԾઆͱ͍͏
Ծઆʹج͍ͮͯλεΫΛઃܭ λεΫͷྫɿ wςϨϏͱϦϞίϯۙ͘ʹग़ݱ͢Δ͔ʁ wલͷϖʔδͷ<."4,>ೖΔݴ༿Կ͔ʁ wఱؾͷޙʹଓ͘ݴ༿ͳʹ͔ʁ ͜ͷλεΫͷਖ਼ղ͕ߴ͘ͳΔΑ͏ʹֶशͤ͞Δ λεΫͱͯ͠ઃܭ ଛࣦؔΛఆٛ ϞσϧΛֶशˠ
ڭ͑ͳ͍ɻ֫ಘͤ͞Δɻ wςϨϏߴ͍ wςϨϏϦϞίϯͰૢ࡞͢Δ wςϨϏݟΔͷ ͜ͷΑ͏ͳࣝΛਓྗͰߏங͢Δͷ໘͗͢Δ ͜ͷࣝΛσʔλ͔ΒࣗಈͰ֫ಘͯ͘͠ΕΔͷ͕"* ߴͳࣝΈࠐΉ͜ͱ͋Δ͕ ҩྍͱ͔
ࣗͷݚڀൣғʹ͍ͭͯগʑʜ ࣝΛΈࠐΉˠΛղ͔ͤΔˠ͕ղ͚Δ Λղ͔ͤΔˠࣝΛ֫ಘ͢Δˠ͕ղ͚Δ Ͱ͖Δ͜ͱ wڧͯ͘ศརͳπʔϧͷ։ൃ ࠷ۙاۀͷಠஃ wࣝͱ͍͏ʹݟ͑ͳ͍ͷΛ۩ݱԽˡͬͪ͜ wਓೳΈͦͷߏΛ࠶ݱͨ͠ͷ
wˠ͡Ό͋ਓؒͱ΄ͱΜͲಉ͡ग़ྗΛ͢ΔਓೳΛ࡞Γɺ ͦͷߏΛௐΕਓؒͷͷߏཧղͰ͖ΔͷͰʁʁ wݴޠͱਤܗతʹͲΜͳܗΛ͍ͯ͠Δʁ wʢ࣮υʔφοπܕʹ͍ͯͨ͠Γͯ͠ʜʣ