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ソーイAI勉強会 第2回:深層学習の計算
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sewii
May 30, 2025
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ソーイAI勉強会 第2回:深層学習の計算
sewii
May 30, 2025
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Transcript
ୈճɿਂֶशͷܭࢉ
ਂֶशͷ෮श
ਂֶशͰͲ͏ݴͬͨ͜ͱΛ͍ͯ͘͠ͷ͔ʁ ਓؒͷΛߟ͑Δ ਆܦࡉ๔ʢχϡʔϩϯʣͷܨ͕Γ ΛཧϞσϧԽ
ೖྗ தؒʢӅΕʣ ग़ྗ
ೖྗ தؒʢӅΕʣ ग़ྗ தؒͷ͕ଟ͍ˠਂֶशͱݺͿ
ͰதؒͰͲͷΑ͏ͳܭࢉΛߦ͏ͷ͔ʁ ࠓͷϝΠϯʂ
׆ੑԽؔͱԿ͔ʁ
தؒͰͷܭࢉͷྲྀΕ ॏΈͷֻ͚ࢉ χϡʔϩϯͷ͠ࢉ ׆ੑԽؔͷม
தؒͰͷܭࢉͷྲྀΕ ॏΈͷֻ͚ࢉ χϡʔϩϯͷ͠ࢉ ׆ੑԽؔͷม ೖྗͷॏཁੑΛԽͨ͠ͷɻ ॏΈΛௐ͢Δ͜ͱͰɺਖ਼֬ͳ༧ଌΛՄೳʹ͢Δɻ
YX YXB ˞ॏΈҎԼͷΑ͏ʹ͏ X XɿॏΈ Y
Yɿೖྗ ྫʣ͠Yͷೖྗ͕ॏཁͰͳͯ͘ɺYͷೖྗ͕ॏཁͩͬͨ߹ Y YB ͷΑ͏ʹ͏ɻ ˠೖྗ৴߸ͷBʹ͍ͨͯ͠ɺΑΓYͷ͕ө͞Ε͍ͯΔɻ
தؒͰͷܭࢉͷྲྀΕ ॏΈͷֻ͚ࢉ χϡʔϩϯͷ͠ࢉ ׆ੑԽؔͷม ೖྗ৴߸͔Βͷใ͕શͯඞཁͳΘ͚Ͱͳ͍ɻ ׆ੑԽؔΛ௨͢͜ͱͰʮͲͷΑ͏ͳใΛ͑Δͷ͔ʯΛܾΊΔɻ ೖྗͷॏཁੑΛԽͨ͠ͷ
Y Y C X X Z
ɿॏΈ X X CɿόΠΞε Yɿೖྗ৴߸ Zɿग़ྗ৴߸ χϡʔϥϧωοτϫʔΫͷܭࢉͷਤࣜԽ χϡʔϩϯͷ͠ࢉΛ ʮZʹมʯͯ͠ग़ྗ
Y Y C X X Z
ɿॏΈ X X CɿόΠΞε χϡʔϥϧωοτϫʔΫͷܭࢉͷਤࣜԽ ग़ྗ ॏΈ͚ͩͰදݱͰ͖ͳ͍෦ ΛόΠΞεͰิڧɻ
BɿZʹૹΒΕͯ͘Δೖྗ৴߸ͷ૯ C YX YXB ॏΈͷֻ͚ࢉ χϡʔϩϯͷ͠ࢉ
ZI B
BɿZʹૹΒΕͯ͘Δೖྗ৴߸ͷ૯ C YX YXB ZI B
׆ੑԽؔͷม ೖྗ৴߸ ೖʂʂ ग़ྗ৴߸ ͜ͷIΛ׆ੑԽؔͱ͍͏ ೖྗΛग़ྗʹมʂʂ
Y Y C X X B
χϡʔϥϧωοτϫʔΫͷܭࢉͷਤࣜԽʢΑΓৄࡉʹʣ Zͱͯ͠ग़ྗ Z I B
׆ੑԽؔͷछྨ γάϞΠυؔ ߃ؔ εςοϓؔ 3FMVؔ ਂֶशͰ ΘΕͳ͍ ݱࡏͰΘ Ε͍ͯΔ ݱࡏओྲྀ
ೖྗΛͦͷ· ·ฦ͢ʢճؼ Ͱ༻ʣ
ޯ๏ͱԿ͔ʁ
ػցֶशͷྲྀΕʢ͓͞Β͍ʣ ֶशʢ܇࿅ʣɿ σʔλΛ͏·͘આ໌Ͱ͖ͦ͏ͳϞσϧΛબͼɺͦͷϞσϧ Λσʔλʹ߹͏Α͏ʹௐ͢Δ͜ͱɻ ਪɿ ֶशͨ͠ϞσϧΛ͔ͭͬͯɺະͷσʔλΛ༧͢Δ͜ͱɻ ˞ʮֶशʹ͓͚Δਖ਼ʯͱʮਪʹ͓͚Δਖ਼ʯ͕͍ۙͱ͖ɺ ֶश͕͏·͍͍ͬͯ͘Δɻ
ਂֶशͰɺ ͲͷΑ͏ʹਖ਼Λ্͍͛ͯ͘ͷ͔ʁ
ଛࣦؔʢϩεؔʣΛ༻͍Δ ਂֶशͰɺ
ଛࣦʢϩεʣؔɿ ʮͲΕ͘Β͍ਖ਼ղσʔλͱҟͳΔ͔ʯΛදؔ͢ ଛࣦؔͱ ͭ·Γਖ਼Λ্͛Δʹɺଛࣦؔখ͍͞ํ͕͍͍ʂʂ
ޯ๏ͱɺ ͜ͷଛࣦؔΛখ͍ͯ͘͘͞͠ख๏Λࢦ͢
ͦͦޯͱʁ ଛࣦؔʹର͢ΔॏΈͷඍ ∂E ∂w = [ ∂E ∂w1 ⋯ ∂E
∂wn ] Ͱද͞ΕΔ XʢॏΈʣΛม͑ͨ࣌ʹɺ&ʢଛࣦؔʣ͕ͲΕ͘Β͍มΘΔ͔
ʮޯ๏ʯͷΠϝʔδ ॏΈ ଛࣦؔ ଛࣦ͕ؔݮগ͢Δํʹ ύϥϝʔλʢॏΈʣΛߋ৽ ˠଛࣦؔΛͰ͖Δ͚ͩখ͘͢͞Δɻ
ʮޯ๏ʯͷࣜ wnew = wold − η × ∂E ∂w ʢߋ৽ޙͷॏΈʣʢߋ৽લͷॏΈʣʢֶशʣºʢޯʣ
˞ֶशʢБʣɿճͷֶशͰͲΕ͘Β͍ύϥϝʔλΛߋ৽͢Δ͔ ޯํʹҠಈ͢Δྔ
ʮޯ๏ʯͷࣜͳʹΛද͍ͯ͠Δͷ͔ʁ ॏΈʢXʣ ଛࣦؔʢ&ʣ ϶X ޯෛ ߋ৽લ ߋ৽ޙ ͲͷΑ͏ʹॏΈ͕ߋ৽͞ΕΔͷ͔ʁ wnew =
wold − η × ∂E ∂w ʢྫʣޯ͕ෛ ˠ"ਖ਼ ˠߋ৽લͷXʹ"͕͞ΕΔ ˠXӈʹҠಈʢߋ৽ʣ "ͱ͢Δ
ɾޯ๏ͱଛࣦؔΛখ͘͢͞ΔͨΊʹɺॏΈΛߋ৽͍ͯ͘͜͠ͱɻ ޯ๏·ͱΊ ɾޯͱ ʮXʢॏΈʣΛม͑ͨ࣌ʹɺ&ʢଛࣦؔʣ͕ͲΕ͘Β͍มΘΔ͔ʯ Λද͢ɻ ɾ ʹΑͬͯॏΈͷߋ৽Λߦ͏ wnew = wold
− η × ∂E ∂w
ޡࠩٯ๏ͱԿ͔ʁ
wnew = wold − η × ∂E ∂w ˣˣˣॏΈͷܭࢉɺԼͷࣜͰٻΊ͍͚͍͍ͯ X
X X ॏΈͷมԽΛΈΑ͏ʂ ˠXΛಈ͔ͯ͠ΈΔ ˠXΛΛม͑Δͱͦͷ͋ͱશͯʹӨڹ ˠܭࢉ͕େมʂʂ ॱ
ޡࠩٯ๏ɿ ॏΈύϥϝʔλʹΑΔޯͷܭࢉΛޮྑ͘ߦͳ͏ํ๏ɻ
ޡࠩٯ๏ɿ ॏΈύϥϝʔλʹΑΔޯͷܭࢉΛޮྑ͘ߦͳ͏ํ๏ɻ ▶︎ ͳʹ͕ٯͳͷ͔ʁ
ޡࠩٯ๏ɿ ॏΈύϥϝʔλʹΑΔޯͷܭࢉΛޮྑ͘ߦͳ͏ํ๏ɻ ˞ॏΈͷߋ৽ˠޯ ▶︎ ͳʹ͕ٯͳͷ͔ʁ ग़ྗΛελʔτͱͯ͠ɺॏΈͷ ߋ৽Λߟ͑Δ ٯ
ޡࠩٯ๏ͰޯΛٻΊΔͷܭࢉ͕͍͠ͷͰলུ͢Δ͕ɺ ޡࠩٯ๏Λ͏ͱ ʮग़ྗͰͷਖ਼ղϥϕϧͱͷޡࠩʯ͕Θ͔Ε શͯͷޯ͕Θ͔Δɻ
ɾॱ༧ଌΛग़ྗ͢ΔͨΊʹ༻͍Δɻ ޡࠩٯ๏·ͱΊ ɾॱͰޯ๏Λܭࢉ͢ΔͱɺͰ͖ͳ͍͜ͱͳ͍͕ɺܭࢉ ίετ͕ߴ͗͢Δɻ ɾޡࠩٯํΛ༻͍Δ͜ͱͰɺ ʮग़ྗͰͷਖ਼ղϥϕϧͱͷޡࠩʯ͕Θ͔Εશͯͷޯ͕Θ͔Δɻ
ਂֶशͷֶशͱਪ·ͱΊ
ॱʹΑΓ༧ଌΛग़ྗ ਂֶशͷֶशํ๏ ༧ଌͱਖ਼ղϥϕϧͷζϨΛ Խ ͦͷζϨΛͬͯҰؾʹޯ Λܭࢉ ֶशΛ͔͚ͯॏΈΛम wnew = wold
− η × ∂E ∂w ▶︎ ▶︎ ▶︎ ▶︎
ਪͲͷΑ͏ʹߦͳ͏ͷ͔ʁ ώϯτɿਪͰະͷσʔλΛ༧ଌ͠ɺϞσϧͷධՁΛߦ͏
ॱʹΑΓ༧ଌΛग़ྗ ਂֶशͷਪํ๏ ༧ଌͱਖ਼ղϥϕϧͷζϨΛ Խ ͦͷζϨΛͬͯҰؾʹޯ Λܭࢉ ֶशΛ͔͚ͯॏΈΛम wnew = wold
− η × ∂E ∂w ▶︎ ▶︎ ▶︎ ▶︎
ॱʹΑΓ༧ଌΛग़ྗ ਂֶशͷਪํ๏ ༧ଌͱਖ਼ղϥϕϧͷζϨΛ Խ ▶︎ ˒ਪͰॱ͔͠ߦΘͳ͍ʂʂ
࣍ճͷ༧ఆ
ਖ਼ଇԽ ΈࠐΈχϡʔϥϧωοτϫʔΫ ࣗવݴޠॲཧಋೖ