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人知工能入門

 人知工能入門

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DaichiWarasuga

June 24, 2025
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  1. ਓޱχϡʔϩϯ  ͜Μͳ΋ͷΛߟ͑·͢  x1 x2 xm + Act ;

    b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ਺ ग़ྗ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳ΋ͷ
  2. ਓޱχϡʔϩϯ  ͜Μͳ΋ͷΛߟ͑·͢  x1 x2 xm + Act ;

    b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ਺ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳ΋ͷ
  3. ਓޱχϡʔϩϯ  ͜Μͳ΋ͷΛߟ͑·͢  x1 x2 xm + Act ;

    b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ਺ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳ΋ͷ ᶄೖྗΛ౷߹
  4. ਓޱχϡʔϩϯ  ͜Μͳ΋ͷΛߟ͑·͢  x1 x2 xm + Act ;

    b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ਺ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳ΋ͷ ᶄೖྗΛ౷߹ ᶅൃՐ͢Δ͔ΛܾΊΔ
  5. ਓޱχϡʔϩϯ  ͜Μͳ΋ͷΛߟ͑·͢  x1 x2 xm + Act ;

    b w1 w2 wm ೖྗ ॏΈ ׆ੑԽؔ਺ ग़ྗ ᶃೖྗΛड͚औΔ χϡʔϩϯͷ݁߹ͷڧ͞ͷΑ͏ͳ΋ͷ ᶄೖྗΛ౷߹ ᶅൃՐ͢Δ͔ΛܾΊΔ ᶆ࣍ͷχϡʔϩϯ΁
  6. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ਺ ॏΈɺύϥϝʔλͱ΋͍͏ ग़ྗ

    ࣍ͷχϡʔϩϯ΁ͷೖྗͱ΋ݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2)  x  z +Act b(1) w(1) w(2) b(2)
  7. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ਺ ॏΈɺύϥϝʔλͱ΋͍͏ ग़ྗ

    ࣍ͷχϡʔϩϯ΁ͷೖྗͱ΋ݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2)  x  z +Act b(1) w(1) w(2) b(2)
  8. ׆ੑԽؔ਺͸͍ͬͺ͍͋Δ  3F-6 -FBLZ3F-6 4XJTI (&-6 1.εςοϓؔ਺(step) 2.߃౳ؔ਺(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਺ ˞೥࣌఺
  9. ׆ੑԽؔ਺ͷ໾ׂ  ReLU(x) = max(0,x) "DUJWBUF x = 0 ཁ͢Δʹ

    ׆ੑԽؔ਺͸ɺ ೖྗΛ࢖͏͔ࣺͯΔ͔ΛܾΊ͍ͯΔ
  10. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ਺ ॏΈɺύϥϝʔλͱ΋͍͏ ग़ྗ

    ࣍ͷχϡʔϩϯ΁ͷೖྗͱ΋ݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) z(x) = 1 ⋅ Act(1 ⋅ x + 0) + 0 ม਺͕ଟ͍ͱ೉͍͠ˠ୯७Խͯ͠৭ʑࢼ͢
  11. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ  z(x) = 1 ⋅ Act(w(1) ⋅ x +

    0) + 0 w(1) = − 2 w(1) = 2 w(1) = 0 ܏͖ͱંΕΔαΠυΛܾఆ͢Δύϥϝʔλ
  12. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ  z(x) = 1 ⋅ Act(1 ⋅ x +

    b(1)) + 0 b(1) = − 2 b(1) = 2 b(1) = 0 ԣҠಈΛܾఆ͢Δύϥϝʔλ
  13. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ  z(x) = w(2) ⋅ Act(1 ⋅ x +

    0) + 0 w(2) = − 2 w(2) = 2 w(2) = 0 ંΕΔ޲͖Λܾఆ͢Δύϥϝʔλ
  14. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ  z(x) = 1 ⋅ Act(1 ⋅ x +

    0) + b(2) b(2) = − 2 b(2) = 2 b(2) = 0 ॎҠಈΛܾఆ͢Δύϥϝʔλ
  15. ࠷΋୯७ͳ//Λ਺ࣜͰॻ͘ͱ x w, b z "DU ೖྗ ׆ੑԽؔ਺ ॏΈɺύϥϝʔλͱ΋͍͏ ग़ྗ

    ࣍ͷχϡʔϩϯ΁ͷೖྗͱ΋ݟ͑Δ z(x) = w(2)Act(w(1)x + b(1)) + b(2) ͸͋ΒΏΔzΧυzΛදݱͰ͖Δ z(x)
  16. ଛࣦؔ਺ͷΠϝʔδ  ଛࣦ͸ਖ਼ղͱϞσϧͷ༧ଌͷࠩ ฏۉೋ৐ଛࣦ ଛ ࣦ  େ Loss =

    ∑ i (y(xi ) − ti) 2 ଛࣦ͸σʔλ ʹґଘ͢Δ (xi , ti ) ଛ ࣦ  খ
  17. ࣮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 ଛࣦؔ਺ɿ ͜ͷͱ͖ଛࣦؔ਺͸ ͨͩͷXʹ͍ͭͯͷ ೋ࣍ؔ਺ʹͳΔ
  18. %FFQͳ//ෳࡶͳଛࣦؔ਺Ͱ͸ʁ  y = fw (x) H(p, q) = −

    ∑ x p(x)log(q(x)) Ϟσϧɿ ଛࣦؔ਺ɿ$SPTTFOUSPQZ-PTT ˞෼ྨ໰୊ͰΑ͘࢖ΘΕΔఆ൪ͷଛࣦؔ਺ ݫີʹ࠷খղΛٻΊΔ͜ͱ͸ෆՄೳʜ ͜ͷͱ͖ͷଛࣦؔ਺ͷܗ͸ʁ
  19. ޯ഑߱Լ๏cΠϝʔδ ہॴతʹଛࣦ͕ݮগ͢Δํ޲ʹύϥϝʔλΛߋ৽͢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৽ͷ෯͸ଛࣦʹґଘ
  20. ਺஋ԽͷҰྫcૄͳϕΫτϧ  ࠓ೔͸੖Εɻ໌೔͸Ӎɻ ࠓ೔͸੖Εɻ໌೔͸Ӎɻ \ɻ ͸ ࠓ೔ ੖Ε Ӎ ษڧ

    ΧϑΣ େ୩ ʜ^ <        ʜ> ಺༰ʹΑͬͯ࢖༻ޠ΋มԽ͢ΔͷͰ͓͓·͔ͳҙຯ͸ଊ͑ΒΕΔ ྫεϙʔπࢴͱܦࡁࢽ 5PLFOJ[F $PVOU 7FDUPSJ[F େ൒͕ૄ
  21. ࣗ෼ͷݚڀൣғʹ͍ͭͯগʑʜ  ஌ࣝΛ૊ΈࠐΉˠ໰୊Λղ͔ͤΔˠ໰୊͕ղ͚Δ ໰୊Λղ͔ͤΔˠ஌ࣝΛ֫ಘ͢Δˠ໰୊͕ղ͚Δ Ͱ͖Δ͜ͱ wڧͯ͘ศརͳπʔϧͷ։ൃ ࠷ۙ͸اۀͷಠஃ৔  w஌ࣝͱ͍͏໨ʹݟ͑ͳ͍΋ͷΛ۩ݱԽˡͬͪ͜ wਓ޻஌ೳ͸೴Έͦͷߏ଄Λ࠶ݱͨ͠΋ͷ

    wˠ͡Ό͋ਓؒͱ΄ͱΜͲಉ͡ग़ྗΛ͢Δਓ޻஌ೳΛ࡞Γɺ ͦͷߏ଄Λௐ΂Ε͹ਓؒͷ೴ͷߏ଄΋ཧղͰ͖ΔͷͰ͸ʁʁ wݴޠͱ͸ਤܗతʹͲΜͳܗΛ͍ͯ͠Δʁ wʢ࣮͸υʔφοπܕʹ෼෍͍ͯͨ͠Γͯ͠ʜʣ