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第3回ソーイAI勉強会:深層学習基礎 最終回
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sewii
May 30, 2025
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第3回ソーイAI勉強会:深層学習基礎 最終回
sewii
May 30, 2025
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Transcript
ୈճɿਂֶशجૅ࠷ऴճ
લճ·Ͱͷ෮श ਫ਼Λ্͛ΔֶशςΫχοΫʢਖ਼ଇԽɿ%SPQPVUʣ ΈࠐΈχϡʔϥϧωοτϫʔΫʢ$//ʣͱʁ
લճ·Ͱͷ෮श
ਂֶशͰͲ͏ݴͬͨ͜ͱΛ͍ͯ͘͠ͷ͔ʁ ਓؒͷΛߟ͑Δ ਆܦࡉ๔ʢχϡʔϩϯʣͷܨ͕Γ ΛཧϞσϧԽ
ೖྗ தؒʢӅΕʣ ग़ྗ தؒͷ͕ଟ͍ˠਂֶशͱݺͿ
ͰதؒͰͲͷΑ͏ͳܭࢉΛߦ͏ͷ͔ʁ
Y Y C X X B
χϡʔϥϧωοτϫʔΫͷܭࢉͷਤࣜԽʢΑΓৄࡉʹʣ Zͱͯ͠ग़ྗ Z I B ׆ੑԽؔ
ଛࣦؔʢϩεؔʣΛ༻͍Δ ਂֶशͰɺ
ޯ๏ͱɺ ͜ͷଛࣦؔΛখ͍ͯ͘͘͞͠ख๏Λࢦ͢
ॏΈʢXʣ ଛࣦؔʢ&ʣ ϶X ޯෛ ߋ৽લ ߋ৽ޙ ͲͷΑ͏ʹॏΈ͕ߋ৽͞ΕΔͷ͔ʁ wnew = wold
− η × ∂E ∂w ʢྫʣޯ͕ෛ ˠ"ਖ਼ ˠߋ৽લͷXʹ"͕͞ΕΔ ˠXӈʹҠಈʢߋ৽ʣ "ͱ͢Δ
wnew = wold − η × ∂E ∂w ˣˣˣॏΈͷܭࢉɺԼͷࣜͰٻΊ͍͚͍͍ͯ X
X X ॏΈͷมԽΛΈΑ͏ʂ ˠXΛಈ͔ͯ͠ΈΔ ˠXΛΛม͑Δͱͦͷ͋ͱશͯʹӨڹ ˠܭࢉ͕େมʂʂ ॱ
ޡࠩٯ๏ɿ ॏΈύϥϝʔλʹΑΔޯͷܭࢉΛޮྑ͘ߦͳ͏ํ๏ɻ ˞ॏΈͷߋ৽ˠޯ ▶︎ ͳʹ͕ٯͳͷ͔ʁ ग़ྗΛελʔτͱͯ͠ɺॏΈͷ ߋ৽Λߟ͑Δ ٯ
ޡࠩٯ๏ͰޯΛٻΊΔͷܭࢉ͕͍͠ͷͰলུ͢Δ͕ɺ ޡࠩٯ๏Λ͏ͱ ʮग़ྗͰͷਖ਼ղϥϕϧͱͷޡࠩʯ͕Θ͔Ε શͯͷޯ͕Θ͔Δɻ
ॱʹΑΓ༧ଌΛग़ྗ ਂֶशͷֶशํ๏ ༧ଌͱਖ਼ղϥϕϧͷζϨΛ Խ ͦͷζϨΛͬͯҰؾʹޯ Λܭࢉ ֶशΛ͔͚ͯॏΈΛम wnew = wold
− η × ∂E ∂w ▶︎ ▶︎ ▶︎ ▶︎
ॱʹΑΓ༧ଌΛग़ྗ ਂֶशͷਪํ๏ ༧ଌͱਖ਼ղϥϕϧͷζϨΛ Խ ͦͷζϨΛͬͯҰؾʹޯ Λܭࢉ ֶशΛ͔͚ͯॏΈΛम wnew = wold
− η × ∂E ∂w ▶︎ ▶︎ ▶︎ ▶︎
ਫ਼Λ্͛ΔֶशςΫχοΫ
աֶशɿֶशʹΘΕͨσʔλʹաʹͯ·ͬͯ͠·͏͜ͱɻ
IUUQTRJJUBDPNDFWBQPSBUPSJUFNTGCFFFGD
ਖ਼ଇԽͱԿ͔ʁ
ਖ਼ଇԽˠաֶशΛ͙ํ๏ ਂֶशͰ༻͍ΒΕΔਖ਼ଇԽͱͯ͠ɺ8FJHIU %FDBZͱ%SPQPVUͳͲ͕͋Δɻ ˠ%SPQPVUʹ͍ͭͯઆ໌͢Δ
%SPQPVUʹ͍ͭͯ IUUQTEBUBBOBMZUJDTGVOVOEFSTUBOEJOHESPQPVU χϡʔϩϯΛϥϯμϜʹফڈֶͯ͠श͢Δํ๏
ʲಛʳ ಛఆͷχϡʔϩϯͷґଘΛݮ Β͢͜ͱͰΦʔόʔϑΟοςΟϯ άΛݮΒ͢ɻ
ʲಛ̎ʳ ෳͷϞσϧΛߏங֤͠Ϟσϧͷ༧ଌΛฏۉ͢Δͱɺଟ͘ͷ ߹Ͱ༧ଌਫ਼্͕͕ΔʢDGΞϯαϯϒϧֶशʣ
ˠόονਖ਼نԽɿޯফࣦɾޯരൃΛ͙ํ๏ %SPQPVUҎ֎ʹਂֶशͰޯരൃɺޯফࣦɺաֶश Λղܾ͢ΔͨΊʹ͍͔ͭ͘ͷํ๏͕औΒΕ͍ͯΔɻ ˠॏΈͷॳظʢখ͘͢͞ΔʣɿաֶशΛ͑Δ ˠ--ਖ਼ଇԽɿաֶशΛ͑Δ
ิ ʢཧ༝ʣॏΈ͕େ͖ա͗Δͱೖྗ৴߸͕աେʹͳͬͯ͠·͏ ೖྗͷ߹ܭ ग़ྗ ೖྗ͕େ͖ա͗Δͱ ग़ྗͷදݱྗ͕গͳ͘ͳΔ
Y Y C X X B
χϡʔϥϧωοτϫʔΫͷܭࢉͷਤࣜԽʢΑΓৄࡉʹʣ Zͱͯ͠ग़ྗ Z I B ׆ੑԽؔ
·ͱΊ ޯരൃɺޯফࣦɺաֶशͱ͍ͬͨ՝Λղܾ͢ΔͨΊʹ ͨ͘͞Μͷํ๏͕औΒΕ͍ͯΔɻ ਖ਼ଇԽաֶशΛ͑ΔͨΊʹ༻͍Δख๏ %SPQPVUਖ਼ଇԽͷҰͭͰχϡʔϩϯΛϥϯμϜʹফڈͯ͠ ֶश͢Δํ๏
ΈࠐΈχϡʔϥϧωοτϫʔΫʢ$//ʣͱʁ
͜Ε·Ͱֶशͨ͠ਂֶशͰ ʮը૾ʯΛͲͷΑ͏ʹදݱ͍ͯͨ͠ͷ͔ʁ IUUQT[FSPPOFKQMFBSOJOHCMPHDOOGPSCFHJOOFST ύϥϝʔλͷΛݮΒ͢͜ͱͰܭࢉྔΛԼ͛Δɻ
̎࣍ݩ͔Β̍࣍ݩʹ͢Δ࣌ʹը૾ͷॏཁͳҐஔใ͕ࣦΘΕͯ͠·͏ɻ
̏࣍ݩͷใΛࣦΘͣʹχϡʔϥϧωοτϫʔΫΛߏங͍ͨ͠ʂʂ ը૾σʔλ3(#ͷΛؚΊͯ̏࣍ݩ ͷσʔλʹͳ͍ͬͯΔɻ
̏࣍ݩͷใΛࣦΘͣʹχϡʔϥϧωοτϫʔΫΛߏங͍ͨ͠ʂʂ ΈࠐΈχϡʔϥϧωοτϫʔΫʢ$//ʣ ը૾σʔλ3(#ͷΛؚΊͯ̏࣍ݩ ͷσʔλʹͳ͍ͬͯΔɻ
$//ͷߏ
$//ͷߏ ΈࠐΈ ׆ੑԽؔ ϓʔϦϯά
ΈࠐΈ
͜Ε·ͰೖྗͷॏཁੑΛ ॏΈʢόΠΞεʣʹΑͬͯཧ͍ͯͨ͠ɻ ˞ॏΈˠೖྗͷॏཁੑ
$//ͰɺॏΈͰͳ͘ϑΟϧλΛ༻͍Δ IUUQT[FSPPOFKQBJXPSEDPOWPMVUJPO ˞ΈࠐΈͰͷग़ྗσʔλΛಛϚοϓͱ͍͏
IUUQTRJJUBDPNOWUPNPJUFNTBGGE ff BCF ΈࠐΈԋࢉͷํ๏ ۙ͘ͷใΛҡ࣋ͨ͠·· ಛྔΛநग़Ͱ͖ͨʂʂ
ΈࠐΈͷϙΠϯτ ΈࠐΈͰɹಛྔͷநग़͕͍ͪΜͷత ը૾ʹ͓͚ΔҐஔใΛอ࣋ͨ͠··ಛΛநग़Ͱ͖Δ
ϓʔϦϯά
நग़͞Εͨಛʹରͯ͠ ʮϩόετੑʢ҆ఆੑʣʯΛ༩͑Δ IUUQTBJTNJMFZDPKQBJ@OFXTDOO ˞ҰͭҰͭͷΈࠐΈԋࢉΛߦͳͬͨޙɺ׆ੑԽؔΛ௨ͯ͠ग़ ྗ͞Εͨಛͷڧ͞Λද͢ɻ
ಛ͕ը૾ͷͲ͜ʹ͋Δ͔ʹࠨӈ͞ΕͣʹॲཧͰ͖ΔΑ͏ʹ͢Δ ը૾̍ ը૾̎
ˠ͜ͷ߹ɺʮ͕͋Δ͔Ͳ͏͔ʯ͕େࣄʂʂ
ಛྔͷ࠷େฏۉΛऔΔ͜ͱͰ ಛྔͷҠಈʢͣΕʣʹڧ͘ͳΔʂʂ ϓʔϦϯάͷϙΠϯτ
$//ͷ·ͱΊ ̏࣍ݩͷใΛࣦΘͣʹχϡʔϥϧωοτϫʔΫΛߏஙͰ͖Δ
࣮ࡍͰ$//ͲͷΑ͏ͳߏͰ༻͍ΒΕΔ͔ʁ
IUUQTYUFDIOJLLFJDPNBUDMMFBSOJOHMFDUVSF ʮΈࠐΈ ϓʔϦϯάʯΛԿॏͶɺ ࠷ޙʹશ݁߹ͰଛࣦؔΛग़ྗ
$//ը૾ೝࣝԻೝࣝͰݱࡏͰඇৗʹ׆ൃʹར༻͞Ε͍ͯΔɻ IUUQTOFXUFDIOPMPHZMJGFTUZMFOFUZPMPEBSLOF IUUQTDWNMFYQFSUHVJEFOFUDBUFHPSZUFSNTEMIVNBOQPTFFTUJBNUJPO IUUQTXXXTLJMMVQBJDPNCMPHUFDITFHNFOUBUJPO ηάϝϯςʔγϣϯ ࢟ਪఆ ମݕग़ ը૾தͷͯ͢ͷϐΫηϧʹҙຯʢΫϥεʣΛׂΓͯΔ ྫ
ˠं ˠೣ
࣍ճͷ༧ఆ
ࣗવݴޠॲཧ