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敷居の低いAI勉強会#3
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asagiman
January 14, 2022
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敷居の低いAI勉強会#3
第3回G検定合格講座
1. 活性化関数
2. 学習率の最適化
3. 更なるテクニック
4. CNN:畳み込みニューラルネットワーク
asagiman
January 14, 2022
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Transcript
Έ͜Ͱ*5 ෑډͷ͍"*ษڧձ ϓϨθϯλʔɹTomohiro Iida ࢀߟॻ੶ɹʮσΟʔϓϥʔχϯάɹGݕఆެࣜςΩετʯɹमɿJDLA
ΞδΣϯμ ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲
./*45ϋϯζΦϯʢʣ
ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲ ./*45ϋϯζΦϯʢʣ
ܦྺ
ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲ ./*45ϋϯζΦϯʢʣ
ࢯ໊ʢϋϯυϧωʔϜՄʣ झຯ ࠓͷே͝ΜԿΛ৯·͔ͨ͠ʁ ࢀՃऀࣗݾհ
ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲ ./*45ϋϯζΦϯʢʣ
(ݕఆ߹֨ߨ࠲ θωϥϦετʹ͍ͭͯ (ݕఆ֓ཁઆ໌ʢఆٛɾࢼݧ༰ʣ ୈ̒ষʢσΟʔϓϥʔχϯάͷख๏ʣ
ࠓޙधཁ͕ߴ·Δ"*ਓࡐͷখ ʮ"*ΤϯδχΞʹݶΒͣͰ͕͢ɺ ࠓɺݱʹΓͳ͍ͷ θωϥϦετͱͯ͠׆༂Ͱ͖Δਓ ͩͱ͍͏͜ͱ͕Α͘ݴΘΕ͍ͯ·͢ɻΞϧΰϦζϜɺΤϯδχΞϦϯάɺϏδ ωεɺͦͷͯ͢ͷͰೳྗΛൃشͰ͖Δਓ͕ٻΊΒΕ͍ͯΔΑ͏Ͱ͢ɻʯ CZגࣜձࣾϝϧΧϦɹ"*ΤϯδχΞɹদԬྰԻ͞Μ IUUQTUZQFKQFUGFBUVSF
IUUQTUZQFKQFUGFBUVSF (ݕఆͷ֓ཁઆ໌ఆٛ (ݕఆͱʁ ɹ"*δΣωϥϦετΛഉग़͢ΔͨΊͷݕఆͷ͜ͱ ɹ"*δΣωϥϦετͱʁ ɹʰσΟʔϓϥʔχϯάͷجૅࣝΛ༗͠ɺదͳ׆༻ํΛܾఆ͠ ͯࣄۀԠ༻͢ΔೳྗΛ࣋ͭਓࡐʱʢ+%-"ެࣜ)1ʣ
(ݕఆͷ֓ཁઆ໌ࢼݧ֓ཁ JDLAެࣜHP ެࣜHPΛࢀর͠·͠ΐ͏ʂ
(ݕఆͷ֓ཁઆ໌ࢼݧ֓ཁ ࣌ؒΊͬͪΌݫ͍͠ ݸͷΛͰղ͢Δʹʹ͔͚ΒΕΔฏۉ࣌ؒඵ ҉هଈͰ͖ΔϨϕϧʹ͠Α͏ʂ ˑ5*14 ɹͯ͢ͷʹνΣοΫϘοΫε͕ଘࡏ͠·͢ɻ ɹগ͠ͰΜͩνΣοΫͯ͠ޙճ͠ʹͯ͠͠·͓͏ʂ
(ݕఆͷ֓ཁઆ໌ࢼݧ֓ཁ ݫ͠Ί ؙ҉هͰͯ͢ʹ͑ΒΕͳ͍ɻ σΟʔϓϥʔχϯάʹؔͯ͠ಛʹཧղΛਂΊ͍ͨͱ͜Ζɻ ˑ5*14 ɹେ·͔ͳߏͪ͜Βɻ ɹਓೳͷجૅࣝʢୈষʙୈষʣɹɹׂ ɹσΟʔϓϥʔχϯάʢୈষʙୈষʣɹɹׂ ɹ࢈ۀͷԠ༻ɾ࣌ࣄʢୈষʙୈষʣׂ
ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲ ./*45ϋϯζΦϯʢʣ
׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ 3//ϦΧϨϯτχϡʔϥϧωοτϫʔΫ
ਂڧԽֶश ਂੜϞσϧ (ݕఆ߹֨ߨ࠲ ୈ6ষ:σΟʔϓϥʔχϯάͷख๏ ׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ
׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ
׆ੑԽؔ ύʔηϓτϩϯʹΑΔܭࢉ ೖྗ தؒ ग़ྗ IUUQTUPLFJOFUOFVSBMOFUXPSLBDUJWBUJPO@GVODUJPO ׆ੑԽؔʹΑΔܭࢉ ׆ੑԽؔ
׆ੑԽؔͷׂ ϞσϧͷදݱྗΛ૿͢ ͜Μͳͷࣅ߹͏ Μ͡Όͳ͍͔͠Β
εςοϓؔ IUUQTUPLFJOFUOFVSBMOFUXPSLBDUJWBUJPO@GVODUJPO ใͷϩε͕ܹ͘͠ දݱྗʹ͍͠ͷ͕ܽ
IUUQTOFXUFDIOPMPHZMJGFTUZMFOFU&&"&#&"&&'&&#&&""&&###&"&$&"&#&"&"' γάϞΠυؔ ೖྗ͕ͨ͠େ͖͚Εେ͖͍΄Ͳʹ͖ۙͮɺ ೖྗ͕ͨ͠খ͚͞Εখ͍͞΄Ͳʹۙͮؔ͘ɻ ݩͷೖྗͷΛࡴ͗͢͠ͳ͍ͱݴ͑Δɻ IUUQTUPLFJOFUOFVSBMOFUXPSLBDUJWBUJPO@GVODUJPO
γάϞΠυؔ χϡʔϥϧωοτϫʔΫͰ༻͍ΒΕΔ׆ੑԽ͕ؔͩݱࡏ͋· ΓΘΕ͍ͯͳ͍ɻ γάϞΠυؔΛ׆ੑԽؔͱͯ͠༻͍Δͱޯফࣦͱ͍͏ݱ ͕ى͜Γɺֶश͕ఀͯ͠͠·͏͜ͱ͕͋ΔͨΊɻ IUUQTJNBHJOHTPMVUJPOOFUEFFQMFBSOJOHNBUIFNBUJDTEFSJWBUJWFPGTJHNPJEGVODUJPO
IUUQTUPLFJOFUOFVSBMOFUXPSLBDUJWBUJPO@GVODUJPO ιϑτϚοΫεؔ ग़ྗͰΘΕΔؔɻ ҰൠతʹྨͰΘΕΔɻ
IUUQTTPOFPIBUFOBCMPHDPNFOUSZ UBOIؔ γάϞΠυؔΑΓਫ਼͕ग़͍͢ͷͷɺ͋͘·Ͱඍͷz࠷େz ͕ʮ̍ʯͰ͋Γɺ̍ΑΓখ͍͞ʹͳͬͯ͠·͏έʔε͕΄΅શͯɻ ਂ͍ωοτϫʔΫͰɺޯফࣦΛ͙͜ͱ͕͍͠ɻ
ೖྗ͕ҎԼͳΒɺҎ্ͳΒͦͷ··ग़ྗ͢Δؔͷ͜ͱɻ ҎԼͷࣜͰදͤΔɻ ZNBY Y IUUQTUFDICMPHHNPBQKQ&"'&"#&"%"&#'&&"&#$&&"&#$&#&#&#&"&#%#'&'&$&#&'#"&$"$&"&"" 3F-6ؔ 3F-6ؔ࠷Ұൠʹ༻͍ΒΕΔ׆ੑԽؔɻ ͭͷେ͖ͳಛɿ ޯফࣦ͕ى͜Γʹ͍͘
ܭࢉ͍͢͠ͱ͍͏ 3F-6ؔ࠷׆ੑԽؔͱ͍ͯ͠উख͕͍͍ͱ͞ΕΔɻ
IUUQTTPOFPIBUFOBCMPHDPNFOUSZ 3F-6ؔ Y͕ΑΓେ͖͍߹ɺඍৗʹ࠷େͰ͋Δ͕ಘΒΕΔɻ ޡࠩٯͷࡍʹޯ͕খ͘͞ͳΓʹ͍͘ ʢޯফࣦ͠ʹ͍͘ʣ
׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ
ޯ߱Լ๏ ඍΛ׆༻͢Δ͜ͱʹΑͬͯɺ Ϟσϧͷ༧ଌͱ ࣮ࡍͷʢຊͷਖ਼ղʣ ͱͷޡࠩΛͳ͍ͯ͘͘͠ɻ ͦͷΞϓϩʔνΛ࣮ݱ͢Δख๏ʹ ޯ߱Լ๏
ޯ߱Լ๏ IUUQXXXQMBODWUJUFDIBDKQGVLVEBMBCCBDCEEBCDCBGDDGDQEG ֶशΛ͏·ʙ͘ௐ͢Δ͜ͱ͕େ⭐ ޯ߱Լ๏ͷߟ͑ํ˰্͔ΒϘʔϧΛམͱ͠Ұ൪͍ͱ͜Ζ୧Γண͘·Ͱͭ େҬ࠷దղʹຊͷ࠷దղ ہॴ࠷దղʹݟ͔͚ͤͷ࠷దղ
ޯ߱Լ๏ ࣌ࠁ𝑡Ͱ𝝎 𝑡 ʹ͋ͬͨϘʔϧΛޯͷٯํಈ͔͢ࡍͷϧʔϧ 𝝎(𝑡+1) = 𝝎(𝑡) + ∆𝝎(𝑡) ,
∆𝝎(𝑡) = −𝜂𝛻𝐸 𝝎 𝑡 (4.9) 𝑡 lͱॱ࣍܁Γฦ͢͜ͱͰɼޡࠩؔάϥϑͷఈ߱Γ͍ͯ͘ ˎ̍εςοϓͷҠಈڑ∆𝝎 𝑡 lֶशz𝜂Ͱܾఆ͞ΕΔ IUUQXXXQMBODWUJUFDIBDKQGVLVEBMBCCBDCEEBCDCBGDDGDQEG
ޯ߱Լ๏ ˎ̍εςοϓͷҠಈڑ ʮޯʹԊͬͯҰʹͲΕ͚ͩ߱Γ͍͔ͯ͘ʯ lֶशzʢϋΠύʔύϥϝʔλʣ
ޯ߱Լ๏ ֶशͷऔΓํτϥΠΞϯυΤϥʔʹجͮ͘ w ֶश͕େ͖͍ ˰ࠁΈ͕ߥ͗ͯ͢ޡࠩؔͷܗঢ়Λଊ͑ΒΕͣɼऩଋ͠ͳ͍ w ֶश͕খ͍͞ ˰ֶश͕Ұʹਐߦ͠ͳ͍ IUUQXXXQMBODWUJUFDIBDKQGVLVEBMBCCBDCEEBCDCBGDDGDQEG
ࣗݾհ IUUQTRJJUBDPN)JSPLJYJUFNTBBCEE
ϋΠύʔύϥϝʔλ ʁʁʁϋΠύʔύϥϝʔλʁʁʁ IUUQTYOUKBBORKNKUGQDKEDPN&&##"&#&"&"#&$"$&#&"&"&&&&'#$&&"#&#"&'&$&&"&"&&'
׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ
υϩοϓΞτ Θͨ͠ͷλʔϯʂ ຐ๏Χʔυɹ lΦʔόʔϑΟοςΟϯάz IUUQTCPLFUFKQCPLF ͋͞ɺ࢝ΊΔΘΑɻ ҋͷήʔϜΛɾɾɾ
υϩοϓΞτ ͦ͜·Ͱͩ;&ͬˑ Θͨ͠ ਓೳքͷࢧऀʹͳΔͷΑ ୭ʹअຐͤ͞ͳ͍Θɾɾɾ
υϩοϓΞτ τϥοϓΧʔυൃಈʂ lυϩοϓΞτ IUUQTNBUPNFOBWFSKQPEBJ
χϡʔϩϯΛϥϯμϜʹυϩοϓΞτ͠ɺ ΦʔόʔϑΟοςΟϯάΛ͙ IUUQTRJJUBDPNNJOFJUFNTECBCCFGD υϩοϓΞτ
ςετσʔλʹର͢Δޡࠩؔͷ্͕Γ࢝Ί ʹଧͪΓʹ࠷దͳλΠϛϯάͱݟͳ͢ FBSMZTUPQQJOH ֶशΛૣΊʹଧͪΔख๏ ./*45ϋϯζΦϯͰ֬ೝ͠·͢ʂ
σʔλͷਖ਼نԽ ֤ಛྔΛdͷൣғʹม͢Δॲཧ ./*45ϋϯζΦϯͰ֬ೝ͠·͢ʂ
σʔλͷඪ४Խ ඪ४Խ͢ΔͱԿ͕ྑ͍ͷ͔ʁ
׆ੑԽؔ ֶशͷ࠷దԽ ߋͳΔςΫχοΫ $//ΈࠐΈχϡʔϥϧωοτϫʔΫ
$//ͱ ը૾σʔλʹదͨ͠ܗͷ χϡʔϥϧωοτϫʔΫ ը૾Λͦͷ··ͷܗʹ̎࣍ݩͰ ѻ͏͜ͱ͕Ͱ͖Δ $POWPMVUJPOBM/FVSBM/FUXPSL
$//ʢશମ૾ʣ $//ɺΈࠐΈϓʔϦϯάʹΑͬͯಘΒΕͨಛϚοϓͷ֤ϐΫηϧσʔλΛɺ χϡʔϥϧωοτϫʔΫͷೖྗͱͯ͠ར༻͢Δɻ IUUQTXXXBUNBSLJUDPKQBJUBSUJDMFTOFXTIUNM
$// ΈࠐΈ IUUQTULFOHPHJUIVCJPCMPHVOEFSTUBOEJOHDPOWPMVUJPOBMOFVSBMOFUXPSLTGPSOMQ
Χʔωϧ ʢϑΟϧλʔʣ
$// ϓʔϦϯά IUUQTULFOHPHJUIVCJPCMPHVOEFSTUBOEJOHDPOWPMVUJPOBMOFVSBMOFUXPSLTGPSOMQ ಛϚοϓͷ࠷େΛநग़͠ɺ ը૾αΠζΛܾΊΒΕͨϧʔϧʹैͬͯ খ͘͢͞Δ NBYϓʔϦϯά
$// શ݁߹ ग़ྗͷܗΛ̍࣍ݩʹมܗ͢Δ ௨ৗͷχϡʔϥϧωοτϫʔΫͱಉ͡ ʮӅΕʯʮग़ྗʯʹଓ͠ɺ
ࣗݾհʢʣ ࢀՃऀͦΕͧΕͷࣗݾհʢʣ (ݕఆ߹֨ߨ࠲ ./*45ϋϯζΦϯʢʣ
./*45ͱ ./*45ͱɺը૾σʔληοτͷ͜ͱɻ ʢखॻ͖ࣈը૾ ຕͱɺςετը૾ ຕΛूΊͨͷʣ ҎԼ͕ϖΞʹͳ͍ͬͯΔɻ खॻ͖ͷʙͷࣈ͕ॻ͔Εͨը૾σʔλͱɺ ͦͷը૾ʹॻ͔Ε࣮ͨࡍͷࣈσʔλ
./*45ͱ IUUQTXFCMBCPPTDBTJFSSBOFUQZUIPOLFSBTNOJTUTBNQMFIUNM σʔλͷ༷ࢠ
./*45ͱ IUUQTXFCMBCPPTDBTJFSSBOFUQZUIPOLFSBTNOJTUTBNQMFIUNM ग़ྗ͜Μͳײ͡ ࣈ ֬ 0 0.014 1 0.001 2
0.013 3 0.719 4 0.034 5 0.016 6 0.023 7 0.065 8 0.086 9 0.029
ͰɺͬͯΈ·͠ΐ͏ ࣮
4FRVFOUJBMϞσϧ IUUQNBSVQFLFDPN*,%"%7@%-@/P@,FSBTIUNM
͓͠·͍ pO