Generative Adversarial Networks ͷ‫ڞ‬ಉֶशʹؔ͢Δ‫ڀݚ‬ࢦಋ‫ڭ‬तɿ౻٢߂࿱

TR19006 ௩‫୓ݪ‬໵
1. ͸͡Ίʹ
Generative Adversarial NetworksʢGANsʣ͸ Generator ͓Αͼ Discriminator Λఢରతʹֶश͢Δ͜ͱͰɼ࣮ࡏ͠ͳ͍ը૾Λੜ੒͢Δख๏Ͱ͋ΔɽGenerator ͸ɼજࡏม਺Λ༻͍ͯը૾Λੜ੒͠ɼੜ੒ը૾͕ Discriminator ʹΑΓ࣮ը૾ͱࣝผ͞ΕΔΑ͏ʹֶश͢ΔɽDiscriminator͸ɼ࣮ը૾ͱੜ੒ը૾ΛࣝผͰ͖ΔΑ͏ʹֶश͢ΔɽGANsͷֶश࣌ɼGenerator ͷੜ੒ը૾ʹภΓ͕ੜ͡ΔͱɼDiscriminator ͸࣮ը૾ͱੜ੒ը૾Λ؆୯ʹࣝผͰ͖ɼϞʔυ่յΛ‫͕͋ͱ͜͢͜ى‬Δɽ͜ͷ໰୊Λղܾ͢ΔͨΊʹɼෳ਺ͷ Generator Λ༻͍Δ͜ͱͰɼϞʔυ่յͷൃੜΛ཈੍
͢Δख๏͕ఏҊ͞Ε͍ͯΔ [2]ɽ͔͠͠ɼ͜ͷख๏͸ Generator ͕ಠཱͯ͠ը૾Λੜ੒͢ΔͨΊɼੜ੒ը૾ʹภΓ͕ੜ͡Δ໰୊͸ղܾ͍ͯ͠ͳ͍ɽͦ͜Ͱɼຊ‫Ͱڀݚ‬͸ੜ੒ը૾ͷภΓΛ཈੍͢ΔͨΊʹɼෳ਺ͷ Generator ͕஌ࣝΛసҠ͠ͳ͕Β‫ڞ‬ಉֶशͯ͠ը૾Λੜ੒͢Δख๏ΛఏҊ͢Δɽ

2. ؔ࿈‫ڀݚ‬ैདྷख๏Ͱ͋Δ Deep Convolutional GANs ͓Αͼ MultiAgent Diverse GANs ʹ͍ͭͯड़΂Δɽ
Deep Convolutional GANsʢDCGANsʣ[1] ͸ɼ৞ΈࠐΈ૚Λ༻͍Δ͜ͱͰੜ੒ը૾ͷ࣭Λ޲্ͤͨ͞ GANsͷख๏Ͱ͋Δɽ࣮ը૾ͱͯ͠ਖ਼໘ͷ‫إ‬ը૾ͷΈͷσʔλ౳ͷྨࣅͨ͠σʔλͷΈѻ͏৔߹ʹ͓͍ͯ͸ɼ࣮ը૾ͱ۠ผ͕Ͱ͖ͳ͍઱໌ͳը૾Λੜ੒Ͱ͖Δɽֶश͢ΔࡍʹϞʔυ่յ͕ൃੜ͢Δ৔߹͕ଟ͘ɼ҆ఆֶͨ͠श͕ࠔ೉Ͱ͋Δɽ
Multi-Agent Diverse GANsʢMAD-GANsʣ[2] ͸ɼෳ਺ͷ Generator ͓Αͼ̍ͭͷ Discriminator Ͱߏ੒͞Εͨ GANs ͷख๏Ͱ͋ΔɽDiscriminator ͸࣮ը૾ͱੜ੒ը
૾Λࣝผ͢ΔͷΈͳΒͣɼͲͷ Generator ͔Βੜ੒͞Εͨੜ੒ը૾Ͱ͋Δ͔Λࣝผ͢ΔΑ͏ʹֶश͢ΔɽMAD-GANs
͸ɼ̍ͭ Generator ͕ੜ੒͢Δը૾ʹภΓ͕ੜͨ͡৔߹ɼ
ଞͷ Generator ͸ภͬͨը૾ͱ͸ҟͳΔը૾Λੜ੒͓ͯ͠ΓɼDiscriminator ͸࣮ը૾ͱੜ੒ը૾Λ؆୯ʹ͸ࣝผͰ͖ͳ͍ɽ͜ΕʹΑΓɼMAD-GANs Λ༻͍Δ͜ͱͰϞʔυ่յͷൃੜΛ཈੍͢Δ͜ͱ͕ՄೳͱͳΔɽ͔͠͠ɼੜ੒ը૾ͷภΓ͕ੜ͡Δ͜ͱࣗମΛ๷͙͜ͱ͸Ͱ͖ͳ͍ɽ3. ఏҊख๏ຊ‫Ͱڀݚ‬͸ෳ਺ͷ Generator Λ༻ֶ͍ͯशΛߦ͍ɼGenerator ͕‫͍ޓ‬ͷ஌ࣝΛసҠ͠ͳ͕Β‫ڞ‬ಉֶशͯ͠ը૾ੜ੒
Λߦ͏ GANs ͷख๏ΛఏҊ͢Δɽ

3.1 GANs ͷ‫ڞ‬ಉֶशఏҊख๏ͷωοτϫʔΫߏ଄Λਤ 1 ʹࣔ͢ɽֶशʹ࢖
༻͢Δ Generator ͷ਺Λ k ͱ͢Δͱɼ֤ Generator ͸
G1 , . . . , Gk Ͱද͞ΕΔɽ֤ Generator ͸ɼજࡏม਺ z ∼ PzΛ༻͍ͯੜ੒ը૾Λੜ੒͢ΔɽͦͷͨΊɼk ຕͷੜ੒ը૾͕
ಘΒΕΔɽ·ͨɼ֤ Generator ͷಛ௃Ϛοϓ·ͨ͸ੜ੒ը૾Λ஌ࣝసҠάϥϑΛ༻͍ͯసҠͤ͞Δ͜ͱͰɼGeneratorಉ࢜Ͱͷ஌ࣝͷ఻ୡΛՄೳʹ͍ͯ͠ΔɽDiscriminator ͸D Ͱද͞Εɼ࣮ը૾ͱੜ੒ը૾Λࣝผ͢ΔͷΈͳΒͣɼͲͷ Generator ͔Βੜ੒͞Εͨੜ੒ը૾Ͱ͋Δ͔Λࣝผ͢ΔɽͦͷͨΊɼ࠷ऴ૚ͷग़ྗ஋ͷϢχοτͷ਺͸ k + 1 ‫ݸ‬ͱͳ͓ͬͯΓɼιϑτϚοΫεؔ਺Λ༻͍ͯΫϥεείΞd1 , . . . , dk+1 Λग़ྗ͢ΔɽείΞ d1 , . . . , dk ͸֤ Generator ͔Βੜ੒͞Εͨੜ੒ը૾Ͱ͋Δ֬཰Λද͠ɼείΞdk+1 ͸࣮ը૾Ͱ͋Δ֬཰Λද͢ɽωοτϫʔΫ಺෦ʹ͸ɼֶशͷ҆ఆԽΛਤΔͨΊɼBatch Normalization ͕༻͍Β
ΕΔ৔߹͕ଟ͍ɽ͔͠͠ɼGANs ʹ͓͚Δֶशͷ҆ఆԽʹ͸ Batch Normalization ͸ෆे෼Ͱ͋Δɽͦ͜Ͱɼຊख๏Ͱ͸ Discriminator ʹ Spectral NormalizationʢSNʣΛಋೖ͢Δɽ͜ΕʹΑΓɼଛࣦؔ਺ʹมߋΛՃ͑Δ͜ͱͳ͘Ϟʔυ่յΛ཈੍͠ɼGANs ʹ͓͚Δֶशͷ҆ఆԽΛਤΔ͜ͱ͕ՄೳͱͳΔɽਤ 1: ఏҊख๏ͷωοτϫʔΫߏ଄

3.2 ஌ࣝసҠάϥϑʹΑΔ࠷దԽఏҊख๏͸ɼ஌ࣝసҠάϥϑΛಋೖ͢Δ͜ͱͰɼ֤ Generator ͕‫ʹ͍ޓ‬஌ࣝసҠ͠ͳ͕Βֶश͢Δɽ̏ͭͷ Generator Λ༻͍ͨ৔߹ʹ͓͚Δ஌ࣝసҠάϥϑΛಋೖͨ͠ఏҊख๏Λਤ 2 ʹࣔ͢ɽֶशʹ࢖༻͢Δ Generator ͷ਺Λ kͱ͢Δͱɼ֤ Generator ͸ G1 , . . . , Gk ɼDiscriminator ͸D ͱͳΓɼϊʔυͱͯ͠ද͢ɽ֤ Generator ͷϊʔυؒʹ͸̎ͭͷΤοδΛఆٛ͠ɼͦΕͧΕҟͳΔ޲͖ͷ༗޲άϥϑͰද͢ɽ֤Τοδͷ޲͖͸ɼֶश࣌ʹޯ഑ͷ৘ใ͕఻ΘΔํ޲Λද͍ͯ͠Δɽ֤ Generator ͷϊʔυؒͷΤοδ͸
Generator ಉ࢜ͷ஌ࣝͷ఻ୡΛද͠ɼi ൪໨ͷ GeneratorͷΤοδ LD,i ͸ i ൪໨ͷ Generator ͕ੜ੒ͨ͠ੜ੒ը૾͕Discriminator ʹ࣮ը૾ͱ൑அ͞Ε͔ͨͲ͏͔ͷ৘ใͷ఻ୡΛද͢ɽ·ͨɼΤοδ Ladversarial ͸ɼDiscriminator ͷࣝผ݁Ռ͕ਖ਼͍͔͠Ͳ͏͔ͷ৘ใͷ఻ୡΛද͢ɽ֤Τοδʹ͸‫ݸ‬ผͷଛࣦؔ਺Λఆٛ͠ɼ֤ Generator ͷํ޲Λ޲͍ͨΤοδͷଛࣦؔ਺ʹ͸ήʔτؔ਺Λಋೖ͢Δ͜ͱͰɼ఻
೻͞ΕΔଛࣦΛ੍‫͢ޚ‬Δɽຊख๏Ͱ͸ɼήʔτؔ਺ͱͯ͠
Through GateɼCutoﬀ GateɼNegative linear Gate ͓Αͼ Positive linear Gate Λ༻͍ΔɽThrough Gate ͸ɼೖྗ͞Εͨαϯϓϧ͝ͱͷଛࣦΛͦͷ··௨ؔ͢਺Ͱ͋Δɽ
Cutoﬀ Gate ͸ଛࣦΛ 0 ͱ͠ɼଛࣦͷ‫ࢉܭ‬ΛߦΘͳ͍ؔ਺Ͱ͋Γɼ೚ҙͷΤοδΛ੾அ͢Δ͜ͱ͕Ͱ͖ΔɽNegativelinear Gate ͸ֶश͕ਐΉʹͭΕͯଛࣦΛ‫ݮ‬গͤ͞Δؔ਺Ͱ͋Γɼֶशͷং൫͸ Through Gateɼऴ൫͸ Cutoﬀ Gateͱಉ͡ॲཧͱͳΔɽPositive linear Gate ͸ֶश͕ਐΉʹͭΕͯଛࣦΛ૿Ճͤ͞Δؔ਺Ͱ͋Γɼֶशͷং൫͸ CutoﬀGateɼऴ൫͸ Through Gate ͱಉ͡ॲཧͱͳΔɽਤ 2: ෳ਺ͷ Generator ʹ͓͚Δ஌ࣝసҠάϥϑʢk = 3ʣ

3.3 ֶशํ๏ఏҊख๏Ͱ͸ɼDiscriminator ͷֶश͓Αͼ GeneratorͷֶशΛަ‫܁ʹޓ‬Γฦ͢͜ͱͰ GANs ͷֶशΛߦ͏ɽ·ͨɼDiscriminator ͷֶश͸ MAD-GANs ͱಉ༷Ͱ͋Δɽ
Generator ͷֶश͸ɼ֤ Generator ͷੜ੒ը૾͕ Discriminator ʹΑΓ࣮ը૾ͱࣝผ͞ΕΔΑ͏ʹߦ͏ɽ·ͨɼఏҊख๏Ͱ͸஌ࣝసҠάϥϑʹԠͯ͡ɼ֤ Generator ͕‫ޓ‬͍ͷ஌ࣝΛసҠ͠ͳ͕Βֶश͢Δɽ֤ Generator ͷϊʔυؒͷΤοδ͸ Generator ಉ࢜ͷ஌ࣝͷ఻ୡΛද͠ɼi ൪໨ͷ Generator ͷΤοδ LD,i ͸ i ൪໨ͷ Generator ͕ੜ੒ͨ͠ੜ੒ը૾͕ Discriminator ʹ࣮ը૾ͱ൑அ͞Ε͔ͨͲ͏͔ͷ৘ใͷ఻ୡΛද͢ɽGenerator ͷϊʔυؒͷΤοδͰɼt ൪໨ͷ Generator ͷ஌ࣝΛ s ൪໨ͷ Generator ʹసҠ͢Δࡍͷଛࣦؔ਺Λ Lt,s ͱ͠ɼi ൪໨ͷ Generator ͕ੜ੒ͨ͠ੜ੒ը૾͕ Discriminator ʹ࣮ը૾ͱ൑அ͞Ε͔ͨͲ͏͔Λද͢ଛࣦؔ਺Λ LD,i ͱ͢Δɽ·ͨɼ֤Τοδʹ͓͚Δήʔτؔ਺͸ Gate(·) ͱ͢ΔɽGenerator ͷֶशͰ͸ɼ֤ Generator ʹೖྗ͞ΕΔજࡏม਺ z ∼ Pz ͸ಉҰͱ͢Δɽ࠷ऴతͳ֤ Generator ͷଛࣦؔ਺͸Τοδ͔ΒಘΒΕͨ Lt,s ͓Αͼ LD,i Λ૯࿨ͯ͠ࢉग़͢Δɽ࢖༻͢ΔGenerator ͷ਺Λ k ͱ͢ΔͱɼDiscriminator ʹରͯ͠ i൪໨ͷ Generator ͕ੜ੒ͨ͠ੜ੒ը૾Λೖྗͨ͠ࡍͷࣝผ(i)(i)
݁Ռ͸ d(i) = d1 , . . . , dk+1 Ͱද͞ΕΔɽ·ͨɼਖ਼ղϥϕggg
ϧ͸ t = t1 , . . . , tk+1 Ͱද͞Εɼtgk+1 ͕ 1 Ͱͦͷଞ͕ 0ͷϕΫτϧͱͳΔɽ͜ͷͱ͖ɼଛࣦؔ਺ LD,i ͸ࣜ (1) ͱͳΔɽ!
#LD,i = Gate −k+1"(i)tgj loge djද 1: IS ͓Αͼ FID ͷൺֱ݁Ռ

DCGANs(m,n)⎛2!

4.77 ± 0.05

21.17

4.77 ± 0.03

28.76

!

23.77

࣮ը૾

5.37 ± 0.09−

8.70 ± 0.14−(a) MAD-GANs(b) ఏҊख๏ਤ 3: ੜ੒ը૾ͷՄࢹԽ݁Ռ

(2)

⎞2 ⎞M
N
(m,n)
(m,n)
Qs
⎜ α " " ⎜ ' Qt
' −'' ⎟ ⎟Lt,s = Gate ⎝⎝' (m,n) ' ⎠ ⎠(m,n) 'M N m=1 n=1 ''Qt''Qs'25.79ఏҊख๏(1)

1 " 2Fi,m,c,nC c=1⎛

4.57 ± 0.03!

j=1=FID ↓MAD-GANsఏҊख๏Ͱ͸ɼಛ௃ϚοϓΛసҠ͢Δ͜ͱʹΑΓɼ஌ࣝసҠΛߦ͏ɽಛ௃Ϛοϓͷνϟωϧ൪߸Λ c = 1, . . . , C ɼಛ௃Ϛοϓͷ૚ͷҐஔΛ m = 1, . . . , M ɼಛ௃ϚοϓͷϕΫτ
ϧ൪߸Λ n = 1 . . . , N ͱ͢Δͱɼi ൪໨ͷ Generator ͷಛ௃Ϛοϓ͸ Fi,m,c,n Ͱද͞ΕΔɽ͜ͷͱ͖ɼϋΠύʔύϥϝʔλΛ α ͱ͢Δͱɼଛࣦؔ਺ Lt,s ͸ࣜ (2) ͓Αͼࣜ (3)
ͱͳΔɽ
CQi

IS ↑SN4.3 ஌ࣝసҠάϥϑͷ࠷దԽ(3)

24. ධՁ࣮‫ݧ‬ैདྷख๏ͱͷൺֱʹΑΓɼఏҊख๏ͷ༗ޮੑΛௐࠪ͠ɼ࠷దͳ஌ࣝͷసҠํ๏Λ୳ࡧ͢Δɽ࣮‫ʹݧ‬͸ɼ10 ΫϥεͷҰൠ෺ମͷΧϥʔը૾Ͱߏ੒͞Ε͍ͯΔ CIFAR-10 σʔληοτΛ༻͍ɼֶश༻ͷαϯϓϧͰ͋Δ 50, 000 ຕΛ 64×64ʹϦαΠζͯ͠࢖༻͢Δɽຊ࣮‫Ͱݧ‬͸ɼϕʔεͷ GANs ͷख๏ͱͯ͠ DCGANs Λ༻͍Δɽ·ͨɼ஌ࣝసҠάϥϑʹ͓͚Δήʔτؔ਺ͷ୳ࡧճ਺Λ 1, 500 ͱ͠ɼ֤ Generator ʹ͓͚Δੜ੒ը૾ͷ Inception ScoreʢISʣΛ࠷େԽ͢Δήʔτؔ਺ͷ૊Έ߹ΘͤΛ୳ࡧ͢Δɽֶश࣌ͷόοναΠζΛ256 ͱ͠ɼֶशճ਺Λ 50ɼ֤ Generator ʹೖྗ͢Δજࡏม਺ͷ࣍‫਺ݩ‬Λ 100ɼϋΠύʔύϥϝʔλ α Λ 1, 000 ͱ͢Δɽੜ੒ը૾ͷ࣭ΛධՁ͢Δࢦඪͱͯ͠ IS ͓Αͼ Fréchet
Inception DistanceʢFIDʣΛ༻͍Δɽ·ͨɼIS ͸ߴ͍஋ɼ
FID ͸௿͍஋ʹͳΔ΄Ͳੜ੒ը૾ͷ࣭͕ߴ͍͜ͱΛදͯ͠
͍ΔɽఏҊख๏ʹ͓͍ͯɼ஌ࣝసҠάϥϑΛ༻͍ͨήʔτؔ਺ͷ୳ࡧΛ 1, 500 ճߦ͍ɼ஌ࣝͷ఻ୡํ๏Λ࠷దԽͨ͠ɽ
࠷దԽର৅Ͱ͋Δ֤ Generator ʹ͓͚Δੜ੒ը૾ͷ IS ͕࠷େͷ஋ͱͳͬͨάϥϑΛਤ 4 ʹࣔ͢ɽ੺৭ͷΤοδ͕Positive linear Gateɼփ৭ͷΤοδ͕ Through Gate Λද͍ͯ͠ΔɽG1 ͸ɼଞͷ Generator ͔Β஌ࣝΛసҠ͞Ε
ͳ͍ G2 ͱൺֱͯ͠ IS ͷ஋͕ߴ͘ɼ஌ࣝͷసҠ͸ੜ੒ը૾ͷ࣭ͷ޲্ʹ༗ޮͰ͋Δͱ͍͑Δɽ·ͨɼGenerator ؒͷ஌ࣝͷసҠ͸ֶशॳ‫ظ‬͸ෆཁͰ͋Γɼֶश͕ਐΉʹͭΕͯసҠ͢Δͱྑ͍͜ͱ΍ɼG3 ͸ G1 ͷόοϑΝͷΑ͏ͳ໾ׂΛՌͨ͢͜ͱͰɼG1 ͷֶशͷ҆ఆԽʹ‫د‬༩͍ͯ͠Δ͜ͱ͕֬ೝͰ͖Δɽ

4.1 ఏҊख๏ͷ༗ޮੑͷௐࠪຊ࣮‫Ͱݧ‬͸ɼDCGANs ͓Αͼ MAD-GANsɼఏҊख๏ʹ͓͚Δੜ੒ը૾ͷ࣭Λൺֱ͢ΔɽDCGANs ͸ SN ͷಋೖͷ༗ແʹΑΔ̎ύλʔϯΛൺֱର৅ͱ͢ΔɽMAD-GANs
͓ΑͼఏҊख๏͸ SN Λಋೖ͠ɼGenerator ͷ਺Λ 3 ͱ͢Δɽֶशճ਺Λ 200 Epoch ͱ͠ɼֶशऴྃ࣌ͷϞσϧύ
ϥϝʔλΛ༻͍ͯධՁΛߦ͏ɽ֤ख๏ͷ IS ͓Αͼ FID Λද 1 ʹࣔ͢ɽද 1 ΑΓɼఏҊख๏͸ IS ͕࠷΋ߴ͍஋ͱͳ
Γɼ࠷΋ੜ੒ը૾ͷ࣭͕ߴ͍͜ͱ͕֬ೝͰ͖ΔɽFID ͸ SNΛಋೖͨ͠ DCGANs ͕࠷΋௿͘ɼఏҊख๏΋ಉ༷ʹ௿͍
஋Ͱ͋ΔɽGAN ͸ֶश͕ਐΉͱɼIS ͱ FID ͕τϨʔυΦϑͷؔ܎ʹ͋Δ͜ͱ͕஌ΒΕ͍ͯΔɽຊ࣮‫͚͓ʹݧ‬ΔఏҊख๏͸ɼ֤ Generator ʹ͓͚Δੜ੒ը૾ͷ IS Λ࠷దԽର৅ͱ͠ɼ࠷େԽ͢Δήʔτؔ਺ͷ૊Έ߹ΘͤΛ୳ࡧͨ͠ɽఏҊख๏͸࠷దԽର৅Λ FID ͱ͠ɼ࠷খԽ͢Δήʔτؔ਺ͷ૊Έ߹Θͤͷ୳ࡧʹΑΓɼFID ʹಛԽͨ͠ख๏΋࣮‫ݱ‬Ͱ͖Δɽ

4.2 ੜ੒ը૾ͷՄࢹԽ
MAD-GANs ͓ΑͼఏҊख๏ʹಉҰͷજࡏม਺Λೖྗ͠ɼੜ੒ͨ͠ը૾Λൺֱ͢Δɽੜ੒ը૾ͷՄࢹԽ݁ՌΛਤ 3 ʹࣔ͢ɽਤ 3 ͷ݁Ռ͔ΒɼఏҊख๏͸࣮ը૾ʹ͍ۙը૾͕ੜ
੒Ͱ͖͍ͯΔ͜ͱ͕֬ೝͰ͖Δɽਤ 4: ஌ࣝసҠάϥϑͷ࠷దԽ݁Ռ

5. ͓ΘΓʹ
ຊ‫Ͱڀݚ‬͸ෳ਺ͷ Generator ͓Αͼ̍ͭͷ Discriminator Λ༻͍ͯɼͦΕͧΕͷ Generator Ͱ஌ࣝΛసҠ͠ͳ͕Β‫ڞ‬ಉֶशΛߦ͏ख๏ΛఏҊͨ͠ɽධՁ࣮‫ʹݧ‬ΑΓఏҊख๏ͷ༗ޮੑΛ֬ೝͨ͠ɽࠓ‫ޙ‬͸ෳ਺ͷ Discriminator Λ༻͍Δ͜ͱͰɼΞϯαϯϒϧޮՌʹΑΓੜ੒ը૾ͷ͞ΒͳΔ࣭ͷ޲্Λ໨ࢦ͢ɽࢀߟจ‫ݙ‬[1] A. Radford, et al., “Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks”, ICLR, 2016.
[2] A. Ghosh, et al., “Multi-Agent Diverse Generative Adversarial Networks”, CVPR, 2018.

‫੷ۀڀݚ‬[1] T. Tsukahara, et al., “Collaborative learning of generative adversarial networks”, VISAPP, 2021.
(ଞ 3 ݅)