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1 /

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lfil Shla k T lfil hla k lfil y v lfil g d thla k e lfil h bp sr n h bo sr W alcil w Msr m x • 25 C? 5 8 1B 9 5D?B 19 B8 • 4 25 C? • 5 7 B 1B 9 5D?B 25 C? • CBD 5 79 25 C? • 15D BG 5 1B 9 5D?B 19 B8 • . 66 25 C? • 3 9 5??9 9 B 1 I 69 H99 29C5D5 98 1B89 • 39 C9D B 1 I 69 H99 1B89 • 9C 15 /9?C 1 I

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• 91 • • 31 6 6 2 8 / / 6 ] 8[ • • 6

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6/ 8 • • • 6 8 • 9 • • 8 1 6 9 • 6 6 4

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1 59 • • 69 8 / Nin : Nout :

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9 6 / 8 • • 8 1

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9 • • 1 1 6 1 76 • • 6 8 6 6/ 8 1 6

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8 /6 6 1 n 9 If Var[f(x)] < ∞: converges to 0 8 /6

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͔͠͠ɼඞͣ͠΋͔̿Β؆୯ʹαϯϓϦϯάͰ͖Δͱ͸ݶΒͳ͍ ॏ఺αϯϓϦϯάͷద༻

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• f • 6 8 0 • • • ) ( , ( • X / / • 8 X 91 • 8 1= X 9 1

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= )1( 1) , )1(/ = 99 = 6 8

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9 ) 2 / 2 = 2 6 2 1( 2 2 2 68

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68 9 3 8 / 8 18 ,

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89 6 1 / 89 6 89 6 1 /4

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E 8 9 = 1 6 Z 6 = 5= V 8 1* / ( ) 1

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6 Z 0 1 8 = 9 8 / V /8

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a ][ ] 1,9/ 6 8 , / , 6 1 ][ ] dg S 6 7 e i 7B ][ ] E dg 9 9 I c

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GE GA • V • /9 • GE GA8 / 8 • • L D GE GA 6 S 1 6 •

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9 6 • 8 1 M • 9 • • 6 • / • C

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M ) ) B • / 8 ( 1 , 2 • ,E ,0 9 6 • E 0, 9 6 • C

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M 2 M 1 68M C 1 C / 1 / 1 8B E 0 M 69

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M = ) ( 9 1 = T / 8 ( ) ) 2 C 6

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)()(M C /0 1tM x M ʼ C 3 1 2 M Mp 9 T • 8 29M q • 8 2 T C M M M | M 6

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2 9 / 1 2 T2 8 6 A6 M2 6 A/C 6t=04/

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M t 9 5 / 6 0 / 91 2 / 9 C A 1 9 819 81 92 / 1 0 5

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8 C M 1 8 1 8C 9 C 96 8 96 1 8C / 2 1

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9 / 1 2 / 6 A ( ) 9M 8 A6 M 6 C78

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( ( 6 1 o 8 9 o 1 o9 C k d .) ( 2 1 M l 2 1 8 0 / m e ) /2) a

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/ 8 2 1 9 6 C

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લͷঢ়ଶͷۙ͘ͷ఺Λ࣍ͷભҠઌީิͱͯ͠બͿʢϚϧίϑ࿈࠯ʣ *G֬཰ൺ S ֬཰ SͰغ٫ ɼFMTFडཧʢϞϯςΧϧϩ๏ʣ ʢ ֬཰ൺʹG Y` G Y IUUQWJTVBMJ[FNDNDBQQTQPUDPN@NFUSPQPMJTIUNM

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Zͷ஋Λݻఆͨ͠৚݅෇͖෼෍͔ΒYΛαϯϓϦϯά Yͷ஋Λݻఆͨ͠৚݅෇͖෼෍͔ΒZΛαϯϓϦϯά IUUQWJTVBMJ[FNDNDBQQTQPUDPN@NFUSPQPMJTIUNM

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/ / ࣍ͷ YJ ͷબ୒Λߟ͑Δ ˠ͜Ε͸ɼ৚݅෇͖֬཰ Q YJ cYJ ʹΑܾͬͯఆ͞ΕΔ ͜͜Ͱɼແ޲άϥϑʹ͓͍ͯɼ YJ ͕ۙ๣ͷม਺ YJ ʹؔͯ͠৚݅෇͖ಠཱ ˠ͜ͷΑ͏ͳ YJ ͕ෳ਺͋Δ৔߹ɼͦΕΒ͸ಉ࣌ʹαϯϓϦϯάՄೳ ˠ͜ͷख๏ΛϒϩοΫΪϒεαϯϓϦϯάͱݺͿ

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1 / ཧ૝తͳ.$.$ ɾ΋ͱͷQ Y ͔ΒαϯϓϦϯά͢ΔΑ͏ʹઃܭ͞Ε͍ͯΔ ɾϚϧίϑ࿈࠯͔Βͷ࿈ଓαϯϓϧ͸ޓ͍ʹ׬શʹಠཱ ɾͦͷ֬཰ʹൺྫͯ͠Yۭؒ಺ͷଟ͘ͷҟͳΔྖҬʹݱΕΔ .$.$๏ͷେ͖ͳ՝୊ ཧ૝తͳ.$.$͸ඇݱ࣮తͰ͋Δ ࣮ࡍʹ͸ɼαϯϓϧ͕ʮෆे෼ʹࠞ߹͢Δ܏޲ʹ͋Δʯ ؇଎ࠞ߹ TMPXNJYJOH ΍ɼࠞ߹ͷࣦഊ GBJMVSFUPNJY ͱݺ͹ΕͨΓ͢Δ

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3 / / /2 49 1/2 49 49 6 98 49 /9

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1 5 5 5 →5 3 5 8 9 2 6 8 / 2 6 8 6 8

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3 8 9 6 GAN 9 6 / 1

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6 6 / 71 8 9 / 31 / 37 Difficult & Slow Easy & Fast

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/6 /6 β EBM 8 1 8 β 98 0 → β ∞ → p = 0 → 38 = ∞→ β 0 → p = 1 → 38

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6 6 86 β = 1 β < 1 39 tempering β < 1 / 3 / , tempered transitions 6 1 → 6 / parallel tempering 6 /

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6 1 / 1 → critical temperatures 04 9 1 181

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9 91 9 Bengio(2013) 81VAE RBM 6h9 6 /1 9 1 6 6 1 /1 / / 4 1 99 9 6

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61 / 9 4MCMC 4 844 6 4 4 1 / / 24 4 8