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ൃදऀɿ༶໌఩ ೥݄೔!ಡΈձ -FBSOJOH3FQSFTFOUBUJPOT CZ)VNBOT GPS)VNBOT

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࿦จ৘ใͱબΜͩཧ༝ બ୒ཧ༝ • ਓؒʹରͯ͠৘ใٕज़Ͱ࡞༻ʢհೖʣʹ͍ͭͯ஌ΔͨΊ • )VNBOJOUIFMPPQܥͷ࿦จ

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ߩݙɿਓؒΛհͯ͠ਓؒʹ༗ӹͳදݱΛ֫ಘՄೳʹ എܠɿػցֶश͕ൃల͖ͯͯ͠ɼҙࢥܾఆʹ࢖ΘΕ͖͍ͯΔ ໰୊ɿ҆શੑɼެฏੑͳͲΛߟྀ͢ΔࡍʹӏವΈʹͣ͠Β͍ ఏҊɿਓ͕ؒཧղՄೳͳํ๏Ͱ৘ใΛఏࣔ͠ɼ 
 ਓؒͷ࠷ऴܾఆΛࢧԉ͢ΔϑϨʔϜϫʔΫ.P.ΛఏҊ ݁ՌɿͭͷλεΫΛ࣮ࢪɽ 
 ਓؒͷҙࢥܾఆʹରͯ͠޲্ͤ͞Δ͜ͱΛࣔͨ͠

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͍··Ͱͷҙࢥܾఆࢧԉɿग़ྗΛӏವΈ͠ͳ͍ ػցͷग़ྗ Λਓ͕ؒड͚औΓɼߦಈ ΛͱΔ ̂ y a fθ ̂ y x a

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͍··Ͱͷख๏ɿΑ͍ग़ྗΛֶशʢ܇࿅࣌ʣ ڭࢣ͋ΓֶशͰྑ͍ग़ྗʹͳΔΑ͏ʹֶश fθ ̂ y x y L(y, ̂ y)

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ݱ࣮ɿਪ࿦݁Ռͱߦಈ͸Ұக͠ͳ͍ ਓ͕ؒؒʹೖΔͷͰ ʹͳΔ͜ͱ͕͋Δ ҙࢥܾఆͷঢ়گʹΑͬͯػցͱਓؒͷҙࢥܾఆ͕Ұக͠ͳ͍ ̂ y ≠ a fθ ̂ y x a ≠ ̂ y

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ཧ૝ɿਓؒͷҙࢥܾఆΛ࠷దԽ ਓؒͷߦಈΛؚΊͯ࠷దԽ͢Δ͜ͱ͕ཧ૝ ͕ͨͩͷग़ྗͰਓؒʹͱͬͯཧղ͠೉͍ ̂ y y fθ ̂ y x a = h(x, ̂ y) L(y, a)

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ՄࢹԽ ఏҊख๏ɿਓؒͰ΋ཧղͰ͖Δํ๏Ͱࢧԉ͍ͨ͠ ਓ͕͍ؒΔͨΊɼޯ഑Λ఻೻Ͱ͖ͳ͍ y දݱֶश x ϕ a = h(z, ̂ y) L(y, a) z

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ਓؒͷ୅ཧϞσϧΛઃఆͯ͠ɼޯ഑Λ఻೻Մೳʹʂ y x ϕ a = h(z, x) L(y, a) h z

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දݱΛ࢖ͬͨద੾ͳՄࢹԽ͸೉͍͠ දݱ ͔Βਓ͕ؒཧղͰ͖ΔΑ͏ʹ͢ΔͨΊʹɼ 
 ՄࢹԽͷૢ࡞͕ඞཁ • ๮άϥϑ΍ɼը૾ɼϋΠϥΠτͱ͔ʜ ҙࢥܾఆʹରͯ͠ɼྑ͍հೖ͕ߦ͑ΔΑ͏ͳՄࢹԽ͸ͦΕ͚ͩͰݚڀʹ ͳΔ͘Β͍೉͍͠ ຊݚڀͰ͸ɼྑͦ͞͏ͳՄࢹԽΛબΜͰར༻͢Δ z

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࣮ݧɿͭͷλεΫͰ༗ޮੑΛࣔ͢ λεΫɿߴ࣍ݩσʔλΛ௿࣍ݩʹѹॖͨ͠ͱ͖ʹ 
 ༗༻ͳදݱΛ֫ಘͰ͖Δ͔ʁ λεΫɿ࣮ࡍͷλεΫͰ΋ 
 ɹɹɹɹ֫ಘͨ͠දݱʹΑΔࢧԉ͸༗ޮ͔ʁ λεΫɿػց͕஌Γಘͳ͍௥Ճ৘ใ΋ 
 ɹɹɹɹදݱͱͯ֫͠ಘͰ͖Δ͔ʁ

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λεΫɿྑ͍දݱΛ֫ಘͰ͖Δ͔ʁ ࣍ݩѹॖΛͯ͠σʔλͷՄࢹԽ͕ՄೳʹͳΔ • طଘͷ࣍ݩѹॖ͸౷ܭతͳ࠷దԽ͔͠ߟ͍͑ͯͳ͍ ߴ࣍ݩͳσʔλΛਓ޻తʹ࡞Γɼ෼ྨ໰୊ʹऔΓ૊Ή • ௚ަࣹӨͨ࣌͠ʹɼz9zͱz0zͷܗʹฒͿΑ͏ʹ࡞੒

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λεΫɿදݱϞσϧͱ୅ཧϞσϧ දݱϞσϧ • Yͷઢܕࣸ૾ߦྻ ୅ཧϞσϧ • Ұ૚ͰYͷ৞ΈࠐΈωοτϫʔΫ • ਓؒͷࢹ֮Λ͓͓·͔ʹ࠶ݱ͢Δ

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λεΫɿ݁Ռ "DDVSBDZˠ ͷ࣮ݧࢀՃऀ͕ਫ਼౓Λୡ੒

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λεΫɿϦΞϧͳσʔλͰ΋ࢧԉͰ͖Δ͔ ϩʔϯ৹ࠪΛ୊ࡐʹͨ͠λεΫ • ׬ࡁͨ͠ɼ ଺ೲɼ ঝೝɼ ڋ൱ • ଛࣦؔ਺ɿ .5VSLͰࢀՃऀΛूΊܭճ౴ΛूΊͨ ໨ඪɿදݱʹΑΔΞυόΠεͰ 
 ҙࢥܾఆͷࢧԉ͕Մೳ͔Ͳ͏͔ y = 1 y = 0 a = 1 a = 0 l(y, a) = 1y≠a

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λεΫɿإද৘ʹΑͬͯදݱΛՄࢹԽ 'BDJBMBWBUBSΛ࢖ͬͯɼإද৘ͰՄࢹԽΛߦ͏ • $IFSOP ff GBDFTإύʔπʹͦΕͧΕ਺஋͕ରԠͯ͠มԽ

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λεΫɿදݱϞσϧͱ୅ཧϞσϧ දݱϞσϧ • શ݁߹ͷϢχοτΛ૚ ୅ཧϞσϧ • શ݁߹ͷϢχοτΛ૚

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λεΫɿ௚઀తͳΞυόΠεͱಉ౳ /PBEWJDFΑΓ޲্ ༧ଌΞυόΠεͱಉ౳

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λεΫɿਓ͔ؒ͠஌Γಘͳ͍৘ใ΋֫ಘͰ͖Δ͔ ਓ͔ؒ͠஌Γಘͳ͍৘ใʢ஌ࣝɼৗࣝͱ͔ʣΛදݱͱͯ֫͠ಘ Ͱ͖Δ͔ΛΈ͍ͨ ҩྍ਍அͷλεΫΛઃܭ • ௥Ճ৘ใ Λઃఆ͢Δˠਓ͔ؒ͠ݟΕͳ͍ • ͜ͷ௥Ճ৘ใ͸ग़ྗʹӨڹΛٴ΅͢ઃఆ σʔληοτࣗମ͸ਓ޻తʹੜ੒ s

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λεΫɿදݱϞσϧͱ୅ཧϞσϧ දݱϞσϧ • ॏΈͱಛ௃ྔͷઢܗ࿨ ୅ཧϞσϧ • ॏΈͱಛ௃ྔͷઢܗ࿨௥Ճ৘ใͷઢܗ࿨

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λεΫɿ • ७ਮʹ܇࿅Λߦ͏৔߹ .P. • දݱ΋Ұॹʹ܇࿅͢Δ .P.Ҏ֎Ͱ͸ɼ௥Ճ৘ใʹ Αͬͯաֶश͕ى͖΍͍͢ h(.BDIJOF)

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·ͱΊͱײ૝ ·ͱΊ ਓ͔ؒΒਓؒͷͨΊʹҙࢥܾఆΛࢧԉ͢Δ 
 ϑϨʔϜϫʔΫΛఏҊ ਓؒͷ࠷ऴܾఆΛࢧԉͰ͖ΔΑ͏ʹɼදݱΛֶश͠ՄࢹԽ