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文献紹介:Relational inductive biases, deep learning...

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December 09, 2019

文献紹介:Relational inductive biases, deep learning, and graph networks

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Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., ... & Gulcehre, C. (2018). Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261.
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December 09, 2019
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  1. ͸͡Ίʹ w ҎԼͷจݙΛ঺հ͠·͢ w ॻࢽ৘ใɿ#BUUBHMJB 18 )BNSJDL +# #BQTU 7

     4BODIF[(PO[BMF[ " ;BNCBMEJ 7 .BMJOPXTLJ .  (VMDFISF $  3FMBUJPOBMJOEVDUJWFCJBTFT EFFQ MFBSOJOH BOEHSBQIOFUXPSLTBS9JWQSFQSJOU BS9JW w εϥΠυதͷਤ͸͢΂ͯݪ࿦จதͷਤʹͳΓ·͢ 2
  2. ਓͷ஌ੑͱ߹੒ੑ w ਓ͸ʮ༗ݶͷखஈΛແݶʹ࢖͏ʯʢ)VNCPMU $IPNTLZ ʣ ʢFHݴޠʣ w ૊Έ߹ΘͤʹΑΔ൚ԽʢDPNCJOBUPSJBMHFOFSBMJ[BUJPOʣ w Ͳ͏ͨ͠Β"*ʹ͜ͷೳྗΛ࣮૷Ͱ͖Δ͔ʁ

    w ਓͷ૊Έ߹Θͤ൚Խೳྗ w ߏ଄Λදݱ͠ɼؔ܎ੑʹ͍ͭͯਪ࿦Ͱ͖Δ w ෳࡶͳܥΛର৅ͱͦΕΒͷ૬ޓ࡞༻ͱͯ͠දݱ͢Δʢ/BWPO ʜʣ w ֊૚ੑΛ༻͍ͯҰൠతͳڞ௨ੑΛೝࣝ͢Δʢ#PUWJOJDL ʣ w ͍࣋ͬͯΔεΩϧΛ૊Έ߹Θͤͯ৽͍͠໰୊Λղ͘ʢ"OEFSTPO  ʜʣ w ྨਪΛ͢Δʢ(FOUOFSBOE.BSLNBO )VNNFMBOE)PMZPBL  ʣ 4
  3. ਂ૚ֶशͷڧΈͱऑΈ w ڧΈɿେྔͷσʔλͱେྔͷܭࢉࢿݯ͔ΒɼlFOEUPFOEzͰ ֶशͯ͠ෳࡶͳ໰୊Λղ͚Δ w ը૾෼ྨɼࣗવݴޠॲཧɼήʔϜʜ w ऑΈɿ૊Έ߹ΘͤʹΑΔ൚Խ͕ඞཁʹͳΔ໰୊ w ෳࡶͳݴޠͱঢ়گͷཧղɼߏ଄Խ͞Εͨσʔλʹؔ͢Δਪ

    ࿦ɼֶशͷసҠɼগྔͷσʔλ͔Βͷֶशʢ.BSDVT  4IBMFW4IXBSU[FUBM -BLFFUBM ʜʣ ‎"*ͷਐలʹ͸૊Έ߹Θͤ൚Խ͕ॏཁ w zOBUVSFWFSTVTOVSUVSFzͰ͸ͳ͘ɼzVTFOBUVSFBOE OVSUVSFKPJOUMZzͰߦ͘΂͠ 5
  4. ૊Έ߹Θͤ൚ԽೳྗΛඋ͑ͨ"*ʹ޲͚ͯɿ άϥϑωοτϫʔΫͷఏҊ w ۙ೥άϥϑͱͯ͠ߏ଄Խ͞Εͨσʔλ্ͷؔ܎΍ର৅Λѻ͏ //͕ఏҊʢ4DBSTFMMJFUBM C#SPOTUFJOFUBM  ʜʣ w ର৅΍ؔ܎ͦͷ΋ͷͷදݱΛֶशՄʂ

    w ର৅΍ؔ܎ΛͲͷΑ͏ʹֶश͢Δ΂͖͔ʹؔ͢ΔόΠΞε ʮؔ܎తؼೲόΠΞεʯΛ࣋ͭ w ͜͏ͨ͠طଘͷϞσϧΛ౷Ұͯ͠ʮάϥϑωοτϫʔΫʯΛ ఏҊ͢Δ 6
  5. ؔ܎తؼೲόΠΞεͱ͸ w ֶशաఔͰର৅ؒͷؔ܎ੑ΍૬ޓ࡞༻ʹ੍໿Λ෇͚Δؼೲό ΠΞεͷ͜ͱ w ؼೲόΠΞεͱ͸ w ֶशΛߦ͏ࡍʹ͸σʔλΛΑ͘આ໌͢ΔղΛݟ͚ͭΔඞཁ ͕͋Δ w

    ͔͠͠ɼಉ༷ʹྑ͍ղ͸ͨ͘͞Μ͋Γ͑Δʂ ʢ(PPENBO ʣ w ؼೲόΠΞε͸ղͷ޷·͠͞ΛܾΊΔ w ϕΠζͰ͸ࣄલ෼෍ w ઢܗ࠷খೋ৐๏ɼ-ਖ਼ଇԽʜ 9
  6. ू߹ͱάϥϑ্ͷܭࢉ 12 w %//΋ؔ܎తؼೲόΠΞεΛ͕࣋ͭɼ࣮ੈքͷ༷ʑͳؔ܎Λѻ͏ʹ͸ෆे෼ w ॱংʢฒ΂ସ͑ʣ΁ͷෆมੑ w O࿭੕͔ΒͳΔଠཅܥͷॏ৺Λܭࢉ͢Δ໰୊Λߟ͑Δ w ࿭੕͸࣭ྔɼҐஔɼ଎౓ͳͲͷଐੑΛ࣋ͭ

    w .-1ʹ΍ΒͤΔͱɼଐੑͷॱংΛม͑Δͱ൚ԽͰ͖ͳ͍ʢ͜͏ͨ͠૊Έ߹Θ ͤ͸O͋Δʂʣ w ղܾࡦɿ༧ଌΛೖྗͷଐੑʹ͍ͭͯରশͳؔ਺ʹґଘ͢ΔΑ͏ʹ͢Δʁ w ฒ΂ସ͑΁ͷෆมੑ͚ͩͰ΋ෆे෼ w ઌ΄Ͳͷ໰୊Ͱɼඍখ࣌ؒޙͷ֤࿭੕ͷҐஔΛܭࢉ͢Δ໰୊Λߟ͑Δ w ֤࿭੕ͷӡಈ͸ͦͷଞ͢΂ͯͷ࿭੕ͷٴ΅͢ྗʹґଘ͢Δ ‎୯ʹฏۉΛऔΔ͚ͩͰ͸ܭࢉͰ͖ͣɽؔ܎Λߟྀ͢Δඞཁ w ࠷ॳͷ໰୊͸ؔ܎̌ɼ̎ͭ໨͸֤ཁૉؒʹؔ܎͕͋Δ w άϥϑ͸೚ҙͷཁૉؒͷؔ܎ߏ଄ΛදݱՄ ‎ڧྗͳؔ܎తؼೲόΠΞεΛ࢖͑Δ
  7. άϥϑωοτϫʔΫͷఏҊ 14 w άϥϑχϡʔϥϧωοτϫʔΫ w ๛෋ͳؔ܎తߏ଄Λ࣋ͭλεΫͰ׆༂ w ը૾ͷγʔϯཧղ w গ਺σʔλֶश

    w ෺ཧγεςϜͷμΠφϛΫε w ϚϧνΤʔδΣϯτγεςϜ w ஌ࣝάϥϑ w ෼ࢠߏ଄ w ͳͲͳͲʜʢQʣ
  8. ॊೈͳදݱ w ଐੑ w ଐੑͷදݱʹ͸ϕΫτϧɼςϯιϧɼू߹ɼάϥϑͳͲ༷ʑͳ ΋ͷΛ࢖༻Մ w ग़ྗ΋ΤοδɼϊʔυɼάϥϑͳͲΛબ୒Մ w άϥϑߏ଄

    w ೖྗͷߏ଄͕ܾ·͍ͬͯΔ৔߹ʢιʔγϟϧωοτϫʔΫɼ஌ࣝ άϥϑʜʣ w ೖྗͷߏ଄Λ൓ө͢ΔΑ͏ʹ(/Λઃܭ w ؔ܎ߏ଄Λਪ࿦͢Δ৔߹ʢࢹ֮తγʔϯɼςΩετίʔύεʜʣ w ର৅͚ͩϊʔυͱͯ͠༩͑ͯɼશͯͷϊʔυؒʹ༗޲Τοδ Λ࡞ֶͬͯश 19
  9. άϥϑωοτϫʔΫ্Ͱͷ૊Έ߹Θͤ൚Խ w (/͸ର৅ͱؔ܎ʹ͍ͭͯͦΕͧΕؔ਺Λڞ༗͢Δ͜ͱͰɼϞσϧʹͱͬͯ৽͍͠ߏ଄ʹ͍ͭͯ΋ਪ࿦Մೳ w (/ͷ૊Έ߹Θͤ൚Խೳྗͷ࣮ূ w #BUUBHMJBFUBM   w

    λΠϜεςοϓΛ༧ଌˠԿઍ΋ͷλΠϜςοϓΛ༧ଌՄ w ܇࿅͔࣌Βର৅਺Λഒɾ൒෼ͯ͠θϩγϣοτՄ w 4BODIF[(PO[BMF[FUBM   w ෳ਺ؔઅͰֶशˠؔઅ਺Λ૿΍ͯ͠΋0, w )BNSJDLFUBM  ͱ8BOHFUBM   w (/Ͱֶशͨ͠ҙࢥܾఆͷํࡦ͸ର৅Λ૿΍ͯ͠΋సҠ w #FMMPFUBM  ͳͲ w ૊Έ߹Θͤ࠷దԽ໰୊ w ܇࿅࣌ͱҟͳΔαΠζͷ໰୊ʹ൚Խ w ܭը໰୊ w ্ͱಉ༷ w ϒʔϧ4"5໰୊ w ໰୊αΠζͱ෼෍ʹ൚Խ 23
  10. ՝୊ w άϥϑ͸Ͳ͔͜ΒདྷΔͷ͔ʁ w ੜͷײ֮σʔλ͔Βάϥϑతͳߏ଄ΛൃݟͰ͖Δ͔ w ର৅ؒͷશ݁߹ΛԾఆ͢Δʢ7BTXBOJFUBM  8BOHFUBM Dʣ

    w ໰୊఺ w Ծఆ͞ΕΔର৅͸ඞͣ͠΋ݱ࣮ͷର৅ʹରԠ͠ͳ͍ w ඞཁͳάϥϑߏ଄͸શ݁߹ΑΓ΋εύʔε w ঢ়گʹԠͯ͡μΠφϛοΫʹάϥϑߏ଄Λมߋͤ͞Δ w (/͕ѻ͏ର৅΍ؔ܎͸ਓ͕௚ײతʹཧղͰ͖Δ΋ͷʹରԠ͢ ΔͷͰղऍ΍෼ੳ͕͠΍͍͢ 25