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分子のグラフ表現と機械学習の最近

itakigawa
April 18, 2022

 分子のグラフ表現と機械学習の最近

講演動画 https://youtu.be/wtrVxZCXnPQ?t=812

理研AIPオープンセミナー, 2021年7月14日, オンライン.
https://aip.riken.jp/event-list/seminars/?lang=ja

itakigawa

April 18, 2022
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  1. / 41 2 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 戣䊛♧㷕 堣唒㷕统䎌稢脄欰暟㷕 堣唒㷕统⻉㷕 ˖ 猰㷕灇瑔顤酡⸔ꆃ

    ˖ 㛇湍灇瑔 $ ؚٓؿ邌植㷕统ך鯄獳䚍٥圓䧭䚍ך栻䖤ה׉ך㹋騧 戣䊛♧㷕  ˖ 㛇湍灇瑔 " ꨄ侔圓鸡Ⳣ椚禸ח㛇בֻ⴨䮙ה剑黝⻉ך窟さ涸䪮岀ך灇瑔 廓溪♧  ˖ 㷕遭㢌ꬠ걄㚖 " 倜׃ְ嚊䙀ח㛇בְ׋،ٕ؞ٔؤي٥剑黝⻉ך㉏겗ⶼ⳿ה׉ך⸬桦涸実鍑倯岀ך灇瑔 㸘ꅿ嫎僇  ˖ 㛇湍灇瑔 4 ꬊ䎂邁麓玎ך㹋瑞꟦錁㻊䩛岀ך鯄䳔5&.ח״׷徇巉ַ׵ך呌欰䧭麓玎ך鍑僇 加募⹃孡  ˖ 䮋䨌涸灇瑔 Ꟛ䬪 ⻉㷕חֶֽ׷㢩䯏䱱稊׾〳腉הׅ׷堣唒㷕统䩛岀ךꟚ涪ה㹋鏾 둷㾊㽵ꥐ  ˖ ⚅歲زحفٖكٕ灇瑔䬿挿 81* فؚٗٓي⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 ⵸歊椚  ˖ +45$3&45㷕统侧椚ٌرٕח㛇בֻ儗瑞꟦㾜Ꟛ㘗،٦ؗذؙثٍךⶼ⳿ה䘔欽 劤募溪➂  ˖ +45$3&45鍗㯭؎ٝؿؓوذ؍ؙأךⶼ䧭ך׋׭ך㹋꿀٥椚锷٥ر٦ة猰㷕灇瑔 幠宏灇♧ ꨄ侔圓鸡٥穈さׇ圓鸡׾⠵ֲ堣唒㷕统 堣唒㷕统荈搫猰㷕 灇瑔ךꟼ䗰 https://itakigawa.github.io/ ٌرָٕꨄ侔圓鸡 㼎韋ָꨄ侔圓鸡 㼎韋꟦ךꟼ⤘ָꨄ侔圓鸡 ͨ ͖ ͕ Θ ͍ ͪ ͕ ͘
  2. / 41 3 劤傈ך鑧겗ⴓ㶨ךؚٓؿ邌植堣唒㷕统 暴䗙كؙزٕ زهٗآ 갥挿暴䗙 鴟暴䗙 CC1CCNO1 Representation

    Learning … ˖ ⴓ겲 ˖ 㔐䌓 ˖ 欰䧭 圫ղז ♴崧ةأؙ ⴓ㶨ך橆㞮勴⟝垥涸湱✼⡲欽瘝ך䞔㜠 NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1 ؚٓؿ邌植 2ⴓ㶨ךו׿ז䞔㜠׾ו׿ז邌植ד堣唒㷕统פⰅ⸂ׅ׸ל葺ְךַ ⻉㷕圓鸡낦呓㸼腉㛇 甧⡤ꂁ䏟ꨵ㶨朐䡾 ⻉㷕⿾䘔圓鸡ך穈剏ִ Task-Specific Head
  3. / 41 4 ז׈ؚٓؿַⴓ㶨邌植ך穈さׇ锷涸⩎꬗ Amide module Proline module Oxazoline module

    / 0 0 0 0 / / ) Phenyl Carboxyl Methyl Tert-butyl Isoprophyl Trifluoromethyl ' ' ' Benzyl 0 0 ˖ 剣堣⻉さ暟כꣲ׵׸׋⯋稆 ⚺ח$)0/41عٗ؜ٝ ך鋉⵱涸ז穈さׇ  3FZNPOEؚٕ٦فך$IFNJDBM4QBDFך⴨䮙灇瑔  ˑؚٓؿ˒הְֲ欽铂כ侧㷕罏4ZMWFTUFSך⻉㷕圓鸡ך➿侧涸⴨䮙דⴱ涫㜥 ⴱ涫㜥⟃勻ךꞿ䎃ך㔓篑 J.J.Sylvester, Chemistry and Algebra, Nature, 17:284 (1878). GDB-11 (Fink+, JCIM 2007) C,N,O,F,ʹΑΔ11ݪࢠҎԼͷ෼ࢠͷશྻڍ (2640ສ) GDB-13 (Blum+, JACS 2009) C,N,O,S,ClʹΑΔ13ݪࢠҎԼͷ෼ࢠͷશྻڍ (9ԯ7700ສ) GDB-17 (Ruddigkeit+, JCIM 2012) C,N,O,S,ϋϩήϯʹΑΔ17ݪࢠҎԼͷ෼ࢠͷશྻڍ (1,664ԯ) ˖ 僇然ז圓䧭䚍ٌآُ٦ٕ䚍 鎉铂俑岀涸銲稆ך穈さׇד醱꧟ז׮ך׾欰䧭 3 3 3 ) Hydrogen / 0 )0 Proline 0 /    Oxazoline 0 /    Amide Ethyl Cyclohexyl adamantyl  3 3 3 ʹ͸༷ʑͳஔ׵ج͕ೖΕΒΕΔ
  4. / 41 5 ז׈ؚٓؿַⴓ㶨邌植ך穈さׇ锷涸⩎꬗ ˖ 鿇ⴓ圓鸡嗚稊٥鿇ⴓ♧荜وحثؚٝךص٦ؤ https://pubchem.ncbi.nlm.nih.gov/#query=C12CC(C(CC1)C2)C ݫີҰகݕࡧ Norbornane ظٕنٕشٝ

    ྨࣅੑݕࡧ ্෦ߏ଄ݕࡧ ෦෼ߏ଄ݕࡧ ཱମྨࣅੑݕࡧ ΫΤϦߏ଄ͱಉ͡ ΫΤϦͱྨࣅ ΫΤϦߏ଄ʹؚ·ΕΔ ΫΤϦߏ଄ΛؚΉ ΫΤϦߏ଄ͱཱମతʹྨࣅ
  5. / 41 6 ז׈ؚٓؿַⴓ㶨邌植ך穈さׇ锷涸⩎꬗ ˖ ⴓ㶨ך؝،װػ٦خך겲⡂䚍ⴓ㶨낦呓 4DBPME הؿًؚٓٝز ˖ 殯䚍⡤הٕ٦ٕك٦أךⴓ㶨欰䧭

    https://www.molgen.de/online.html EXAMPLE 5: Generate all (theoretically possible) structures of mass ≤ 40 with elements, C, H, N3, O Hu, Stumpfe, Bajorath, J Med Chem (2016) https://doi.org/10.1021/acs.jmedchem.5b01746 Liu, Naderi, Alvin, Mukhopadhyay, Brylinski, JCIM (2017) https://doi.org/10.1021/acs.jcim.6b00596
  6. / 41 8 ˖ 痥♧⾱椚 4DISµEJOHFS倯玎䒭 הꆀ㶨⻉㷕涸זꨵ㶨朐䡾 3FBMJUZ#JUFT僇׵ַזꬊ穈さׇ锷涸⩎꬗ ˖ ؚٓؿػة٦ٝך窟鎘ⴓ匿דכ䲕׫חְֻ㼎韋٥植韋㢳侧

    #*/"1ꐪ⡤ ♶俕さ䧭ؒشٝثؔو٦ ꖎ⫷殯䚍⡤ &2 &2ˏ 54 &2 54 &2ˏ <latexit sha1_base64="dwtAUUE0cfsFu6+2FLg7b109CNE=">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</latexit> ✓i <latexit sha1_base64="tkPRNIYeS8tNgbH62CO/ULi3LDw=">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</latexit> ✓j https://en.wikipedia.org/wiki/Chirality_(chemistry) ⾱㶨騃ꨄ遤⴨٥暟颵ꆀ٥ؒطٕ ؘ٦ֶ״ן暟椚涸䚍颵כⰋֻずׄ ׌ָ➭ךⴓ㶨ה湱✼⡲欽ׅ׷הֹ 䚍颵ָ麩ְֲ׷  欰⡤ⰻⴓ㶨װ剣堣⻉㷕ך⚺㼎韋 ꐪ⡤זוꆃ㾩ך⾱㶨ָⰅ׷㜥さֿ׸כ鿇ⴓ圓鸡 ✺ղך㉏겗דכזֻ⯋稆暴䚍ך罋䣁ָ䗳銲˘
  7. / 41 9 ٌرٕ䒭 CH 3 N N H N

    H H 3 C N ⢽圓鸡崞䚍湱ꟼ 4"3 չ䕎圓鸡պַ׵欰暟崞䚍װ暟䚍׾✮庠ׅ׷ <latexit sha1_base64="tiacEhQgmTkomNeV5LHmrY6hmbk=">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</latexit> x1 <latexit sha1_base64="4Sn0JXQ8Nli9zYaRMiYfd4a9JHg=">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</latexit> x2 <latexit sha1_base64="4+jTZNjL3Gn2jlRZoSuvOUm3czc=">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</latexit> . . . <latexit sha1_base64="9bGzB58W461U5gZXfti9NDCxbbY=">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</latexit> y Hansch-Fujita QSAR (Hammetଇͷੜ෺ֶ൛) (Hammettఆ਺) Hammettଇ <latexit sha1_base64="Rtaf0NASFdmDpXAc2f6wWTFtSe0=">AAACnnichVHLSsNAFD3G97NVN4qbYFF0UycqKoIgCiKIWB/Vgi0lidM6mBdJWtAi7v0BF64UXIigSz/AjT/gop8gLhXcuPA2DYiK9YbJnDlzz50zczXHEJ7PWLlOqm9obGpuaW1r7+jsikS7e7Y9u+DqPKnbhu2mNNXjhrB40he+wVOOy1VTM/iOdrBY2d8pctcTtrXlHzo8Y6p5S+SErvpEZaP9acPOj6yMrWSXR+U5Oe3u23LaE3lTzUZjLM6CkH8DJQQxhJGwo/dIYw82dBRggsOCT9iACo++XShgcIjLoEScS0gE+xzHaCNtgbI4ZajEHtA/T6vdkLVoXanpBWqdTjFouKSUMcSe2DV7ZY/shj2zjz9rlYIaFS+HNGtVLXeykdO+zfd/VSbNPva/VDU9+8hhJvAqyLsTMJVb6FV98ejsdXN2Y6g0zC7ZC/m/YGX2QDewim/61TrfOK/hRyMv9GLUIOVnO36D7fG4MhWfWJ+MzS+ErWrBAAYxQv2YxjyWkUCS6p/gCre4k2RpSVqV1qqpUl2o6cW3kFKfW6GYqg==</latexit> log(K/K H ) = ⇢ 9) 㸜䜁껺ꃐ ךהֹה9ח⡦ַⴽך縧䳔㛇׾ Ⰵ׸׋儗ך⿾䘔鸞䏝嫰ָ♧如䒭חז׷穗꿀⵱ “Linear Free Energy Relationships (LFERs)” ꨵ㶨׾⳿ַׅ 《׷ַ䏝さְ 毙宏䚍ך 䏝さְ 甧⡤⸬卓ך 䏝さְ <latexit sha1_base64="Xiu9z9gQDsGsRYjNbuMpINCUhK0=">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</latexit> log(1/C) = 1(log P)2 + 2 log P + 3 + 4Es + Const. (Taftఆ਺) (෼഑܎਺) ੜ෺׆ੑ΍ ೱ౓ ػًٓة鎸鶢㶨 崞䚍暟䚍 圓鸡 堣唒㷕统ח実׭׵׸׷ֿה穗꿀⵱ךさ椚⻉٥礵篈⻉
  8. / 41 10 岣䠐ׅץֹֿה 0QFO1SPCMFN ٌرٕ䒭 CH 3 N N

    H N H H 3 C N ػًٓة鎸鶢㶨 <latexit sha1_base64="tiacEhQgmTkomNeV5LHmrY6hmbk=">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</latexit> x1 <latexit sha1_base64="4Sn0JXQ8Nli9zYaRMiYfd4a9JHg=">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</latexit> x2 <latexit sha1_base64="4+jTZNjL3Gn2jlRZoSuvOUm3czc=">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</latexit> . . . 崞䚍暟䚍 <latexit sha1_base64="9bGzB58W461U5gZXfti9NDCxbbY=">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</latexit> y 圓鸡 ˖ չ崞䚍͏f 鎸鶢㶨 պה׃ג؛ٌ؎ٝؿؓوذ؍ؙأך⚺㉏겗ך♧אח ˖ 植㖈דכⴓ㶨鎸鶢㶨׾侧⼪珏겲鎘皾׃גֻ׸׷اؿزؐؑ،זו׮֮׷ ˖ 䘔欽窟鎘㷕ך㛇劤ךؗ⡦ד׮ַ׿ד׮铡僇㢌侧חְ׸גכְֽזְ 剑鵚ך 堣唒㷕统ך罋ִ倯姻⵱⻉װر٦ة鏣鎘 USBJOJOHWBMJEBUJPOUFTU ד PWFSUװMFBLBHFךٔأָؙ黝ⴖח㔐鼘ׁ׸גְ׸ל0,זךדכ  ⤘侧׾鍑ꅸ׃׋ְ 毙宏䚍ꨵ㶨⸬卓甧⡤⸬卓ו׸ָ⸬ְ׋ַ ָծ湱ꟼָ䓼ְ㢌侧ָ醱侧֮׷ה 堣唒㷕统涸חכ׉ך⚥ךו׸ַ♧אדקר葺ְךד ו׸ָ⸬ְ׋ה鎉ִזֻז׷ծְ׻ײ׷ չوٕث؝ 㢳ꅾⰟ简䕎䚍 պ㉏겗  ؗحثٝءؙٝ 椚锷涸呎䬿ז׃ח⡦ד׮ַ׿ד׮铡僇㢌侧ח⸇ִ׷ 㔐䌓׾ׅ׷הPWFSUׅ׷ ׌ֽ؟ٝفٕ侧״׶㢌侧ָ㢳ְז׿ג،مזך
  9. / 41 圓鸡ָ⡂גְג׮崞䚍鼅䫛䚍ָ⡂גְזְ⢽׮㢳ְ˘ 11 Stumpfe and Bajorath, J Med Chem

    (2012) https://doi.org/10.1021/jm201706b Activity cliffs Selectivity cliffs 㹋ꥷחכ圓鸡ָק׿ך㼰׃㢌׻׷ה崞䚍װ鼅䫛䚍ָ㣐ֹֻ 㢌׻׏ג׃תֲ⢽ָ㢳ֻ㶷㖈ׅ׷
  10. / 41 12 ؝ٝؾُ٦ةفؚٗٓي CH 3 N N H N

    H H 3 C N 0.739 ꣖㹱慬䏝    H 3 C H 3 C NH O N O N O CH3 O N NH 2 O CH3 Br CH3 N H 3 C H N S N O CH3 N OH CH3 CH3 N N N CH3 H 3 C H2 N NH2   Ⰵ⳿⸂ך 鋅劤⢽ 堣唒㷕统ַ׵כֲֿ鋅ִָ׍˘ ݟຊྫ͔ΒͷϓϩάϥϜੜ੒
  11. / 41 13 㹋ꥷךر٦ةإحزך圫㶨 • Mutagenic potency • Carcinogenic potency

    • Endocrine disruption • Growth inhibition • Aqueous solubility N NH O O H H H H H H H H H H H H H H H   H H H H H H H H H H  O O O O O O Cl H H H H H H H H H H H H H H H H H  Br Br O P O O Br Br O Br Br H H H H H H H H H H H H H H H  N S N N H H H H H H H  H H H H H H H H O N O O H  H H O O H H N O O Cl Cl Cl  H H H H H H H N O O   H H H H H H H H H N O O  H H H H H H H N H N O O N O O H H H H H H H H N   CH3 O O H N Cl Cl Cl Cl Cl   H 3 C O O O O O O H 3 C CH3 CH2  O HN O O NH  CH3 HO OH CH 3 N O O  CH 3 N N H N H H 3 C N  H 3 C H 3 C NH O N O N O  CH3 O N NH 2 O CH3 Br  CH3 N H 3 C H N S N O CH3 N OH  CH3 CH3 N N N CH3 H 3 C H2 N NH2  H OH O HO CH 3 H H O CH 3  H O O H 3 C H H H O H 3 C S CH3 O  H H O CH3 CH3 O O HO H 3 C H HO F H O H 3 C  NH 2 O N HO H O O  H H O O O H 3 C O O O CH 3 O CH 3 H O CH 3 H O O CH 3 H H N H N O H 3 C  O O O 
  12. / 41 14 植㖈תדך堣唒㷕统ך娄׫׾꽀ֽ駈ד䮶׶鵤׷ ˖ ,BTIJNB,FSOFM ˖ 8FJTGFJMFS-FINBO,FSOFM ˖ &$'1

    $JSDVMBS'JOHFSQSJOU  ˖ 걼⳿鿇ⴓؚٓؿ圓鸡 ˖ .%-."$$4,FZT ˖ 1VC$IFN'JOHFSQSJOU ꨄ侔ٓكٕאֹؚٓؿ邌植鿇ⴓ圓鸡ך剣搀װ侧ַ׵ך✮庠 鿇ⴓؚٓؿ䱱稊ٌرٕ㷕统 ꨄ侔ٓكٕ׾馄ִג邌植㷕统הؚٓؿصُ٦ٕٓطحزٙ٦ؙ (// ؚٓؿؕ٦طٕؕ٦طٕ岀 ✲⵸ח㹀纏ׁ׸׋鿇ⴓ圓鸡暴䗙 ر٦ةח欰饯ׅ׷鿇ⴓ圓鸡暴䗙 ˖ 鿇ⴓؚٓؿ⴨䮙加♳דך简䕎㷕统٥寸㹀加㷕统 ˖ H-"34H#PPTU ˖ (//ה8FJTGFJMFS-FINBOؚٓؿず㘗嗚叨 8-  ˖ &$'1ה/FVSBM'JOHFSQSJOU ˖ .1//ה%.1//$IFN1SPQ ˖ ("5ה5SBOTGPSNFS㘗(// ˖ ⴓ㶨邌植ך✲⵸㷕统ה鯄獳㷕统 ˖ ⴓ㶨邌植ך欰䧭 ˖ 䎗⡦涸(//הꆀ㶨⻉㷕鎘皾ך넝礵䏝넝鸞鵚⡂
  13. / 41 15 ꨄ侔ٓكٕאֹؚٓؿה׃גך邌植 =@<TRIPOS>MOLECULE ***** 13 13 0 0

    0 SMALL GASTEIGER @<TRIPOS>ATOM 1 C -2.5458 -9.4750 0.0000 C.2 1 UNL1 0.3080 2 C -3.3708 -9.4750 0.0000 C.2 1 UNL1 0.2529 3 C -2.2875 -8.6917 0.0000 C.2 1 UNL1 0.3838 4 C -3.6208 -8.6917 0.0000 C.3 1 UNL1 0.2067 5 O -2.9583 -8.2042 0.0000 O.3 1 UNL1 -0.4441 6 C -4.3583 -8.3125 0.0000 C.3 1 UNL1 0.2245 7 O -1.5000 -8.4375 0.0000 O.2 1 UNL1 -0.2412 8 O -2.0583 -10.1417 0.0000 O.2 1 UNL1 -0.2764 9 O -3.8500 -10.1417 0.0000 O.2 1 UNL1 -0.2843 10 O -5.0500 -8.7542 0.0000 O.3 1 UNL1 -0.2164 11 O -3.6958 -7.0417 0.0000 O.3 1 UNL1 -0.2174 12 C -4.3958 -7.4875 0.0000 C.3 1 UNL1 0.2185 13 H -4.2083 -9.2667 0.0000 H 1 UNL1 0.0853 @<TRIPOS>BOND 1 2 1 2 2 3 1 1 3 4 2 1 4 5 3 1 5 6 4 1 6 7 3 2 7 8 1 1 8 9 2 1 9 6 10 1 10 11 12 1 11 12 6 1 12 4 13 1 13 5 4 1 $BOPOJDBM4.*-&4 OC[C@H](O)[C@H]1OC(=O)C(=C1O)O 4UBOEBSE*O$I* 4UBOEBSE*O$I*,FZ CIWBSHSKHKDKBQ-JLAZNSOCSA-N .0-'PSNBU InChI=1S/C6H8O6/ c7-1-2(8)5-3(9)4(10)6(11)12-5/ h2,5,7-10H,1H2/t2-,5+/m0/s1 1 2 3 4 5 6 7 8 9 10 11 12 13 2 2 1 1 1 1 1 1 1 1 1 1 1 single single single double double double double double double single single single aromatic aromatic aromatic aromatic aromatic aromatic كٝئٝ橆ך黝ⴖזⰻ鿇邌植 Kekulé Form
  14. / 41 16 'JOHFSQSJOU ⴓ㶨䭷秘 ה鿇ⴓ圓鸡暴䗙 ✲⵸ח㹀纏ׁ׸׋⦐ך圓鸡暴䗙ך剣搀 MDL MACCS Keys

    ΑΓෳࡶͳߏ଄ಛ௃ύλʔϯΛ໢ཏͨ͠PubChem Fingerprint (881bit)ͳͲ΋ 00000000000000000000000000000000000000000000000000001100 00000000000000000000000000000000010000100000000000000000 0100000100011101000101010001001111100010101011111111110 Aromatic Ring>1 [F,Cl,Br,I] Heterocycle ֤ߏ଄ಛ௃ͷ༗ແΛ ֤bit(0/1)ʹ ECFP (Extended Connectivity Fingerprint) 00001000100011001011001000001000010 HashingͰݻఆ௕ͷ bit string΁ม׵ ֤ۙ๣ߏ଄ʹuniqueͳ id൪߸Λׂ౰ͯΔ https://docs.chemaxon.com/display/docs/extended-connectivity-fingerprint-ecfp.md ⼱䖇Sך갥挿鵚⩸圓鸡暴䗙׾⸬桦涸חⰋ⴨䮙 ୳ࡧ൒ܘͷ্ݶͱϏοτ௕͸ύϥϝλ …
  15. / 41 17 &$'1ד⢪׻׸׷ⴓ㶨ؚٓؿ邌植 %POPS     

    "DDFQUPS      "SPNBUJD      )BMPHFO      #BTJD      "DJEJD      زهٗآ ؚٓؿ圓鸡 &$'1͏3%LJUך⾱㶨♶㢌ꆀ VTF'FBUVSFT'BMTF ぐ갥挿 װぐ鴟װぐ갥挿㼎 חչ♶㢌ꆀ ⾱㶨׀הח㔿剣ך㢳㢌ꆀ պ׾➰♷׃׉׸׾ ꨄ侔ٓكٕה׃ג䪔ֲ Implicit Hydrogens Explicit Hydrogens Structural Formula ⴓ㶨ؚٓؿפ ؒٝ؝٦ر؍ؚٝ BUPNJDOVNCFS       UPUBMEFHSFF       )T       GPSNBMDIBSHF       JTPUPQF       JO3JOH       '$'1͏3%LJUך⾱㶨♶㢌ꆀ VTF'FBUVSFT5SVF Atomic Invariants
  16. / 41 <latexit sha1_base64="9kTSgBYDa8jzBNKjMs5WyhQ5V3k=">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</latexit> K , ! = 18 0.1

    0.7 0.9 ⋮ ⋮ 1.2  0 0 1 1 1 0  1 0 0 0 0 1  1 1 0 1 1 0  ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ 1 0 1 1 1 0  y 鿇ⴓ圓鸡暴䗙ך剣搀ח״׷暴䗙كؙزٕ⻉ Ⰵ⸂圓鸡 ؙؒٔ鿇ⴓ圓鸡ה׃ג⡦׾׮׏גֻ׷ַָ殯ז׷ ٙ؎ٕسؕ٦س俑㶵׾鏩㺁ׅ׷ַזו׮ろ׭ג ؚٓؿؕ٦طٕؕ٦طٕ岀 鿇ⴓؚٓؿ䱱稊ٌرٕ㷕统 ꤿח暴䗙كؙزٕ⻉ׇ׆ծⰻ琎⦼ך׫׾ ت؎ؙٖزח鎘皾 ؕ٦طٕزٔحؙ ׃ 47.זוⰻ琎ך׫ד鎘皾〳腉ז䩛岀פ䌓滠 Ⱏ鸐ׅ׷鿇ⴓ ؚٓؿך侧 ׅץגך欰饯鿇ⴓ圓鸡ך⚥ַ׵⦪酡׾䱱稊׃ 䨽♷ةأؙח㺔♷׃ֲ׷׮ך׌ֽ׾鼅䫛涸ח 㢌侧ה׃ג堣唒㷕统ٌرٕפ鷄⸇׃גְֻ ر٦ةإحزח걼⳿ׅ׷鿇ⴓ圓鸡׾ꤿח⴨䮙 WTؕ٦طٕ 䌢חⰋ㢌侧׾罋䣁׃ג׃תֲ
  17. / 41 19 ؚٓؿؕ٦طٕؕ٦طٕ岀 Kashima Kernel (Kashima+ 2003) Weisfeiler-Lehman Kernel

    (Shervashidze+ 2011) <latexit sha1_base64="wzm3ilbAnfk/uMMoZ6aWms13YM8=">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</latexit> G1 <latexit sha1_base64="FUojSoBiuD8NhDGX50StN4VMT70=">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</latexit> G2 1 1 2 2 2 3 3 4 4 5 5 1,4 1,4 2,35 2,45 2,3 3,245 3,245 4,1235 4,1135 5,234 5,234 1,4 1 6 6 8 9 7 10 10 12 11 13 13 6 … … … … 2 1 1 1 1 2 0 1 1 2 3 4 5 6 7 8 1 2 1 1 1 1 1 0 ⰻ琎⦼ 8FJTGFJMFS-FINBO暴䗙كؙزٕ 鵚⩸꧊秈ⱄٓكؚٔٝ 㢌⻉ָזֻז׷תד粸׶鵤ׅ Marginalized Kernel (Tsuda+ 2002) 錁庠㢌侧 ꦀ׸㢌侧 R-Convolution Kernel (Haussler 1999)  ꟼ⤘RדD⦐ך鿇ⴓפⴓ鍑 ؚٓؿ♳ךׅץגךٓكٕ⴨♳ך俑㶵⴨ؕ٦طٕ ך劍䖉⦼ה׃ג㹀纏ׁ׸׷➿邌涸ؚٓؿؕ٦طٕ ؚٓؿ♳ךٓٝتيؐؓ٦ؙ ד欰䧭ׁ׸׷ٓكٕ⴨ 8FJTGFJMFS-FINBOذأزֿךאך瘝⣣䚍ד ؚٓؿず㘗ⴻ㹀׾遤ֲ〢Ⱙ涸)FVSJTUJDT <latexit sha1_base64="wpyn9s0DvnQcyTF5k8mpdFbbQqA=">AAACjXichVHLSsNAFD2N7/po1Y3gplgqFaRM6hMRKbqo4KZV+8AHJYnTGpomIUkLWvwB14ILUVBwIX6AH+DGH3DhJ4hLBTcuvE0DokW9YTJnztxz58xc2dRU22HsySe0tXd0dnX3+Hv7+gcCwcGhrG1ULYVnFEMzrLws2VxTdZ5xVEfjedPiUkXWeE4urzT2czVu2aqhbzoHJt+tSCVdLaqK5BC1tRZNFsTJZCE+UQiGWYy5EWoFogfC8CJlBO+wgz0YUFBFBRw6HMIaJNj0bUMEg0ncLurEWYRUd5/jCH7SVimLU4ZEbJn+JVpte6xO60ZN21UrdIpGwyJlCBH2yG7YK3tgt+yZffxaq+7WaHg5oFluarlZCByPbLz/q6rQ7GD/S/WnZwdFzLteVfJuukzjFkpTXzs8fd1YWI/Ux9kVeyH/l+yJ3dMN9Nqbcp3m62d/+JHJC70YNUj82Y5WkI3HxNnYVHo6nFj2WtWNUYwhSv2YQwKrSCFD9XWc4BwXQkCYERaFpWaq4PM0w/gWQvITcWuSUA==</latexit> K(G1, G2)
  18. / 41 20 鿇ⴓؚٓؿ䱱稊ٌرٕ㷕统 ؚٓؿ꧊さח欰饯ׅ׷ׅץגך鿇ⴓؚٓؿ׾䱱稊 H4QBOך加朐ך䱱稊瑞꟦ ⴨䮙加 <latexit sha1_base64="JQWY0sKtSB2gZKyDx03+dQGakWQ=">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</latexit> {Gi

    }n i=1 ⢽H4QBO :BOBOE)BO *$%. ד걼⳿鿇ⴓؚٓؿ׾⴨䮙 8BMF /JOH ,BSZQJT  ˖ GQ )BTIFEOHFSQSJOUXQBUIT DZDMFT  ˖ &$'1 ˖ ., ."$$4,FZT  ˖ '4 걼⳿鿇ⴓؚٓؿ  ˖ (' ♧㹀؟؎ؤ⟃♴ךⰋ欰饯鿇ⴓؚٓؿ 걼⳿׌ֽכ葺ֻזְ #SBODI#PVOEד䗳銲ז鿇ⴓؚٓؿ暴䗙׾㷕统׃זָ׵ず儗ח堣唒㷕统ٌرٕ׾圓眠 欰饯鿇ⴓؚٓؿַ׵剣⸬ז׮ך׾鷵如涸ח鼅䫛׃ծず儗חٌرٕ׾㷕统 欰饯鿇ⴓؚٓؿך⴨䮙加♳דך简䕎㷕统 ˖ "EBCPPTU ,VEPFUBM /*14  ˖ H-"34 5TVEB *$.- H1-4 4BJHPFUBM ,%% H#PPTU 4BJHPFUBM .BDI-FBSO  ˖ &MBTUJD/FU姻⵱⻉אֹ♧菙ך简䕎㷕统פך䭁䓸 5BLJHBXBBOE.BNJUTVLB 51".* 欰饯鿇ⴓؚٓؿך⴨䮙加♳דךꬊ简䕎㷕统 ˖ 寸㹀加 ⴓ겲加٥㔐䌓加 ׾㷕统加،ٝ؟ٝـٕ㷕统 4IJSBLBXBFUBM .-(!,%% Wale N., Ning X., Karypis G. (2010) Trends in Chemical Graph Data Mining. In: Aggarwal C., Wang H. (eds) Managing and Mining Graph Data. Advances in Database Systems, vol 40. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6045-0_19
  19. / 41 20 鿇ⴓؚٓؿ䱱稊ٌرٕ㷕统 ؚٓؿ꧊さח欰饯ׅ׷ׅץגך鿇ⴓؚٓؿ׾䱱稊 H4QBOך加朐ך䱱稊瑞꟦ ⴨䮙加 <latexit sha1_base64="JQWY0sKtSB2gZKyDx03+dQGakWQ=">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</latexit> {Gi

    }n i=1 ⢽H4QBO :BOBOE)BO *$%. ד걼⳿鿇ⴓؚٓؿ׾⴨䮙 8BMF /JOH ,BSZQJT  ˖ GQ )BTIFEOHFSQSJOUXQBUIT DZDMFT  ˖ &$'1 ˖ ., ."$$4,FZT  ˖ '4 걼⳿鿇ⴓؚٓؿ  ˖ (' ♧㹀؟؎ؤ⟃♴ךⰋ欰饯鿇ⴓؚٓؿ 걼⳿׌ֽכ葺ֻזְ #SBODI#PVOEד䗳銲ז鿇ⴓؚٓؿ暴䗙׾㷕统׃זָ׵ず儗ח堣唒㷕统ٌرٕ׾圓眠 欰饯鿇ⴓؚٓؿַ׵剣⸬ז׮ך׾鷵如涸ח鼅䫛׃ծず儗חٌرٕ׾㷕统 欰饯鿇ⴓؚٓؿך⴨䮙加♳דך简䕎㷕统 ˖ "EBCPPTU ,VEPFUBM /*14  ˖ H-"34 5TVEB *$.- H1-4 4BJHPFUBM ,%% H#PPTU 4BJHPFUBM .BDI-FBSO  ˖ &MBTUJD/FU姻⵱⻉אֹ♧菙ך简䕎㷕统פך䭁䓸 5BLJHBXBBOE.BNJUTVLB 51".* 欰饯鿇ⴓؚٓؿך⴨䮙加♳דךꬊ简䕎㷕统 ˖ 寸㹀加 ⴓ겲加٥㔐䌓加 ׾㷕统加،ٝ؟ٝـٕ㷕统 4IJSBLBXBFUBM .-(!,%% 24"3דך✮庠礵䏝כ&$'1 3BOEPN'PSFTUהず玎䏝˘ Wale N., Ning X., Karypis G. (2010) Trends in Chemical Graph Data Mining. In: Aggarwal C., Wang H. (eds) Managing and Mining Graph Data. Advances in Database Systems, vol 40. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6045-0_19
  20. / 41 21 ⴓ㶨ةأؙךٖكٕה害欽ךⴓ㶨邌植ך㷕统 Wu et al, MoleculeNet: a benchmark

    for molecular machine learning, Chem Sci (2017) https://doi.org/10.1021/jm201706b http://moleculenet.ai ⴓ㶨荈⡤ך暴䚍ה׃ג㹀ת׷ ءىُٖ٦ءّٝ椚锷鎘皾ָ〳腉 ➭ךⴓ㶨הך湱✼⡲欽װ橆㞮勴⟝זו㢳㔓㶨涸ח㹀ת׷ ˖ 鿇ⴓؚٓؿػة٦ٝך剣搀װ侧דכ䯝ִ׵׸זְꬊ穈さׇ锷涸⩎꬗׾罋䣁דֹ׷ַ ˖ 䎢ְٖكٕד⢪ִ׷害欽ךⴓ㶨邌植׾ر٦ةַ׵㷕统דֹ׷ַ
  21. / 41 22 NPSFUIBO EFTDSJQUPST ˖ %鎸鶢㶨 ˖ DPOTUJUVUJPOBMEFTDSJQUPST ˖

    DPVOUEFTDSJQUPST ˖ %鎸鶢㶨 ˖ MJTUPGTUSVDUVSBMGSBHNFOUT ˖ GJOHFSQSJOUT ˖ %鎸鶢㶨 ˖ HSBQIJOWBSJBOUT ˖ %鎸鶢㶨 ˖ %.P34& 8)*. (&5"8":  ˖ RVBOUVNDIFNJDBMEFTDSJQUPST ˖ TJ[F TUFSJD TVSGBDF WPMVNF FUD ˖ %鎸鶢㶨 ˖ (3*% $P.'" 7PMTVSG  %3"(0/  EFTDSJQUPST ㉀欽ך鎸鶢㶨اؿزؐؑ، ˖ 㹋꿀涸ז鎘庠ꆀ ˖ 鎘皾涸ז鎸鶢㶨 Quantitative Structure–Property Relationship Modeling of Diverse Materials Properties. Chem Rev, 2012, 112 (5), pp 2889–2919 ؔ٦فٝا٦أؿٖ٦يٙ٦ؙ • Descriptors • Descriptors3D • GraphDescriptors • Fingerprints • ChemicalFeatures • ChemicalForceFields rdkit.Chem rdkit.ML.Descriptors ⦐ⴽח➂䩛דرؠ؎ׁٝ׸׋ⴓ㶨鎸鶢㶨כ㢳侧˘ Todeschini and Consonni, Molecular Descriptors for Chemoinformatics. Wiley‐VCH, 2009. https://doi.org/10.1002/9783527628766
  22. / 41 23 邌植㷕统ך鑐׫(SBQI/FVSBM/FUXPSLT (//T 暴䗙كؙزٕ زهٗآ 갥挿暴䗙 鴟暴䗙 CC1CCNO1

    Representation Learning … ˖ ⴓ겲 ˖ 㔐䌓 ˖ 欰䧭 圫ղז ♴崧ةأؙ ⴓ㶨ך橆㞮勴⟝垥涸湱✼⡲欽瘝ך䞔㜠 NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1 ؚٓؿ邌植 ⻉㷕圓鸡낦呓㸼腉㛇 甧⡤ꂁ䏟ꨵ㶨朐䡾 ⻉㷕⿾䘔圓鸡ך穈剏ִ Task-Specific Head
  23. / 41 24 .FTTBHF1BTTJOH/FVSBM/FUXPSLT .1//T N O C C C

    C H H H H H N O C C C C H H H H H ぐ暴䗙كؙزٕך刿倜 .-1זו (sum, mean or max) 갫殢װ侧ח⣛㶷׃זְ꧊秈乼⡲ .-1זו Ԯ ԯ ԰ Ԯ ԯ ԰ 縧䳔♶㢌 JOWBSJBOU + attention 縧䳔ず㢌 FRVJWBSJBOU <latexit sha1_base64="WNEpfX6Bt3G9f3Toyi7bd0iGAgY=">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</latexit> hi 0 @hi, M j2Ni (hi, hi, eij) 1 A
  24. / 41 25 (//ך㛇劤涸䚍颵חאְגך椚鍑 ˖ 8FJTGFJMFS-FINBOذأزהךꟼ⤘ <latexit sha1_base64="g4+ASD58WMoop6pPZrlXxKmH4Ao=">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</latexit> h(l+1) i

    0 @h(l) i , M j2Ni cij (h(l) j ) 1 A 갫殢װ侧ח⣛㶷׃זְ꧊秈乼⡲ IBTI乼⡲׾䗍ⴓ〳腉ז怴皾חׅ׷ה($/ח (Kipf and Welling, ICLR ︎2017) ˖ ؚٓؿず㘗ⴻ㹀ך䠐㄂דכ(//כ8-"MHPSJUINה邌植⸂ָずׄ ˖ ꧊秈乼⡲ך鼅䫛ד邌植⸂ָ㢌׻׷TVNNFBONBY <latexit sha1_base64="/ysxkHppQdzDUyY3/GZwEdDJ/xs=">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</latexit> M <latexit sha1_base64="wzm3ilbAnfk/uMMoZ6aWms13YM8=">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</latexit> G1 <latexit sha1_base64="FUojSoBiuD8NhDGX50StN4VMT70=">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</latexit> G2 ✳אךؚٓؿכず㘗דכזְָ 8-װ(//דכ⼒ⴽדֹזְ Xu, Hu, Leskovec, Jegelka, How powerful are graph neural networks? ICLR (2019) Kipf and Welling, Semi-supervised classification with graph convolutional networks. ICLR (2017)
  25. / 41 26 &$'1ה/FVSBM(SBQI'JOHFSQSJOU ˖ /FVSBM(SBQI'JOHFSQSJOU剑ⴱ劍ח䲿周ׁ׸׋(//ך♧א ˖ (SBQI$POWPMVUJPO׾欽ְ׋(//ך♧珏ה׫זׇ׷ ˖ &$'1

    $JSDVMBS'JOHFSQSJOU ך'JOHFSQSJOU鎘皾׾ػًٓة׾䭯א䗍ⴓ〳腉ז 怴皾ד剅ֹ湫ֿׅהד䖤׵׸׷㷕统〳腉ז'JOHFSQSJOUהְֲ⡘縧בֽ Duvenaud, Maclaurin, Aguilera-Iparraguirre, Gómez-Bombarell, Hirzel, Aspuru-Guzik, Adams, Convolutional networks on graphs for learning molecular fingerprints. NIPS (2015)
  26. / 41 27 %.1//$IFN1SPQ <latexit sha1_base64="cBeKmO56fa7C7dRhqoeO+wzPccY=">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</latexit> 1 <latexit sha1_base64="M4MwU1uekvwiIbvhYrrTkZ2bkH0=">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</latexit> 2

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sha1_base64="HUwuCxIfVPe4d9fD0xY/i61Z2jg=">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</latexit> e4 in-edges aggregate <latexit sha1_base64="bY/zJsMyfi+VfZIaAVc1VF0vNBA=">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</latexit> v1 concat update 鴟ךꦀ׸㢌侧׾刿倜 5㔐 갥挿ך㢌侧׾刿倜 Directed MPNN (Dai et al, ICML 2016) node feature ChemProp (Yang et al, JCIM 2019) https://github.com/chemprop/chemprop .BDIJOF-FBSOJOHGPS1IBSNBDFVUJDBM%JTDPWFSZ BOE4ZOUIFTJT$POTPSUJVN!.*5ָꟚ涪׃ծ㹋ꥷ ך䫑欰暟颵䱱稊ח欽ְ׵׸׋剣せז(//ך䧭⸆⢽ ꦀ׸㢌侧׾갥挿דכזֻ剣ぢ鴟ח㼎䘔בֽג刿倜 Stokes et al, Cell (2020) https://doi.org/10.1016/j.cell.2020.01.021 Marchant, Nature (2020) https://doi.org/10.1038/d41586-020-00018-3
  27. / 41 28 ("5ה5SBOTGPSNFS㘗(// (Multihead) Self-attention Feed-forward NN Add +

    LayerNorm Add + LayerNorm ˖ ぐ갥挿ך暴䗙كؙزٕ׾刿倜ׅ׷ꥷח"UUFOUJPO׾Ⰵ׸׋ְ ˖ 5SBOTGPSNFSכزهٗآⵖ秈ךזְ(SBQI"UUFOUJPO/FUXPSL ("5 㢌珏ה׫זׇ׷ ˖ 鷞ח׮׍׹׿5SBOTGPSNFS㘗ך4FMG"UUFOUJPO׾(//ח׮׍ֿ׬ֿה׮דֹ׷ Transformer GNN Layer ⡂גְ׷˘ Embedding + Pos Encoding A Generalization of Transformer Networks to Graphs Dwivedi & Bresson (2020) https://arxiv.org/abs/2012.09699 Do Transformers Really Perform Bad for Graph Representation? Ying et al (2021) https://arxiv.org/abs/2106.05234 Communicative Representation Learning on Attributed Molecular Graphs Song et al (2020) https://www.ijcai.org/proceedings/2020/0392.pdf Graph-BERT: Only Attention is Needed for Learning Graph Representations Zhang et al (2020) https://arxiv.org/abs/2001.05140 Veličković, Cucurull, Casanova, Romero, Liò, Bengio, Graph Attention Networks (ICLR 2018) https://arxiv.org/abs/1710.10903 Joshi, Transformers are Graph Neural Networks. (2020) https://graphdeeplearning.github.io/post/transformers-are-gnns/ Ying et al (2021) ͷGraphormer͸ KDDCup 2021ͷOpen Graph Benchmark Large-Scale Challenge(ޙड़)ͷGraph-level λεΫͷ༏উϞσϧͰ࢖ΘΕͨ େن໛σʔλͳΒάϥϑͰ΋ Transformer͸༗ޮ…!?
  28. / 41 29 ⴓ㶨邌植ך✲⵸㷕统ה鯄獳㷕统 ˖ 5SBOTGPSNFSפךꟼ䗰כ 4FMG4VQFSWJTFEז 㣐鋉垷✲⵸㷕统ה鯄獳פך劍䖉ך植׸ ˖ ⴓ㶨ةأؙ׮植㹋ך⦐ⴽ朐屣דכ㼭؟ٝفٕד֮׷ֿהָקה׿ו

    ˖ ׮׃害欽ךⴓ㶨邌植׾㣐鋉垷✲⵸㷕统ח״׶栻䖤׃'FXTIPU;FSPTIPU鯄獳ָדֹ׷ ךז׵岚⿹⸬卓כ鎘׶濼׸זְ DG$7ך*NBHF/FUQSFUSBJOFE$// /-1ך#&35瘝 Strategies for Pre-training Graph Neural Networks Hu, Liu, Gomes, Zitnik, Liang, Pande, Leskovec (ICLR 2020) https://arxiv.org/abs/1905.12265 Self-Supervised Graph Transformer on Large-Scale Molecular Data Rong, Bian, Xu, Xie, Wei, Huang, Huang (NeurIPS 2020) https://arxiv.org/abs/2007.02835
  29. / 41 31 ⿫罋ؚٓؿ涸דכזְ暴䗙ָ⣛搫剣⸬ז㜥さ׮ ٕؗٓ#*/0-ٔٝꃐ 3חו׿ז 縧䳔㛇׾ Ⰵ׸׷ַ  鍗㯭鏣鎘ךꟼ䗰

    낦呓כ㔿㹀 Zahrt, Henle, Rose, Wang, Darrow, Denmark, Prediction of higher-selectivity catalysts by computer-driven workflow and machine learning. Science, 363(6424), 2019. https://doi.org/10.1126/science.aau5631
  30. / 41 32 䎗⡦涸(//ה( https://arxiv.org/abs/2104.13478 https://youtu.be/uF53xsT7mjc https://youtu.be/w6Pw4MOzMuo ICLR 2021 Keynote

    (Michael Bronstein) Seminar Talk (Petar Veličković) (//כ䌴䎢ְ䎗⡦圓鸡׾窟♧涸ח䪔ִ׷単穈׫ 堣唒㷕统ךٕؒٓٝ؜ٝ٥فؚٗٓي  (T(SJET (SPVQT (SBQIT (FPEFTJDT(BVHFT
  31. / 41 33 倜׋ז㉏겗הص٦ؤꆀ㶨⻉㷕鎘皾ך넝礵䏝넝鸞鵚⡂ N O C C C C

    H H H H H Dipole moment Isotropic polarizability HOMO energy LUMO energy Gap between HOMO and LUMO Electronic spatial extent Zero point vibrational energy Internal energy at 0K Internal energy at 298.15K Enthalpy at 298.15K Free energy at 298.15K Heat capavity at 298.15K Atomization energy at 0K Atomization energy at 298.15K Atomization enthalpy at 298.15K Atomization free energy at 298.15K Rotational constant A Rotational constant B Rotational constant C ICML 2017 https://arxiv.org/abs/1704.01212 JCTC 2017 https://doi.org/10.1021/acs.jctc.7b00577 (// ꆀ㶨⻉㷕鎘皾 㺘䏝害ꟼ侧岀 %'5 鎘皾 椚锷ח㛇בֻ怴糊涸זءىُٖ٦ءّٝ鎘皾׾堣唒㷕统ד➿椚ׇׁ׷ص٦ؤ 暴חⴓ㶨⹛⸂㷕鎘皾 .%鎘皾 זוך欽鷿ד넝礵䏝ז⾱㶨꟦هذٝءָٍٕק׃ְ ♷ִ׵׸׋⾱㶨ך瑞꟦⡘縧ַ׵⾱㶨禸ךهذٝءٍٕؒطؘٕ٦׾鎘皾ׅ׷ꟼ侧
  32. / 41 34 ⢽0(#-BSHF4DBMF$IBMMFOHF ,%%$VQ 1st place: 10 GNNs (12-Layer

    Graphormer) + 8 ExpC*s (5-Layer ExpandingConv) 73 GNNs (11-Layer LiteGEMConv with Self-Supervised Pretraining) 20 GNNs (32-Layer GNN with Noisy Nodes) Test MAE 0.1200 (eV) 2nd place:Test MAE 0.1204 (eV) 3rd place: Test MAE 0.1205 (eV) %ךⴓ㶨ؚٓؿַ׵ꆀ㶨⻉㷕鎘皾 %'5鎘皾 ד実׭׋)0.0-6.0ٍؘحف׾✮庠ׅ׷ةأؙ ر٦ةإحز1VC$IFN2$ַ׵  ؚٓؿ DG2.כ ؚٓؿ Results: https://ogb.stanford.edu/kddcup2021/results/#awardees_pcqm4m https://ogb.stanford.edu/kddcup2021/
  33. / 41 35 ؔٔآشٕך'$'1⾱㶨♶㢌ꆀ ؔٔآشٕך&$'1⾱㶨♶㢌ꆀ • the number of immediate

    neighbors who are “heavy” (non-hydrogen) atoms • the valence minus the number of hydrogens • the atomic number • the atomic mass • the atomic charge • the number of attached hydrogens • whether the atom is contained in at least one ring %BZMJHIU ⾱㶨♶㢌ꆀ • hydrogen-bond acceptor or not? • hydrogen-bond donor or not? • negatively ionizable or not? • positively ionizable or not? • aromatic or not? • halogen or not? 䎗⡦涸(//ד⢪׻׸׷ⴓ㶨邌植 Rogers and Hahn, JCIM (2005) https://doi.org/10.1021/ci100050t Faber et al, JCTC (2017) https://doi.org/10.1021/acs.jctc.7b00577 .1//ח״׷ꆀ㶨⻉㷕鎘皾鵚⡂ד欽ְ׵׸׋갥挿٥鴟暴䗙 鸬竲ꆀٓكٕ
  34. / 41 36 4DI/FUה$POUJOVPVT'JMUFS$POWPMVUJPOT ぐ⾱㶨ך呌ꨵ蚚הYZ[䏟垥⦼׌ָֽ♷ִ׵׸׷הֹך➿邌涸(// 4DI»UU /FVS*14 Continuous-Filter Convolutions (cfconv

    layers) <latexit sha1_base64="flzLPrMsSS6k1am7yfKyC95kal4=">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</latexit> dij rbf(γ,μ) #rbf MLP dim of element-wise product Gaussian Smearing <latexit sha1_base64="CP/gGUdLE1ahITrVyosFmAESNpw=">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</latexit> xi X j2Ni xj (exp( (dij µ))) <latexit sha1_base64="sUht8Mvlx5JoWAMHabceBQWRmAs=">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</latexit> xi 歗⫷זוꨄ侔ؚٔحسך$POWPMVUJPO怴皾ך 鸬竲䭁䓸חז׏גְ׷ Schütt, Kindermans, Sauceda, Chmiela, Tkatchenko, Müller, SchNet: A continuous-filter convolutional neural network for modeling quantum interactions. https://arxiv.org/abs/1706.08566 ぐ⾱㶨ך呌ꨵ蚚 ぐ⾱㶨ךYZ[䏟垥⦼
  35. / 41 37 ِ٦ؙٔحسך麊⹛纇חꟼׅ׷♶㢌䚍٥ず㢌䚍 ˖ ِ٦ؙٔحس纇&  %ך⚛鹌٥㔐鯄㼎獥䚍 ˖ 暴婊ِ٦ؙٔحس纇4&

     %ך⚛鹌٥㔐鯄٥ꖎ⫷㼎獥䚍 Schütt et al, SchNet. (2017) https://arxiv.org/abs/1706.08566 Satorras et al, E(n) Equivariant Graph Neural Networks. (2021) https://arxiv.org/abs/2102.09844 Anderson et al, Cormorant. (2019) https://arxiv.org/abs/1906.04015 Unke et al, PhysNet. (2019) https://arxiv.org/abs/1902.08408 Klicpera et al, DimeNet++. (2020) https://arxiv.org/abs/2011.14115 Fuchs et al, SE(3)-Transformers. (2021) https://arxiv.org/abs/2006.10503 Köhler et al, Equivariant Flows (Radial Field). (2020) https://arxiv.org/abs/2006.02425 Thomas et al, Tensor Field Networks. (2018) https://arxiv.org/abs/1802.08219 ⱖ⫷ָ㢌䳔חꟼ׃ג ♶㢌 JOWBSJBU ず㢌 FRVJWBSJBOU <latexit sha1_base64="NH4UQ68bqmsH0AzQM//vHVYIu40=">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</latexit> f(g · x) = g · f(x) <latexit sha1_base64="z65vGkIR8AznuZeRro+w9TcH+xY=">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</latexit> f(g · x) = f(x) 㢌䳔׃ג׮׃זְהֹה㢌׻׵זְ 㢌䳔׃גַ׵ⱖ⫷׃ג׮ⱖ⫷׃גַ׵㢌䳔׃ג׮㢌׻׵זְ <latexit sha1_base64="h5Nu57LzNEgsKVoc7SjFgDOfXxQ=">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</latexit> g 2 G <latexit sha1_base64="98i0QCpyFbQuYbP7ylFU0FuKpWo=">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</latexit> f : X ! Y 䎗⡦涸(//דכ㛇劤涸ז銲锜 暴חꆀ㶨⻉㷕鎘皾鵚⡂ך㜥さ &  ず㢌 &  ♶㢌 4&  ず㢌 ⾱㶨ךYZ[䏟垥⦼׾׉ךתת갥挿暴䗙ꆀחׅ׷ךכ– ➿周ך⢽⾱㶨꟦騃ꨄ׾鴟暴䗙ח 䎂遤獳⹛װ㔐鯄דYZ[כ㢌׻׷ָ⢽ִל׉ךⴓ㶨ךؒطؘٕ٦כ㢌׻׵זְ 갥挿װ鴟ך暴䗙ꆀװ(// ⱖ⫷ ךرؠ؎ٝד㹋植ׅ׷
  36. / 41 39 NeurIPS 2020 ICML 2020, 2021 ICLR 2020,

    2021 • Self-Supervised Graph Transformer on Large-Scale Molecular Data • RetroXpert: Decompose Retrosynthesis Prediction Like A Chemist • Reinforced Molecular Optimization with Neighborhood- Controlled Grammars • Autofocused Oracles for Model-based Design • Barking Up the Right Tree: an Approach to Search over Molecule Synthesis DAGs • On the Equivalence of Molecular Graph Convolution and Molecular Wave Function with Poor Basis Set • CogMol: Target-Specific and Selective Drug Design for COVID-19 Using Deep Generative Models • A Graph to Graphs Framework for Retrosynthesis Prediction • Hierarchical Generation of Molecular Graphs using Structural Motifs • Learning to Navigate in Synthetically Accessible Chemical Space Using Reinforcement Learning • Reinforcement Learning for Molecular Design Guided by Quantum Mechanics • Multi-Objective Molecule Generation using Interpretable Substructures • Improving Molecular Design by Stochastic Iterative Target Augmentation • A Generative Model for Molecular Distance Geometry • GraphDF: A Discrete Flow Model for Molecular Graph Generation • An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming • Equivariant message passing for the prediction of tensorial properties and molecular spectra • Learning Gradient Fields for Molecular Conformation Generation • Self-Improved Retrosynthetic Planning • Directional Message Passing for Molecular Graphs • GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation • Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space • A Fair Comparison of Graph Neural Networks for Graph Classification • MARS: Markov Molecular Sampling for Multi-objective Drug Discovery • Practical Massively Parallel Monte-Carlo Tree Search Applied to Molecular Design • Learning Neural Generative Dynamics for Molecular Conformation Generation • Conformation-Guided Molecular Representation with Hamiltonian Neural Networks • Symmetry-Aware Actor-Critic for 3D Molecular Design 堣唒㷕统ⴓꅿךمحززؾحؙד׮֮׷
  37. / 41 40 铬겗ה㾜劄 ˖ ꆀ㶨⻉㷕鎘皾זוر٦ةָ鎘皾歋勻ך㜥さծ堣唒㷕统ד葺ְ➿椚ٌرٕ׾⡲׷׋׭ך ワⵋזر٦ة栻䖤鎘歗ָ铬겗 鎘皾ָ؜٦يך㜥さך״ֲח鯪ֻזְ  ˖

    黝ⴖז䌓秛غ؎،أך鏣鎘ָ铬겗 $IFNJDBM4QBDFכ䎢㣐ֺׅ׷ךד痥♧⾱椚 ꆀ㶨⻉㷕 װ攦⸂㷕ծ$POGPSNFSװ %ZOBNJDTזו怴糊涸暟椚ⵖ秈׾欽ְגٌرٕ׾ⵖ秈姻⵱⻉ׅ׷ךָ剣劄  ˖ 䎗⡦涸(//ך䖤䠐ةأؙכ,BTIJNBؕ٦طٕװ40"1ؕ٦طٕ ("1瘝ד׮鍑ֽ׷ךד 㹋欽ٖكٕך邌植㷕统ך鑐ꆃ瀖כ㣐鋉垷✲⵸㷕统GFXTIPU[FSPTIPU鯄獳ך㹋植  ˖ 㣐鋉垷זر٦ةָ֮׸לⴓ㶨ך邌植㷕统חـٖ؎ؙإٔ٦כ饯ֿ׷ךַ  害欽ٌرٕה䌓秛غ؎،أ$//TWT5SBOTGPSNFSTWT(//TWT.-1T https://arxiv.org/abs/2102.06321 https://arxiv.org/abs/1911.10084
  38. / 41 41 劤傈ך鑧겗ⴓ㶨ךؚٓؿ邌植堣唒㷕统 暴䗙كؙزٕ زهٗآ 갥挿暴䗙 鴟暴䗙 CC1CCNO1 Representation

    Learning … ˖ ⴓ겲 ˖ 㔐䌓 ˖ 欰䧭 圫ղז ♴崧ةأؙ ⴓ㶨ך橆㞮勴⟝垥涸湱✼⡲欽瘝ך䞔㜠 NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1 ؚٓؿ邌植 ⻉㷕圓鸡낦呓㸼腉㛇 甧⡤ꂁ䏟ꨵ㶨朐䡾 ⻉㷕⿾䘔圓鸡ך穈剏ִ Task-Specific Head https://itakigawa.github.io/data/aipseminar_202107.pdf 劤傈ךأٓ؎س https://youtu.be/wtrVxZCXnPQ?t=813 闌怴⹛歗