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(2021.11) 機械学習と機械発見:データ中心型の化学・材料科学の教訓とこれから

itakigawa
September 27, 2023
20

(2021.11) 機械学習と機械発見:データ中心型の化学・材料科学の教訓とこれから

2021年11月12日 13:25 ~ 16:30

第142回 フロンティア材料研究所学術講演会
「データ科学と機械学習の最前線 ーデータを基軸とした材料開発に向けてー」

[主催] 東京工業大学 科学技術創成研究院 フロンティア材料研究所
[共催] 東京工業大学 物質・情報卓越教育院

itakigawa

September 27, 2023
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Transcript

  1. 戣䊛♧㷕
    [email protected]
    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 *$3F%%

    堣唒㷕统ה堣唒涪鋅
    ر٦ة⚥䗰㘗ך⻉㷕٥勞俱猰㷕ך侄鎮הֿ׸ַ׵
    2021䎃11剢12傈

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  2. 戣䊛♧㷕
    ׋ָֹ׻ ְ׍ָֻ
    堣唒㷕统׾灇瑔׃גְ׷䪮遭㾊رأ
    ˖ 껺䊛源넝匟䋐欰ת׸
    ˖ ։⻌嵲麣㣐 䊨㷕灇瑔猰

    ⽆㡦 䊨㷕
    ⸋寸㹀⥋〾彁ⴓꨄך鍑ך椚锷ⴓ匿
    ˖ ։❨鿪㣐 ⻉㷕灇瑔䨽讒㷕灇瑔猰

    غ؎ؔ؎ٝؿؓوذ؍ؙأإٝة٦⸔侄
    ˖ ։⻌嵲麣㣐 䞔㜠猰㷕灇瑔猰

    㣐鋉垷濼陎Ⳣ椚灇瑔㹓Ⲥ侄䱇
    ։+45ָֹֽׁ 勞俱؎ٝؿؓوذ؍ؙأ

    ˖ ։⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 *$3F%%

    ։椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ "*1

    兛媮כ❨鿪㣐J14稢脄灇הך鸬䵿ٓن!❨ꢻ㣽חְתׅ
    J14稢脄鸬䵿⼔㷕涸ٔأؙ㔐鼘ث٦ي

    https://itakigawa.github.io

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  3. ➙傈ך鑧堣唒㷕统ך⸂ך⯔僇꬗ה农랲꬗
    堣唒㷕统ה堣唒涪鋅ך䪮遭㾊ַ׵鋅׋ر٦ة⚥䗰㘗ך⻉㷕٥勞俱猰㷕ך侄鎮הֿ׸ַ׵
    ๏ ⴓ㶨ך邌植㷕统ה(SBQI/FVSBM/FUXPSLT
    ๏ 䌓秛غ؎،أך鏣鎘הؚٖ؎نحؙأ剑黝⻉
    ٓ؎ز؟؎س⯔僇꬗
    ت٦ؙ؟؎س农랲꬗
    ๏ 繎欰Ꟍ⸬卓ה6OEFSTQFDJDBUJPO
    ๏ չ✮庠ָדֹ׷ֿהպכչ椚鍑պװչ涪鋅պָדֹ׷ֿה׾䠐㄂׃זְ
    May the ML force be with you…
    堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ䓼⸂זذؙظٗآ٦
    荈搫猰㷕ך㹋植韋ر٦ةד⢪ֲךכְ׹ְ׹慧يؤ
    ؿؓ٦أ

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  4. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ

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  5. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    ꅾׁ H
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  6. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
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  7. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
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  11. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    ꅾׁ H
    ה넝ׁ DN
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    Ӫ׫ַ׿
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    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي

    View full-size slide

  12. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  13. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  14. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  15. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  16. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  17. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  18. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  19. 堣唒㷕统כչر٦ة׾✮庠ח㢌ִ׷պ
    鋅劤ر٦ةַ׵⡲׏גְֶ׋✮庠فؚٗٓي
    Ӫ׶׿׀
    Ӫ׫ַ׿
    ✮庠فؚٗٓي׾⡲׏׋הֹח鋅ׇ׋鋅劤⢽דכזְ⢽ח㼎׃ג
    չ׫ַ׿պPSչ׶׿׀պ׾✮庠ׅ׷ֿהָדֹ׷
    5 6.25 7.5 8.75 10
    90 112.5 135 157.5 180










    ꅾׁ H

    넝ׁ DN

    넝ׁ DN

    ꅾׁ H

    Ӫ׶׿׀
    Ӫ׫ַ׿

    View full-size slide

  20. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    ♧菙暟⡤钠陎
    ؜٦يفٖ؎
    ˑ֮׶ָהֲ˒
    J’aime la
    musique I love music
    갈㡮钠陎
    堣唒缺鏬
    馄鍑⫷
    فؚٗٓيךⰅ⸂ה⳿⸂ךꟼ⤘ָ״ֻⴓַ׵זְ㜥さד׮ծ
    ׋ֻׁ׿ךⰅ⳿⸂ך鋅劤ر٦ةח״׏ג꟦䱸涸ח׉׸׾ⱄ植דֹ׷فؚٗٓي׾⡲׶⳿ׅ䪮遭

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  21. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    ֿך⽃秪ז׃ֻ׫כ♳䩛ח⢪ֲהչ׭׍ׯֻ׍ׯ䓼⸂պדְ׹ְ׹ז嚂׃ְֿה׮דֹ׷

    View full-size slide

  22. ⢽堣唒㷕统–ꆀ㶨⻉㷕
    input output
    gdb_21014
    1000 猱
    Density Functional Theory (DFT)
    B3LYP/6-31G(2df, p)
    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
    ˆ
    H = E

    ♧ꨵ㶨晛ך4DISµEJOHFS倯玎䒭
    ,PIOˊ4IBN倯玎䒭
    ך実鍑
    ꆀ㶨⻉㷕鎘皾
    ˖ ⰻ鿇ؒطؘٕ٦
    ˖ 荈歋ؒطؘٕ٦
    ˖ ئٗ挿䮶⹛ؒطؘٕ٦
    ˖ 剑넝鄃⽑鮨麣 )0.0

    ˖ 剑⡚瑞鮨麣 -6.0

    ˖ ⴓ噰桦
    ˖ ⿽噰㶨ٌ٦ًٝز
    ˖ 攦㺁ꆀ
    ˖ ؒٝةٕؾ٦

    View full-size slide

  23. ⢽堣唒㷕统–ꆀ㶨⻉㷕
    input output
    gdb_21014
    1000 猱
    Density Functional Theory (DFT)
    B3LYP/6-31G(2df, p)
    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
    ˆ
    H = E

    ♧ꨵ㶨晛ך4DISµEJOHFS倯玎䒭
    ,PIOˊ4IBN倯玎䒭
    ך実鍑
    ػցֶश
    0.01 猱

    ⦓넝鸞
    ꆀ㶨⻉㷕鎘皾
    ˖ ⰻ鿇ؒطؘٕ٦
    ˖ 荈歋ؒطؘٕ٦
    ˖ ئٗ挿䮶⹛ؒطؘٕ٦
    ˖ 剑넝鄃⽑鮨麣 )0.0

    ˖ 剑⡚瑞鮨麣 -6.0

    ˖ ⴓ噰桦
    ˖ ⿽噰㶨ٌ٦ًٝز
    ˖ 攦㺁ꆀ
    ˖ ؒٝةٕؾ٦

    View full-size slide

  24. ⢽堣唒㷕统–ꆀ㶨⻉㷕
    https://qcarchive.molssi.org/apps/ml_datasets/

    View full-size slide

  25. ⢽堣唒㷕统–ꆀ㶨⻉㷕
    ਅ஋(x࣠) vs ༧ଌ஋(y࣠) by SchNet (Schütt et al, 2017) ਅ஋(x࣠) vs ༧ଌ஋(y࣠) by DimeNet (Klicpera et al, 2020)
    Dipole Moment Energy U
    HOMO
    LUMO Heat Capacity
    Enthalpy H Dipole Moment Energy U
    HOMO
    LUMO Heat Capacity
    Enthalpy H
    堣唒㷕统ח״׷✮庠כ׭׏׍ׯ䔲׋׷ر٦ةך䲧ִ倯如痥דכ㣐ֹז〳腉䚍ָ֮׷

    View full-size slide

  26. ⢽堣唒㷕统–ꆀ㶨⻉㷕
    ਅ஋(x࣠) vs ༧ଌ஋(y࣠) by SchNet (Schütt et al, 2017) ਅ஋(x࣠) vs ༧ଌ஋(y࣠) by DimeNet (Klicpera et al, 2020)
    Dipole Moment Energy U
    HOMO
    LUMO Heat Capacity
    Enthalpy H Dipole Moment Energy U
    HOMO
    LUMO Heat Capacity
    Enthalpy H
    ⦓鸞ְז׵
    ⼧ⴓ鏩㺁דֹ׷✮庠铎䊴
    ֿ׸כذأزر٦ة 鎮箺儗ח
    鋅ׇגזְر٦ة
    ך穠卓
    堣唒㷕统ח״׷✮庠כ׭׏׍ׯ䔲׋׷ر٦ةך䲧ִ倯如痥דכ㣐ֹז〳腉䚍ָ֮׷

    View full-size slide

  27. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    堣唒㷕统ך،ٕ؞ٔؤيך麩ְכ㞮歲简ך䒷ֹ倯ך倯ꆙך׍ְָ׌ֽ
    ر٦ة Decision
    Tree
    Random
    Forest GBDT
    Nearest
    Neighbor
    Logistic
    Regression
    SVM
    Gaussian
    Process
    Neural
    Network

    View full-size slide

  28. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    㞮歲简ך䒷ֹ倯ך倯ꆙ 䌓秛غ؎،أ

    ⰻ鿇⾱椚כչ刼꬗ٌرٕպ׾挿חؿ؍حذ؍ؚٝ׃גְ׷׌ֽ

    View full-size slide

  29. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    㞮歲简ך䒷ֹ倯ך倯ꆙ 䌓秛غ؎،أ

    ⰻ鿇⾱椚כչ刼꬗ٌرٕպ׾挿חؿ؍حذ؍ؚٝ׃גְ׷׌ֽ

    View full-size slide

  30. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    㞮歲简ך䒷ֹ倯ך倯ꆙ 䌓秛غ؎،أ

    ⰻ鿇⾱椚כչ刼꬗ٌرٕպ׾挿חؿ؍حذ؍ؚٝ׃גְ׷׌ֽ

    View full-size slide

  31. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    ։ך然桦⦼
    1 ⳿⸂SFE

    1 ⳿⸂CMVF

    1 ⳿⸂SFE

    㞮歲简ך䒷ֹ倯ך倯ꆙ 䌓秛غ؎،أ

    ⰻ鿇⾱椚כչ刼꬗ٌرٕպ׾挿חؿ؍حذ؍ؚٝ׃גְ׷׌ֽ

    View full-size slide

  32. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    Random Forest
    Gaussian Process
    Logistic Regression
    ։ך然桦⦼
    1 ⳿⸂SFE

    1 ⳿⸂CMVF

    1 ⳿⸂SFE

    㞮歲简ך䒷ֹ倯ך倯ꆙ 䌓秛غ؎،أ

    ⰻ鿇⾱椚כչ刼꬗ٌرٕպ׾挿חؿ؍حذ؍ؚٝ׃גְ׷׌ֽ

    View full-size slide

  33. 堣唒㷕统כչ倜׃ְ ꧟ז
    ؝ٝؾُ٦ةفؚٗٓيך⡲׶倯պ
    չ刼꬗ٌرٕպךⰻ鿇ػًٓة⦼׾锃侭׃ג鋅劤挿חֲ֮״ֲؿ؍حذ؍ؚׅٝ׷
    Random Forest Neural Network SVR Kernel Ridge
    p1 p2 p3 p4

    刼꬗ٌرٕ

    View full-size slide

  34. 跐駈䋞劄涸ㄎן倯ח״׷䎐䟝ח׀岣䠐׾
    植㖈ך堣唒㷕统כ♧菙ח鸬䟝ׁ׸׷4'涸זչ➂䊨濼腉 "*
    պהכַז׶ַֽꨄ׸גְ׷ָծ
    չر٦ة׾✮庠ח㢌ִ׷պ⩎꬗ָ֮ת׶ח䓼⸂ז׋׭ծ猘׋׍ך傈䌢欰崞ַ׵➙䖓ך爡⠓ך
    ؕةثחתד䕦갟׾⿹ר׉ֲה׃גְ׷˘
    չ➂䊨濼腉պչ堣唒㷕统պזוך䋞劄涸ㄎן倯כ劤颵׾ىأٔ٦س׃װְׅךד׀岣䠐׾
    wishful mnemonics
    Why Is AI So Dumb?
    A SPECIAL REPORT
    https://spectrum.ieee.org/files/11920/10_Spectrum_2021.pdf

    View full-size slide

  35. 帾㾴㷕统ה邌植㷕统
    q1 q2 q3 q4

    刼꬗ٌرٕ
    Ⰵ⸂㢌侧
    垥彊涸ז
    堣唒㷕统
    Random
    Forest
    GBDT
    Nearest
    Neighbor
    SVM
    Gaussian
    Process
    Neural
    Network

    View full-size slide

  36. 帾㾴㷕统ה邌植㷕统
    q1 q2 q3 q4

    刼꬗ٌرٕ
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统

    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
    z1
    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
    z2
    Ⰵ⸂㢌侧

    View full-size slide

  37. 帾㾴㷕统ה邌植㷕统
    q1 q2 q3 q4

    刼꬗ٌرٕ
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统

    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
    z1
    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
    z2
    Ⰵ⸂㢌侧

    View full-size slide

  38. 帾㾴㷕统ה邌植㷕统
    q1 q2 q3 q4

    刼꬗ٌرٕ
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统

    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
    z1
    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
    z2
    Ⰵ⸂㢌侧

    View full-size slide

  39. 帾㾴㷕统ה邌植㷕统
    q1 q2 q3 q4

    刼꬗ٌرٕ
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统

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  40. 帾㾴㷕统ה邌植㷕统
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  41. 帾㾴㷕统ה邌植㷕统
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  42. 帾㾴㷕统ה邌植㷕统
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  43. 帾㾴㷕统ה邌植㷕统
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    View full-size slide

  44. 帾㾴㷕统ה邌植㷕统
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    View full-size slide

  45. 帾㾴㷕统ה邌植㷕统
    https://colah.github.io/posts/2014-03-NN-Manifolds-Topology/
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    ر٦ة Decision
    Tree
    Random
    Forest GBDT
    Nearest
    Neighbor
    Logistic
    Regression
    SVM
    Gaussian
    Process
    Neural
    Network

    View full-size slide

  46. 㹋⢽ⴓ㶨٥勞俱ך邌植㷕统ה(SBQI/FVSBM/FUXPSLT
    زهٗآ
    ⴓ㶨٥勞俱ך橆㞮勴⟝垥涸湱✼⡲欽˘
    ؚٓؿ邌植
    鴟暴䗙
    갥挿暴䗙
    p1 p2 p3

    邌植㷕统
    Ⰵ⸂䞔㜠ךさ䧭怴皾
    q1 q2 q3

    刼꬗ٌرٕ

    View full-size slide

  47. ➂꟦ָ罋ִ׋搀侧ךⴓ㶨鎸鶢㶨׾馄ִ׷害欽邌植כ֮׷ַ
    珏겲ך鎸鶢㶨ָ鯹׏גְ׷
    ˖ %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/
    ⦐ך鎸鶢㶨׾鎘皾׃גֻ׸׷
    ㉀欽ך鎸鶢㶨اؿزؐؑ،
    ˖ 㹋꿀涸ז鎘庠ꆀ
    ˖ 鎘皾涸ז鎸鶢㶨
    ؔ٦فٝا٦أؿٖ٦يٙ٦ؙ
    • Descriptors
    • Descriptors3D
    • GraphDescriptors
    • Fingerprints
    • ChemicalFeatures
    • ChemicalForceFields
    rdkit.Chem
    rdkit.ML.Descriptors
    Todeschini and Consonni, Molecular Descriptors
    for Chemoinformatics. Wiley‐VCH, 2009.
    https://doi.org/10.1002/9783527628766

    View full-size slide

  48. ⴓ㶨ךؚٓؿ邌植
    explicit Hs

    atom features bond features
    topology
    Molecular Graph
    read out
    graph-level
    output
    • sum, mean or max
    • attentive pooling
    CID 204
    • atomic_num (one-hot, 101)
    • total_degree (one-hot, 7)
    • formal_charge (one-hot, 6)
    • chiral_tag (one-hot, 5)
    • num_Hs (one-hot, 6)
    • hybridization (one-hot, 6)
    • is_aromatic (binary, 1)
    • atomic_mass (real, 1)
    17
    edge(bond) features
    • no_bond (binary, 1)
    • is_single (binary, 1)
    • is_double (binary, 1)
    • is_triple (binary, 1)
    • is_aromatic (binary, 1)
    • is_connjugated (binary, 1)
    • is_in_ring (binary, 1)
    • stereo (one-hot, 7)
    17
    14
    133
    node(atom) features
    133 features 14 features
    $IFN1SPQ
    :BOHFUBM

    ך暴䗙ꆀך⢽
    atoms → nodes
    bonds → edges 1
    2
    1
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    1. ஔ׵ෆมੑ
    2. ஔ׵ಉมੑ
    ה挿ה简ד䬄韋⻉
    ぐ挿הぐ简ח暴䗙ꆀ׾➰♷
    ֿך殢〾➰ֽך䛬䠐䚍ד
    穠卓ָ㢌׻׵זְ״ֲח

    View full-size slide

  49. (SBQI/FVSBM/FUXPSLT
    N O
    C
    C
    C
    C
    H
    H
    H
    H
    H
    N O
    C
    C
    C
    C
    H
    H
    H
    H
    H
    GNN Layer Ԯ
    ԮMessage
    縧䳔ず㢌ז乼⡲
    ˖ OO-JOFBSזו
    鴟暴䗙ꆀכⰩ㘗涸חכ
    ֿךԮד⢪ֲ
    ԯ
    • sum, mean or max
    • attentive pooling
    ԯAggregate
    縧䳔♶㢌ז乼⡲
    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
    hi
    0
    @hi,
    M
    j2Ni
    (hi, hj, eij)
    1
    A
    鵚⩸ַ׵ךˑ.FTTBHF1BTTJOH˒ד刿倜
    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
    hi
    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
    eij
    갥挿暴䗙ꆀ
    鴟暴䗙ꆀ
    ԰
    ԰Update
    ˖ OO-JOFBSזו
    剣ぢ鴟♳ד暴䗙ꆀ׾刿倜׃גַ׵갥挿暴䗙ꆀפさ䧭ׅ׷
    غٔؒ٦ءّٝ %JSFDUFE.1//
    כ֮׷ָֿ׸ָ㛇劤䕎

    View full-size slide

  50. 7JSUVBM4DSFFOJOH 24"32413

    https://pubchem.ncbi.nlm.nih.gov/bioassay/1

    View full-size slide

  51. 7JSUVBM4DSFFOJOH 24"32413

    input output
    ML
    BDUJWJUZˑ"DUJWF˒ ⴓ겲

    -PH(* 㔐䌓

    CID 11978790
    GI50: concentration required
    for 50% inhibition of growth

    View full-size slide

  52. 7JSUVBM4DSFFOJOH 24"32413

    ChemProp
    (Directed MPNN)
    ExtraTrees
    w/ ECFP6(1024)
    Standard ML GNN
    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
    ChemProp (Yang et al, 2019)
    from MIT MLPDS (Machine Learning for Pharmaceutical
    Discovery and Synthesis) Consortium
    95.079% (Active/Inactive) 95.604% (Active/Inactive)
    ˖ ✮庠礵䏝 ⴓ겲
    ˖ ✮庠礵䏝 ⴓ겲

    RMSE 0.6076
    RMSE 0.7970
    ˖ ✮庠礵䏝 㔐䌓
    ˖ ✮庠礵䏝 㔐䌓

    鴟♳ד刿倜ׅ׷
    ءٝفٕז(//

    View full-size slide

  53. &$'1ה/FVSBM(SBQI'JOHFSQSJOU
    ˖ /FVSBM(SBQI'JOHFSQSJOU剑ⴱ劍ח䲿周ׁ׸׋(//ך♧א
    ˖ &$'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)

    View full-size slide

  54. ("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
    Ying et al (2021) ͷGraphormer͸KDDCup 2021ͷ
    Graph-levelλεΫͷ༏উϞσϧͰ࢖ΘΕͨ
    ✲⵸㷕统ָ⸬ַזְהׁ׸׋/-1װ
    $//♧䫛ַח鋅ִ׋$7׾㢌ꬠ׃גֹ׋
    5SBOTGPSNFSכⴓ㶨ةأؙ׮㢌ִ׷ךַ

    View full-size slide

  55. 㼭؟ٝفٕ㉏겗ך⯘剪ⴓ㶨邌植ך✲⵸㷕统ה鯄獳㷕统
    ˖ 5SBOTGPSNFSפךꟼ䗰כ4FMG4VQFSWJTFEז㣐鋉垷✲⵸㷕统ה鯄獳פך劍䖉ך植׸
    ˖ ׮׃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$7ך*NBHF/FUQSFUSBJOFE$//װ/-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
    4FMG4VQFSWJTFEזךד
    㣐鋉垷ر٦ةָ֮׸ל
    侄䌌ٓكٕ➰ָֽ♶銲
    ✲⵸㷕统׃׋ⴓ㶨邌植כ
    圫ղז♴崧ةأؙד鯄獳
    ˖ 㢳圫זⴓ겲٥㔐䌓
    ˖ ⴓ㶨欰䧭

    View full-size slide

  56. ⴓ㶨邌植ך欰䧭(FOFSBUJWF$IFNJTUSZ
    ˖ ׮ֲמהאךⴓ㶨ך邌植㷕统פך劍䖉כⴓ㶨ؚٓؿװⴓ㶨圓鸡ך欰䧭
    ˖ %FDPEFSָꬊ荈僇ծ圓䧭䚍ٌآُ٦ٕ䚍װ⻉㷕涸ٕ٦ٕ׮罋䣁׃זְה䠐㄂ךזְ⳿⸂חז׶䖤׷
    ˖ 俑㶵⴨邌植 4.*-&4鎸岀
    ַ׵ך欰䧭כ湫䱸涸זךדؚٓؿ邌植ך⮚⡘䚍׮銲嗚鏾
    https://arxiv.org/abs/2012.15544

    View full-size slide

  57. 0(#-BSHF4DBMF$IBMMFOHF ,%%$VQ

    1st place: 10 GNNs (12-Layer Graphormer) + 8 ExpC*s (5-Layer ExpandingConv)
    Test MAE 0.1200 (eV)
    73 GNNs (11-Layer LiteGEMConv with Self-Supervised Pretraining)
    2nd place:Test MAE 0.1204 (eV)
    20 GNNs (32-Layer GNN with Noisy Nodes)
    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
    Results: https://ogb.stanford.edu/kddcup2021/results/#awardees_pcqm4m
    https://ogb.stanford.edu/kddcup2021/
    ر٦ةإحز1VC$IFN2$ַ׵ ؚٓؿ DG2.כ ؚٓؿ

    View full-size slide

  58. 堣唒㷕统ך植➿涸⩎꬗΍Ⰵ⸂㢌侧ָ׭׏׍ׯ㢳ְ˘
    p1 p2 p3 p4

    刼꬗ٌرٕ
    〸ך窩׾滗׭׷הծ堣唒㷕统ָխהխ⟃㢩ך
    Ⰵ⸂ׁ׸גזְ䞔㜠׾Ⰻֻ罋䣁׃גֻ׸זְֿהכ♧湡澗搫
    ⳿⸂ך✮庠ח劤䔲כ䗳銲ז䞔㜠׾Ⰵ⸂׃גְזַ׏׋׵
    堣唒㷕统כ亻⡂湱ꟼח麓ֺ׆⡦׮劤颵׾䯝ִ׵׸זְ
    spurious correlation

    View full-size slide

  59. 堣唒㷕统ך植➿涸⩎꬗΍Ⰵ⸂㢌侧ָ׭׏׍ׯ㢳ְ˘
    p1 p2 p3 p4

    刼꬗ٌرٕ
    〸ך窩׾滗׭׷הծ堣唒㷕统ָխהխ⟃㢩ך
    Ⰵ⸂ׁ׸גזְ䞔㜠׾Ⰻֻ罋䣁׃גֻ׸זְֿהכ♧湡澗搫
    ⳿⸂ך✮庠ח劤䔲כ䗳銲ז䞔㜠׾Ⰵ⸂׃גְזַ׏׋׵
    堣唒㷕统כ亻⡂湱ꟼח麓ֺ׆⡦׮劤颵׾䯝ִ׵׸זְ
    spurious correlation
    堣唒㷕统–⻉㷕أة٦زٓ؎ٝדךאתבֹ
    ˖ 㢳ֻך㜥さծꟼ䗰ך⳿⸂׾䖤׷׋׭ח䗳銲⼧ⴓזⰅ⸂ָ⡦
    זךַכ״ֻⴓַ׵זְ
    ˖ הְֲַծ׉׮׉׮״ֻⴓַ׵זְַ׵堣唒㷕统׾⢪ְ׋ְկ
    זךחծ堣唒㷕统ֲָתְֻֻ׋׭חכו׿זⰅ⸂ָ䗳銲ַ
    椚鍑׃גֶֻ䗳銲ָ֮׷׏גוײֿה "

    View full-size slide

  60. 堣唒㷕统ך植➿涸⩎꬗΍Ⰵ⸂㢌侧ָ׭׏׍ׯ㢳ְ˘
    䗳搫涸חչ㼰׃ד׮ꟼ⤘֮׶׉ֲז䞔㜠כⰅ⸂׃גպ邌植㷕统דꅾ銲ז׮ך׾䃓ⴽהְֲ䨌殛ח
    q1 q2 q3 q4

    刼꬗ٌرٕ
    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
    x1
    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
    x2
    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
    xd
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统


    ׋ֻׁ׿ך
    Ⰵ⸂㢌侧

    View full-size slide

  61. 堣唒㷕统ך植➿涸⩎꬗΍Ⰵ⸂㢌侧ָ׭׏׍ׯ㢳ְ˘
    䗳搫涸חչ㼰׃ד׮ꟼ⤘֮׶׉ֲז䞔㜠כⰅ⸂׃גպ邌植㷕统דꅾ銲ז׮ך׾䃓ⴽהְֲ䨌殛ח
    q1 q2 q3 q4

    刼꬗ٌرٕ
    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
    x1
    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
    x2
    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
    xd
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统


    ׋ֻׁ׿ך
    Ⰵ⸂㢌侧
    ⢽չ歗⫷ח⡦ָⱖ׏גְ׷ַպז׵歗⫷ךぐؾؙإٕך鰛䏝⦼׾Ⰻ鿇׉ךתתⰅ׸׷
    –ؾؙإٕךؕٓ٦歗⫷כ
    ––⦐ך侧⦼ך֮את׶
    –խխ̔ 㢌侧
    –̔ 㢌侧
    ⾱葿邌植

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  62. 堣唒㷕统ך植➿涸⩎꬗Ύⰻ鿇ػًٓةך侧׮娤טקו㢳ְ˘
    3FT/FU♰ػًٓة
    3FT/FU♰ػًٓة
    &DJFOU/FU#♰ػًٓة
    7((⭙♰ػًٓة
    MBZFS IFBET#&35⭙♰ػًٓة
    MBZFS IFBET#&35⭙♰ػًٓة
    (159-⭙♰ػًٓة
    (15⭙ػًٓة
    植➿ך堣唒㷕统ך䪮遭灇瑔ָぢֹさֲ鏣㹀
    ⭙⦐ךػًٓة⦼׾䭯אٌرٕ׾侧⼧♰ך㢌侧׾䭯א侧⼪♰⦐ךر٦ةחؿ؍حذ؍ؚٝ
    넝如⯋ךⰅ⳿⸂ꟼ⤘ָוך״ֲז׮ךד֮׏ג׮邌植ׅ׷׋׭ػًٓة侧׮娤טקו㢳ְ
    q1 q2 q3 q4

    刼꬗ٌرٕ
    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
    x1
    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
    x2
    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
    xd
    p1 p2 p3 p4

    㢌侧㢌䳔 邌植㷕统


    ׋ֻׁ׿ך
    Ⰵ⸂㢌侧

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  63. 穠卓ծ植㖈ך堣唒㷕统ٌرٕכ،م׫׋ְחر٦ة׾굸ֲ˘
    ˖ ⡦ד׮ַ׿ד׮Ⰵ⸂㢌侧חⰅ׸תֻ׷Ⰻ鿇Ⰵ׶ٌرٕכչؗحثٝءؙٝ㔐䌓պה䴅䲪ׁ׸
    ⠗窟涸ז䘔欽窟鎘㷕דכةـ٦׌׏׋˘ 麓黝さךٔأָؙ㣐ֹֺׅג葺ְֿהזְַ׵

    ˖ 葺䚍ך麓黝さչؽحؚر٦ةպדכ麓黝さ荈⡤ָ׉׮׉׮ꨇ׃ְךד孡ח׃זְ甧㜥׮
    ءّنְ钠濼腉⸂ךֶתִ׵➂꟦חה׏׋׵չؽحؚպر٦ةַ׮׃׵׿ֽוծ
    مٝوח䗳銲ז䞔㜠ꆀַ׵׃׋׵عشؙا׫׋ְז׮׿װזխ
    CZر؍٦فٓ٦صؚٝ圫
    堣唒㷕统–⻉㷕椚锷٥悵㖈涸〳腉䚍ה植㹋ך㣐ֹזٍؘحف
    植➿ך堣唒㷕统כ䓼⸂ד葺ְر٦ةָ⼧ⴓח֮׸ל醱꧟זⰅ⳿⸂ꟼ⤘ד׮㷕统דֹ׷
    植㹋חכծ鍑瑞꟦ך䎢ַׁ׵罋ִ׸לչؽحؚر٦ةպדׅ׵չ⼧ⴓպך宏彊חכקו黅ְ˘

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  64. 繎欰Ꟍ⸬卓ה6OEFSTQFDJGJDBUJPO
    繎欰Ꟍ⸬卓葺ְ堣唒㷕统ٌرٕך㢳ꅾ䚍 ꬊ♧䠐䚍

    ずׄ鋅劤⢽ر٦ةַ׵ず玎䏝ך넝ְ✮庠礵䏝׾䭯א葺ְ堣唒㷕统ٌرٕכ搀侧ח⡲׸׷
    ⾱㔓Ⰵ⸂㢌侧ך鼅ן倯ծٌرٕך鼅䫛װ鏣鎘ծⴱ劍⦼ך麩ְծػًٓةך㢳ꅾ䚍ծ˘

    View full-size slide

  65. 繎欰Ꟍ⸬卓ה6OEFSTQFDJGJDBUJPO
    繎欰Ꟍ⸬卓葺ְ堣唒㷕统ٌرٕך㢳ꅾ䚍 ꬊ♧䠐䚍

    ずׄ鋅劤⢽ر٦ةַ׵ず玎䏝ך넝ְ✮庠礵䏝׾䭯א葺ְ堣唒㷕统ٌرٕכ搀侧ח⡲׸׷
    ⾱㔓Ⰵ⸂㢌侧ך鼅ן倯ծٌرٕך鼅䫛װ鏣鎘ծⴱ劍⦼ך麩ְծػًٓةך㢳ꅾ䚍ծ˘
    ˖ 植韋ךչ椚鍑պך׋׭栻䖤׃׋堣唒㷕统ٌرٕ׾ⴓ匿׃ג爙㇗׾䒷ֹ⳿׉ֲהׅ׷הֹך
    剑㣐ךꥺ㹱կ溪㹋㄂׾䌒ן׋鍑ꅸָ搀侧ח֮׷ֿהחז׶תׁח溪㹋כչ谞ך⚥պ˘
    ˖ ׁ׵ח㹋ꥷכ劤颵涸חر٦ةָ駈׶גזְ 6OEFSTQFDJDBUJPO
    ֿהד㢳ꅾ䚍כׁ׵ח䝤⻉
    ׌ְ׋ְך倯岀ד겲⡂ 䩛岀װٌرٕח״׏ג✮庠儗ך䮙⹛חַז׶䊴ָ⳿ג׃תֲ

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  66. 植➿ך䪮遭涸ꟼ䗰כֿך넝如⯋䚍׾וֲ䩛䥿ֽ׷ַ
    然桦涸剑黝⻉٥姻⵱⻉
    ✲⵸㷕统 8BSN4UBSU
    ך鯄獳
    ٌرָٕ㣐ְֹ荈歋䏝ך⚥ד凐׸תֻ׵זְ״ֲ
    ⹛ֽ׷眔㔲׾⡦הַ׃גⵖ䖴٥ⵖꣲ٥㸜㹀⻉ׅ׷
    ✲⵸ח䱱׃גְֶ׋葺ְ䠬ׄךػًٓةⴱ劍⦼׾⢪ֲ

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  67. 植➿ך䪮遭涸ꟼ䗰כֿך넝如⯋䚍׾וֲ䩛䥿ֽ׷ַ
    然桦涸剑黝⻉٥姻⵱⻉
    ✲⵸㷕统 8BSN4UBSU
    ך鯄獳
    ٌرָٕ㣐ְֹ荈歋䏝ך⚥ד凐׸תֻ׵זְ״ֲ
    ⹛ֽ׷眔㔲׾⡦הַ׃גⵖ䖴٥ⵖꣲ٥㸜㹀⻉ׅ׷
    p1 p2 p3 p4

    刼꬗ٌرٕ
    刼꬗ٌرָٕו׿זⰅ⳿⸂ꟼ⤘ד׮邌植דֹ׷ֿהָ鷞ח
    亻⡂湱ꟼװ6OEFSTQFDJDBUJPOך㉏겗׾䝤⻉ׇׁגְ׷
    䌓秛غ؎،أך鏣鎘
    ✲⵸ח䱱׃גְֶ׋葺ְ䠬ׄךػًٓةⴱ劍⦼׾⢪ֲ

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  68. 植➿ך䪮遭涸ꟼ䗰כֿך넝如⯋䚍׾וֲ䩛䥿ֽ׷ַ
    然桦涸剑黝⻉٥姻⵱⻉
    ✲⵸㷕统 8BSN4UBSU
    ך鯄獳
    ٌرָٕ㣐ְֹ荈歋䏝ך⚥ד凐׸תֻ׵זְ״ֲ
    ⹛ֽ׷眔㔲׾⡦הַ׃גⵖ䖴٥ⵖꣲ٥㸜㹀⻉ׅ׷
    ⻉㷕涸ח㧅䔲䚍׾妀ֻ״ֲזٌرָٕ䠐㔳ׇ׆邌植ׁ׸ג
    ׃ת׻זְ״ֲח⻉㷕ך濼陎װ椚锷猰㷕٥鎘皾⻉㷕ך濼鋅׾
    筨⹛㆞׃גٌرٕך荈歋䏝׾䪮遭涸חⵖꣲׅ׷
    堣唒㷕统–⻉㷕⻉㷕ח黝さ׃׋䌓秛غ؎،أךرؠ؎ٝ
    p1 p2 p3 p4

    刼꬗ٌرٕ
    刼꬗ٌرָٕו׿זⰅ⳿⸂ꟼ⤘ד׮邌植דֹ׷ֿהָ鷞ח
    亻⡂湱ꟼװ6OEFSTQFDJDBUJPOך㉏겗׾䝤⻉ׇׁגְ׷
    䌓秛غ؎،أך鏣鎘
    ✲⵸ח䱱׃גְֶ׋葺ְ䠬ׄךػًٓةⴱ劍⦼׾⢪ֲ

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  69. ؚٖ؎نحؙأ剑黝⻉⻉㷕ח黝さ׃׋䌓秛غ؎،أך鏣鎘
    ICML 2017 https://arxiv.org/abs/1704.01212
    JCTC 2017 https://doi.org/10.1021/acs.jctc.7b00577
    (PPHMFָ葿ղז(//׾.1// .FTTBHF1BTTJOH//
    ה׃ג窟♧⻉׃׋ꥷծ%'5鎘皾鵚⡂׾ة٦؜حزח
    堣唒㷕统ך⠓陽ד
    涪邌ׁ׸׋

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  70. ؚٖ؎نحؙأ剑黝⻉⻉㷕ח黝さ׃׋䌓秛غ؎،أך鏣鎘
    '$'1⾱㶨♶㢌ꆀ
    &$'1ך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?
    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//ד欽ְ׵׸׋갥挿٥鴟暴䗙
    鸬竲ꆀٓكٕ
    ؛ٌ؎ٝؿؓوذ؍ؙأך⾱㶨♶㢌ꆀ
    &$'1ך،ٕ؞ٔؤيדכ
    ⾱㶨♶㢌ꆀח鸬竲⦼׾Ⰵ׸׷ךכ
    ֮׶ִזַ׏׋ 갥挿ٓكٕך䕵ⶴ

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  71. 4DI/FU䎗⡦涸(//ך⯓꽀涸أةٝت٦س
    input molecule H2O
    gdb_3
    atom features

    0 1 2
    0
    bond features
    0 1
    1
    0 2
    2
    1 2
    0.9620 0.9622 1.5133
    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
    rij := kri rj
    k
    0
    1 2
    graph (SchNet)
    0 1
    2
    edges w/ cutoff (10Å)
    edge_index
    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
    Z0 = 8
    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
    Z1 = 1
    AAACinichVHLSsNAFL2Nr1qrrboR3ARLxVWZlOIToagLl33YB1YpSZzWoWkSkmmhFn/AnSvBrhRciB/gB7jxB1z0E8RlBTcuvEkDosV6w2TOnLnnzpm5iqkxmxPS9Qkjo2PjE/7JwFRweiYUnp3L20bDUmlONTTDKiqyTTWm0xxnXKNF06JyXdFoQantOvuFJrVsZugHvGXS47pc1VmFqTJHqnBYjovbolQOR0iMuCEOAskDEfAiZYQf4QhOwAAVGlAHCjpwxBrIYONXAgkImMgdQxs5CxFz9ymcQwC1DcyimCEjW8N/FVclj9Vx7dS0XbWKp2g4LFSKECUv5J70yDN5IK/k889abbeG46WFs9LXUrMculjIfvyrquPM4fRbNdQzhwqsu14ZejddxrmF2tc3z6562c1MtL1Mbskb+r8hXfKEN9Cb7+pdmmY6Q/wo6AVfDBsk/W7HIMjHY9JqLJFORJI7Xqv8sAhLsIL9WIMk7EMKcm79S7iGjhAU4sKGsNVPFXyeZh5+hLD3BSN2kVU=
    Z2 = 1
    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
    r0 = [ 0.0344, 0.9775, 0.0076]
    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
    r1 = [0.0648, 0.0206, 0.0015]
    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
    r2 = [0.8718, 1.3008, 0.0007]
    SchNet (Schütt et al, 2017)
    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
    xi xi +
    0
    @
    X
    j2Ni
    (xj) !ij
    1
    A
    Message Passing with
    residual connections
    AAACi3ichVHNSgJRFD5Of2aZVpugjSRGKzmWVEgLKYKW/uQPqMjMdLXB+WNmlGzwBVq2aWGbghbRA/QAbXqBFj5CtDRo06LjOBAl2Rnu3O9+93znfvceQZcl00LsebiJyanpGe+sb27evxAILi7lTa1piCwnarJmFAXeZLKkspwlWTIr6gbjFUFmBaFxMNgvtJhhSpp6bLV1VlH4uirVJJG3iCqWBcU+61SxGgxjFJ0IjYKYC8LgRkoLPkIZTkADEZqgAAMVLMIy8GDSV4IYIOjEVcAmziAkOfsMOuAjbZOyGGXwxDboX6dVyWVVWg9qmo5apFNkGgYpQxDBF7zHPj7jA77i55+1bKfGwEubZmGoZXo1cLGS/fhXpdBswem3aqxnC2qw63iVyLvuMINbiEN96/yqn01kIvY63uIb+b/BHj7RDdTWu3iXZpnuGD8CeaEXowbFfrdjFOQ3o7HtaDwdDyf33VZ5YRXWYIP6sQNJOIIU5Jw+XEIXrjk/t8UluL1hKudxNcvwI7jDL6M0kvA=
    x0 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
    x1 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
    x2
    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
    w01 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
    w02 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
    w12
    #JP24"3ח⢪ֲ(//ה嫰ץ׷הַז׶
    䌓秛غ؎،أ׾⻉㷕ח㺔ׇג鏣鎘

    View full-size slide

  72. 4DI/FU䎗⡦涸(//ך⯓꽀涸أةٝت٦س
    input molecule H2O
    gdb_3
    atom features

    0 1 2
    0
    bond features
    0 1
    1
    0 2
    2
    1 2
    0.9620 0.9622 1.5133
    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
    rij := kri rj
    k
    0
    1 2
    graph (SchNet)
    0 1
    2
    edges w/ cutoff (10Å)
    edge_index
    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
    Z0 = 8
    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
    Z1 = 1
    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
    Z2 = 1
    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
    r0 = [ 0.0344, 0.9775, 0.0076]
    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
    r1 = [0.0648, 0.0206, 0.0015]
    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
    r2 = [0.8718, 1.3008, 0.0007]
    nn.Embedding
    128
    -1.249
    1.6278
    -0.1370

    -0.9488
    0.3105
    -1.6185
    0.1960

    -0.5310
    0.3105
    -1.6185
    0.1960

    -0.5310
    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
    x0 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
    x1 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
    x2
    SchNet (Schütt et al, 2017)
    AAAC9XichVHNShxBEK6d+BeNuiaXgJchi7IiLL0iieQk5pKT+Lcq2DL0jL27vfZMDz29a3SYF8gL5BByiKgQcvDoA3jxBRLwEYJHBS8erJ0dEqKoNcz011/VV/N1lxtKERlCznPWs67unt6+5/0DLwaHhvMjL1cj1dQer3hKKr3usohLEfCKEUby9VBz5ruSr7nbH9r5tRbXkVDBitkN+abPaoGoCo8ZpJx8SF0//pQ4wqaSVw3TWu3Yf7lJm4aRSDNFGjV9J27YVAQ29Zmpe0zG81iVYFFdFDNRY8KmakuZtAlVPq+xxIlFI6Fa1OpmwskXSImkYd8H5QwUIIsFlT8BClugwIMm+MAhAINYAoMInw0oA4EQuU2IkdOIRJrnkEA/aptYxbGCIbuN3xruNjI2wH27Z5SqPfyLxFej0oYx8ov8IJfkjPwkf8jNg73itEfbyy6ubkfLQ2f48+vl6ydVPq4G6v9Uj3o2UIWZ1KtA72HKtE/hdfStvS+Xy++XxuJxsk8u0P93ck5O8QRB68o7XORLXx/x46IXvDEcUPnuOO6D1alS+W1penG6MDuXjaoPRuENFHEe72AWPsICVLD/b7jJded6rB3rm3VgHXVKrVymeQX/hXV8C560vMU=
    xi xi +
    0
    @
    X
    j2Ni
    (xj) !ij
    1
    A
    Message Passing with
    residual connections
    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
    w01 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
    w02 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
    w12
    #JP24"3ח⢪ֲ(//ה嫰ץ׷הַז׶
    䌓秛غ؎،أ׾⻉㷕ח㺔ׇג鏣鎘

    View full-size slide

  73. 4DI/FU䎗⡦涸(//ך⯓꽀涸أةٝت٦س
    input molecule H2O
    gdb_3
    atom features

    0 1 2
    0
    bond features
    0 1
    1
    0 2
    2
    1 2
    0.9620 0.9622 1.5133
    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
    rij := kri rj
    k
    50
    MLP 50 →128
    0.1803
    0.0826
    0.3349

    -0.474
    0.0403
    -0.003
    0.0802

    -0.061
    0.1803
    0.0826
    0.3349

    -0.474
    128
    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
    exp( ↵(rij µ↵)2)
    0
    1 2
    graph (SchNet)
    0 1
    2
    edges w/ cutoff (10Å)
    edge_index
    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
    Z0 = 8
    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
    Z1 = 1
    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
    Z2 = 1
    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
    r0 = [ 0.0344, 0.9775, 0.0076]
    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
    r1 = [0.0648, 0.0206, 0.0015]
    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
    r2 = [0.8718, 1.3008, 0.0007]
    nn.Embedding
    128
    -1.249
    1.6278
    -0.1370

    -0.9488
    0.3105
    -1.6185
    0.1960

    -0.5310
    0.3105
    -1.6185
    0.1960

    -0.5310
    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
    x0 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
    x1 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
    x2
    Weighted ACSFs (ACSFs = atom-
    centered symmetry functions)
    for Behler-Parrinello potentials
    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
    1
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    cos

    ⇡rij
    rc

    + 1

    cutoff function
    element-wise product
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    w02 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
    w12
    SchNet (Schütt et al, 2017)
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    xi xi +
    0
    @
    X
    j2Ni
    (xj) !ij
    1
    A
    Message Passing with
    residual connections
    #JP24"3ח⢪ֲ(//ה嫰ץ׷הַז׶
    䌓秛غ؎،أ׾⻉㷕ח㺔ׇג鏣鎘

    View full-size slide

  74. 4DI/FU䎗⡦涸(//ך⯓꽀涸أةٝت٦س
    SchNet (Schütt et al, 2017) DimeNet (Klicpera et al, 2020)
    Free Energy Free Energy
    y_true
    y_true
    y_pred y_pred
    ExtraTrees w/ ECFP6 LightGBM w/ ECFP6 3-Layer MLP w/ ECFP6
    (without 3D geometry) (without 3D geometry) (without 3D geometry)
    Free Energy Free Energy Free Energy
    錬䏝׮⢪ֲ
    3BEJBM#BTJT 2D Spherical (Fourier-Bessel) Basis
    穠さ錬׾罋䣁׃
    鴟♳ד刿倜ׅ׷
    何葺晛
    ⸂׮✮庠ׅ׷

    鴟♳ד刿倜

    View full-size slide

  75. 4DI/0SC岚⹛ꟼ侧荈⡤׾堣唒㷕统

    View full-size slide

  76. (//ַ׵䎗⡦涸帾㾴㷕统פ
    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

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  77. ِ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
    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–
    䎂遤獳⹛װ㔐鯄דYZ[כ㢌׻׷ָ⢽ִל׉ךⴓ㶨ךؒطؘٕ٦כ㢌׻׵זְ
    ̔穠さꞿ ⾱㶨꟦ך騃ꨄ
    ծ穠さ錬ծ✳꬗錬זו׾僇爙涸ח罋䣁ׅ׷䗳銲ָ֮׷
    갥挿װ鴟ך暴䗙ꆀװ(// ⱖ⫷
    ךرؠ؎ٝד㹋植ׅ׷ ⱖ⫷ָ㢌䳔חꟼ׃ג
    ♶㢌 JOWBSJBU

    ず㢌 FRVJWBSJBOU
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    f(g · x) = g · f(x)
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    f(g · x) = f(x)
    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
    g 2 G
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    f : X ! Y

    View full-size slide

  78. 灇瑔כ竲ֻׁ׵חⴓ㶨׾״׶葺ֻ邌植ׅ׷חכ˘
    (FP.PM
    4QIFSF/FU (FN/FU
    Liu et al
    https://arxiv.org/abs/2102.05013
    Klicpera et al (NeurIPS2021)
    https://arxiv.org/abs/2106.08903
    Ganea et al (NeurIPS2021)
    https://arxiv.org/abs/2106.07802
    4QIFSJDBM.FTTBHF1BTTJOH 4.1

    ה׃ג♧菙䕎׾ⴓ匿
    ✳꬗錬׮罋䣁ׅ׷
    %JNF/FUך䭁䓸晛
    ⡚ְؒطؘٕ٦ך$POGPSNFS،ٝ؟ٝـٕך
    欰䧭חאְג4&
    ♶㢌ז䩛갫ד㹋植

    View full-size slide

  79. 堣唒㷕统–ꆀ㶨⻉㷕鎘皾
    Machine Learning at the Atomic Scale (Chem. Rev.)
    https://pubs.acs.org/toc/chreay/121/16
    Data Science Meets Chemistry (Acc. Chem. Res.)
    https://pubs.acs.org/page/achre4/data-science-meets-chemistry

    View full-size slide

  80. 堣唒㷕统–ءىُٖ٦ءّٝ
    Annu. Rev. Phys. Chem. 71:361–90 (2020)
    PNAS (2020)
    Acc. Chem. Res. 54(7):1575–1585 (2021)
    ꆀ㶨⻉㷕鎘皾׌ֽדכזֻ圫ղזⴓꅿדءىُٖ٦ءّٝה堣唒㷕统ך輐さ灇瑔ָ渿׿ח灇瑔ׁ׸׷״ֲח

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  81. 堣唒㷕统–䩛竲ֹ涸乼⡲锷椚䱿锷
    https://uclnlp.github.io/nampi/
    Machine intelligence capable of learning complex procedural
    behavior, inducing (latent) programs, and reasoning with these
    programs is a key to solving artificial intelligence. Recently, there
    have been a lot of success stories in the deep learning
    community related to learning neural networks capable of using
    trainable memory abstractions.
    Neural Abstract Machines & Program Induction
    • Differentiable Neural Computers /
    Neural Turing Machines (Graves+ 2014)
    • Memory Networks (Weston+ 2014)
    • Pointer Networks (Vinyals+ 2015)
    • Neural Stacks (Grefenstette+ 2015, Joulin+ 2015)
    • Hierarchical Attentive Memory
    (Andrychowicz+ 2016)
    • Neural Program Interpreters (Reed+ 2016)
    • Neural Programmer (Neelakantan+ 2016)
    • DeepCoder (Balog+ 2016)
    :
    䩛竲ֹ涸٥鎸〾涸乼⡲׮㷕统דֹ׷فؚٗٓيה׃ג䪔ִ׷״ֲחז׏גֹ׋
    僇爙涸ז⻉㷕濼陎׮
    輐さ׃גְֽ׷ַ

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  82. ت٦ؙ؟؎سפ״ֲֿ׉ֿ׿ח׍כծ⚅歲
    Ԩ ֿ׸תדך鑧כ⚺חչꆀ㶨⻉㷕鎘皾ח״׷ر٦ةպדغ٦ثٍٕז⚅歲
    錁庠ظ؎ؤָזְ٥⳿⸂׾䖤׷ךח䗳銲⼧ⴓזⰅ⸂䞔㜠ָⴓַ׏גְ׷٥ְ׹ְ׹ז㣐鋉垷ז
    ؔ٦فٝر٦ةָⵃ欽דֹ׷ 2. "/* 0$ 1VC$IFN2$ $0-- .% (VBDB.PM 

    Ԩ ٔ،ٕז⚅歲כא׵ְ˘׉׿זח㿊קוךず颵זر٦ة《׸זְ״˘
    ˖ 錁庠ظ؎ؤָ֮׶暟椚涸醱醡ָ䗳銲 ✳䏝庠׷ה⦼ָ殯ז׷倯ָ兛鸐

    ˖ 椚锷鎘皾ח《׶Ⰵ׸׵׸גזְ搀侧ך❛窃㔓㶨װ㢩✉㔓㶨ך䕦갟
    ˖ 醱꧟禸דכⰅ⸂㢌侧ח⡦׾Ⰵ׸׷ץֹזךַָ♶僇הְֲآٖٝو
    ̔Ⰵ⳿⸂ꟼ⤘ך堣䎷ָⴓַ׵זְַ׵堣唒㷕统׾⢪ְ׋ְךח䗳銲ז䞔㜠׾Ⰵ⸂ח
    Ⰵ׸זְה堣唒㷕统חכ亻⡂湱ꟼ׃ַ鋅ִזְ
    ˖ ׉׮׉׮鎘庠٥ⵖ䖴דֹזְ׋ֻׁ׿ךغحؙؚٓؐٝس㔓㶨ָ֮׷
    ˖ ➂꟦ָ㹋꿀׾鎘歗ׅ׷ה䖤׵׸׷ر٦ةכ䌢חغ؎،أ׾ろ׬
    ̔չ葺ְㅷ颵ךպ䗳銲⼧ⴓז鋅劤⢽׾⡲׷ךכ劤䔲חꨇ׃ְ
    )FMMP 8PSME

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  83. 堣唒㷕统–⻉㷕ך溪ך㉏겗
    ♴鎸כו׸׮堣唒㷕统דַז׶넝礵䏝ז✮庠ָדֹתָׅծ׉׸כ猘׋׍ָ׉ך➬穈׫׾
    椚鍑דֹ׋ֿה׾㼰׃ד׮䠐㄂ׅ׷׌׹ֲַ
    וֲװ׏ג鋅ִגְ׷׮ך׾钠陎
    וֲװ׏׋׵㔲烝⹧ג׷
    ˑ֮׶ָהֲ˒
    J’aime la
    musique
    I love music
    וֲװ׏ג갈岚ַ׵鎉衝׾椚鍑
    וֲװ׏ג㢳鎉铂׾椚鍑
    չ✮庠ָדֹ׷պֿהכչ椚鍑պװչ涪鋅պָדֹ׷ֿה׾湫䱸כ䠐㄂׃זְ

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  84. 㔓卓ך椚鍑חכ㹋꿀灇瑔 ➜Ⰵ灇瑔
    ָ䗳銲♶〳妀
    堣唒㷕统כֻ֮תדر٦ةך⚥ך㢳如⯋湱ꟼ׾䯝ִծ׉׸ח״׏ג✮庠ׅ׷䪮遭
    Ը錁㻊ׁ׸׋湱ꟼָ劤䔲ח㔓卓䚍׾ろ׬ךַ׾然ַ׭׷׋׭חכ㹋꿀ׅ׷׃ַזְ
    ⡤ꅾ
    魦ꞿ
    傈劤فٗꅿ椔Ꟛ䍊♧鮩鼅䩛ך魦ꞿ٥⡤ꅾر٦ة
    䎃椔㔚Ⱅ䒭؟؎ز鼅䩛ر٦ة״׶荈⡲

    չ⡤ꅾ׾㟓װׇל魦ꞿ׮⠼ן׷պָ姻׃ְַכ
    ֿך錁㻊ر٦ة׌ַֽ׵כ寸׃גⴓַ׵זְ
    䘔欽窟鎘㷕ך㛇劤ךؗ
    湱ꟼꟼ⤘כ䗳׆׃׮㔓卓ꟼ⤘׾䠐㄂׃זְ
    չ✮庠ָדֹ׷պֿהכչ椚鍑պװչ涪鋅պָ
    דֹ׷ֿה׾湫䱸כ䠐㄂׃זְ

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  85. 邌植ה➜Ⰵ✮庠ַ׵椚鍑٥涪鋅פ
    ✲⟝כ؝ٝؾُ٦ة 堣唒㷕统
    ך⚥ד饯ֹג׷׿ׄׯזְծ植㜥ד饯ֹגְ׷׿׌CZ⥯
    邌植 ➜Ⰵ
    ˖ 剣⸬זⰅ⸂㢌侧ךず㹀
    ˖ 堣唒㷕统ةأؙךرؠ؎ٝ
    ˖ 鎮箺ر٦ةך鏣鎘ה ꧊
    ˖ 傀㶷ךر٦ة٥濼陎ךⵃ欽
    ˖ 㹋꿀ך鎘歗ה㹋倵
    ˖ 穠卓ך鐰⣣ה鍑ꅸ
    ˖ 㹋꿀⻉㷕罏הך⼿⫴
    ˖ 椚锷⻉㷕罏הך⼿⫴
    堣唒㷕统ٌرٕ
    植㜥
    ؝ٝؾُ٦ةך⚥
    猘׋׍װ㹋植韋

    植㜥ך䞔㜠׾Ⰵ׸׷ 䞔㜠׾植㜥ח䨱ׅ

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  86. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷

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  87. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ

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  88. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ
    ˖ 剣ꣲך儗꟦׃ַ欰ֹ׵׸זְ猘׋׍חչ涪鋅պהְֲ⡤꿀׾ֶ苇甧גׅ׷׋׭ךؼٝز
    ⳿׃ָ実׭׵׸גְ׷կ➂겲窫徦ךة؎ئىحزⰻח

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  89. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ
    ˖ 剣ꣲך儗꟦׃ַ欰ֹ׵׸זְ猘׋׍חչ涪鋅պהְֲ⡤꿀׾ֶ苇甧גׅ׷׋׭ךؼٝز
    ⳿׃ָ実׭׵׸גְ׷կ➂겲窫徦ךة؎ئىحزⰻח
    ˖ 䞔㜠ך鿇ⴓ䚍ر٦ةחדֹ׷䞔㜠כְאד׮⚅歲ך䞔㜠ꆀךק׿ךמהַֽ׵׌ֽկ
    ײֻ屎ך崧׸כ窫ִ׆׃גծ׃ַ׮׮הך宏ח֮׵׆կׅץג׾錁庠ׅ׷ֿהכדֹזְկ

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  90. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ
    ˖ 剣ꣲך儗꟦׃ַ欰ֹ׵׸זְ猘׋׍חչ涪鋅պהְֲ⡤꿀׾ֶ苇甧גׅ׷׋׭ךؼٝز
    ⳿׃ָ実׭׵׸גְ׷կ➂겲窫徦ךة؎ئىحزⰻח
    ˖ 䞔㜠ך鿇ⴓ䚍ر٦ةחדֹ׷䞔㜠כְאד׮⚅歲ך䞔㜠ꆀךק׿ךמהַֽ׵׌ֽկ
    ײֻ屎ך崧׸כ窫ִ׆׃גծ׃ַ׮׮הך宏ח֮׵׆կׅץג׾錁庠ׅ׷ֿהכדֹזְկ
    ˖ ➂꟦ָ♧欰䧄ㄏ꧊׭׋ر٦ةכוֲ׃׋׏ג⡦׵ַך⨉׶ַ׵鷕׸׵׸זְկ

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  91. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ
    ˖ 剣ꣲך儗꟦׃ַ欰ֹ׵׸זְ猘׋׍חչ涪鋅պהְֲ⡤꿀׾ֶ苇甧גׅ׷׋׭ךؼٝز
    ⳿׃ָ実׭׵׸גְ׷կ➂겲窫徦ךة؎ئىحزⰻח
    ˖ 䞔㜠ך鿇ⴓ䚍ر٦ةחדֹ׷䞔㜠כְאד׮⚅歲ך䞔㜠ꆀךק׿ךמהַֽ׵׌ֽկ
    ײֻ屎ך崧׸כ窫ִ׆׃גծ׃ַ׮׮הך宏ח֮׵׆կׅץג׾錁庠ׅ׷ֿהכדֹזְկ
    ˖ ➂꟦ָ♧欰䧄ㄏ꧊׭׋ر٦ةכוֲ׃׋׏ג⡦׵ַך⨉׶ַ׵鷕׸׵׸זְկ
    䗳銲ז䞔㜠ךֲ׍ծְא׮⨉׏׋չ♧鿇պ׃ַر٦ةחכדֹזְ⵸䲿דծ猘׋׍荈魦ך鏩㺁
    ꣲ歲ח鋅さֲ䞔㜠װ爙㇗׾䖤׷׋׭חչر٦ة׾✮庠ח㢌ִ׷麣Ⱗպ׾וֲ⢪ִ׷ַ

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  92. 侄鎮猰㷕灇瑔הכ穠㽷➂꟦ך㌀׫
    չ椚鍑պװչ涪鋅պ׃׋ְךכ堣唒דכזֻ猘׋׍➂꟦
    את׶ծ荈搫岀⵱ך㉏겗דכזֻ猘׋׍荈魦ך礵牞ה⚅歲ך֮׶倯ך㉏겗׾㉏ֲֿהחז׷
    ˖ 猘׋׍ךءّنְ钠濼腉⸂ח ת׷״ֲזչ䎂僒ז椚鍑պָ実׭׵׸גְ׷կ
    ˖ 剣ꣲך儗꟦׃ַ欰ֹ׵׸זְ猘׋׍חչ涪鋅պהְֲ⡤꿀׾ֶ苇甧גׅ׷׋׭ךؼٝز
    ⳿׃ָ実׭׵׸גְ׷կ➂겲窫徦ךة؎ئىحزⰻח
    ˖ 䞔㜠ך鿇ⴓ䚍ر٦ةחדֹ׷䞔㜠כְאד׮⚅歲ך䞔㜠ꆀךק׿ךמהַֽ׵׌ֽկ
    ײֻ屎ך崧׸כ窫ִ׆׃גծ׃ַ׮׮הך宏ח֮׵׆կׅץג׾錁庠ׅ׷ֿהכדֹזְկ
    ˖ ➂꟦ָ♧欰䧄ㄏ꧊׭׋ر٦ةכוֲ׃׋׏ג⡦׵ַך⨉׶ַ׵鷕׸׵׸זְկ
    ءّنְ钠濼腉⸂ךֶתִ׵➂꟦חה׏׋׵չؽحؚպر٦ةַ׮׃׵׿ֽוծ
    مٝوח䗳銲ז䞔㜠ꆀַ׵׃׋׵عشؙا׫׋ְז׮׿װז

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  93. 堣唒㷕统ַ׵堣唒涪鋅פ
    Science 363 (2019)
    Nature 583 (2020) Nature Reviews Drug Discovery 17 (2018)
    㹋꿀荈⹛⻉ך䪮遭涸涪㾜⻉㷕ד׮ꬊ⸬桦ז⸤⫴ְָ׆׸荈⹛⻉ׁ׸׷ךכ娖〷涸䗳搫

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  94. 堣唒㷕统ַ׵堣唒涪鋅פ
    ˖ 堣唒涪鋅䪮遭ך灇瑔㛇湍ה׃גꬊ䌢חꅾ銲ⱄ植䚍٥㾩➂䚍זוر٦ةך颵הꆀך然⥂
    㣟侁ر٦ة׾《׷㹋꿀װٓٝتي㹋꿀כر٦ة猰㷕♳כ䗳銲׌ָ➂꟦כװ׶׋ֻזְ˘
    Science 363 (2019)
    Nature 583 (2020) Nature Reviews Drug Discovery 17 (2018)
    㹋꿀荈⹛⻉ך䪮遭涸涪㾜⻉㷕ד׮ꬊ⸬桦ז⸤⫴ְָ׆׸荈⹛⻉ׁ׸׷ךכ娖〷涸䗳搫

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  95. 堣唒㷕统ַ׵堣唒涪鋅פ
    ˖ 堣唒涪鋅䪮遭ך灇瑔㛇湍ה׃גꬊ䌢חꅾ銲ⱄ植䚍٥㾩➂䚍זוر٦ةך颵הꆀך然⥂
    㣟侁ر٦ة׾《׷㹋꿀װٓٝتي㹋꿀כر٦ة猰㷕♳כ䗳銲׌ָ➂꟦כװ׶׋ֻזְ˘
    ˖ 涪鋅ָ荈⹛⻉דֹ׷ַכ"*ⴓꅿחה׏ג׮琎䎃ך劢鍑寸㉏겗կչ➂䊨濼腉պ׾⡲׶׋ְז׵
    猘׋׍ָ傈ղ㼭ׁזչ涪鋅պהչ㷕统պ׾粸׶鵤׃ג⚅歲׾椚鍑׃גְֻ麓玎ך椚鍑כ♶〳鼘
    Science 363 (2019)
    Nature 583 (2020) Nature Reviews Drug Discovery 17 (2018)
    㹋꿀荈⹛⻉ך䪮遭涸涪㾜⻉㷕ד׮ꬊ⸬桦ז⸤⫴ְָ׆׸荈⹛⻉ׁ׸׷ךכ娖〷涸䗳搫

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  96. 堣唒㷕统ַ׵堣唒涪鋅פ
    ˖ 堣唒涪鋅䪮遭ך灇瑔㛇湍ה׃גꬊ䌢חꅾ銲ⱄ植䚍٥㾩➂䚍זוر٦ةך颵הꆀך然⥂
    㣟侁ر٦ة׾《׷㹋꿀װٓٝتي㹋꿀כر٦ة猰㷕♳כ䗳銲׌ָ➂꟦כװ׶׋ֻזְ˘
    ˖ 涪鋅ָ荈⹛⻉דֹ׷ַכ"*ⴓꅿחה׏ג׮琎䎃ך劢鍑寸㉏겗կչ➂䊨濼腉պ׾⡲׶׋ְז׵
    猘׋׍ָ傈ղ㼭ׁזչ涪鋅պהչ㷕统պ׾粸׶鵤׃ג⚅歲׾椚鍑׃גְֻ麓玎ך椚鍑כ♶〳鼘
    ˖ 㹋꿀荈⹛⻉ָ㹋植ׁ׸ג׮չ䌢חמהַֽ׵ך鿇ⴓ䞔㜠׃ַ䩛חⰅ׵זְպ劤颵כ㢌׻׵זְ
    Science 363 (2019)
    Nature 583 (2020) Nature Reviews Drug Discovery 17 (2018)
    㹋꿀荈⹛⻉ך䪮遭涸涪㾜⻉㷕ד׮ꬊ⸬桦ז⸤⫴ְָ׆׸荈⹛⻉ׁ׸׷ךכ娖〷涸䗳搫

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  97. 堣唒㷕统㾊״ծչ걧ד׏ַ׍պַ׵膴׃ծ植㜥ח⳿״ֲ
    ✲⟝כ؝ٝؾُ٦ة 堣唒㷕统
    ך⚥ד饯ֹג׷׿ׄׯזְծ植㜥ד饯ֹגְ׷׿׌CZ⥯
    邌植 ➜Ⰵ
    ˖ 剣⸬זⰅ⸂㢌侧ךず㹀
    ˖ 堣唒㷕统ةأؙךرؠ؎ٝ
    ˖ 鎮箺ر٦ةך鏣鎘ה ꧊
    ˖ 傀㶷ךر٦ة٥濼陎ךⵃ欽
    ˖ 㹋꿀ך鎘歗ה㹋倵
    ˖ 穠卓ך鐰⣣ה鍑ꅸ
    ˖ 㹋꿀⻉㷕罏הך⼿⫴
    ˖ 椚锷⻉㷕罏הך⼿⫴
    堣唒㷕统ٌرٕ
    植㜥
    ؝ٝؾُ٦ةך⚥
    猘׋׍װ㹋植韋

    植㜥ך䞔㜠׾Ⰵ׸׷ 䞔㜠׾植㜥ח䨱ׅ

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  98. ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 *$3F%%

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    猘ך״ֲז䪮遭㾊חה׏ג׮堣唒㷕统٥堣唒涪鋅ך䪮遭灇瑔ה㹋⚅歲嗚鏾ך׋׭ך脼،خז植㜥
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  99. תה׭.BZUIF.-GPSDFCFXJUIZPV
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    ๏ 䌓秛غ؎،أך鏣鎘הؚٖ؎نحؙأ剑黝⻉
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    ،ٝٔ٥ه،ٖٝؕչ猰㷕ה⟎铡պ

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