Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Graph Neural Networks概観

Graph Neural Networks概観

Graph Neural Networks (GNNs)についてまとめました
実際にどんなことに使えるかイメージを持ってもらうことを意識しました。
内容は以下の通りです。

・グラフ構造とは
・GNNsの発展
・いくつかのGNNsの特徴
・NLPにおける利用例
・その他の領域における利用例

勉強会好評でやってよかったです!
フィードバックはTwitter (roy29fuku)にお願いします。

追記:
なるべくリンク埋め込んで簡単に参照できるようにしたので、ダウンロードしておつかいただくと便利です

Ryota Yamada

June 01, 2019
Tweet

More Decks by Ryota Yamada

Other Decks in Technology

Transcript

  1. ୈ1ճάϥϑษڧձ@KERNEL Graph Neural Networks֓؍ 2019.06.01 fukuגࣜձࣾ ࢁాྋଠ@roy29fuku 1

  2. Swampdog ࣗݾ঺հ ࢁాྋଠ@roy29fuku 2013೥ʙ
 ɹ౦େ्ҩֶՊͰ໔Ӹݚڀ 2017೥ʙ ɹ޻ֶ෦΁సֶ෦ ɹVRղ๤ֶڭࡐΛେֶͱڞಉ։ൃ 2018೥ ɹfukuגࣜձࣾઃཱɾࢿۚௐୡ

    ɹ࿦จ෼ੳࣄۀΛ։࢝ ɹ9೥͔͚ͯଔۀͰ͖·ͨ͠ 2
  3. # ਪ঑ϓϩτίϧ 1. 8िྸΦεͷϚ΢εAΛ12ඖ༻ҙ 2. 5×105ͷࡉ๔BΛi.v. 3-1. ౤༩܈6ඖʹༀࡎYΛ10μg/kg i.p. 3-2.

    ରর܈6ඖʹsalineΛi.p. # ධՁ ମԹɾ݂ѹ ࣬ױXʹༀࡎY͕ ޮ͔͘ௐ΂͍ͨ ࣄۀ֓ཁ 3 3 ৽͍͠ݚڀΞΠσΟΞʹରͯ͠ɺ աڈͷ࿦จ͔Βऔಘ࣮ͨ͠ݧ৚݅Λ΋ͱʹ࣮ݧϓϩτίϧΛఏҊ ௐࠪ࣌ؒ΍࣮ݧͷ΍Γ௚͠Λ࡟ݮ
  4. ख๏ 4 4 named entity recognition, relation extraction, coreference resolutionΛ༻͍ͯ

    ࿦จ͔Βϓϩτίϧ΍݁Ռʹؔ͢ΔσʔλΛநग़ɺߏ଄Խ σʔλΛάϥϑߏ଄ʹஔ͖׵͑Δ͜ͱͰϓϩτίϧͷൺֱ΍ੜ੒͕Ͱ͖Δ
  5. ख๏ 5 5 named entity recognition, relation extraction, coreference resolutionΛ༻͍ͯ

    ࿦จ͔Βϓϩτίϧ΍݁Ռʹؔ͢ΔσʔλΛநग़ɺߏ଄Խ σʔλΛάϥϑߏ଄ʹஔ͖׵͑Δ͜ͱͰϓϩτίϧͷൺֱ΍ੜ੒͕Ͱ͖Δ ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ͔Ͳ͏͔֬ೝ͢ΔͨΊʹGNNsษڧ࢝Ί·ͨ͠
  6. ख๏ 6 https://speakerdeck.com/ioki/development-of-mrr-at-cookpadtechconf2019 named entity recognition, relation extraction, coreference resolutionΛ༻͍ͯ

    ࿦จ͔Βϓϩτίϧ΍݁Ռʹؔ͢ΔσʔλΛநग़ɺߏ଄Խ σʔλΛάϥϑߏ଄ʹஔ͖׵͑Δ͜ͱͰϓϩτίϧͷൺֱ΍ੜ੒͕Ͱ͖Δ ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ͔Ͳ͏͔֬ೝ͢ΔͨΊʹGNNsษڧ࢝Ί·ͨ͠ Luan et al., 2018 # ઌߦݚڀ Պֶ࿦จ͔Βknowledge graph ϨγϐΛػցՄಡʹ
  7. ख๏ 7 named entity recognition, relation extraction, coreference resolutionΛ༻͍ͯ ࿦จ͔Βϓϩτίϧ΍݁Ռʹؔ͢ΔσʔλΛநग़ɺߏ଄Խ

    σʔλΛάϥϑߏ଄ʹஔ͖׵͑Δ͜ͱͰϓϩτίϧͷൺֱ΍ੜ੒͕Ͱ͖Δ ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ͔Ͳ͏͔֬ೝ͢ΔͨΊʹGNNsษڧ࢝Ί·ͨ͠ Luan et al., 2018 # ઌߦݚڀ Պֶ࿦จ͔Βknowledge graph ϨγϐΛػցՄಡʹ ϝϯόʔืूத ڵຯ͋Δํ ࿈བྷ͍ͩ͘͞ʂ Twitter: @roy29fuku https://speakerdeck.com/ioki/development-of-mrr-at-cookpadtechconf2019
  8. ษڧձͷ໨త 8 8 Graph Neural Networks͕Ͳ͏͍ͬͨྖҬɺ՝୊Λ্ख͘ѻ͑Δ͔஌Γ͍ͨ ɾGNNsʹ͍ͭͯҰॹʹษڧ͠·͠ΐ͏ʂ ɾ֤ྖҬʹ͓͚Δ੒ޭɺࣦഊࣄྫͷڞ༗Λ͠·͠ΐ͏ʂʂ ɾݴޠॲཧֶձͰҟ෼໺ަྲָྀ͕ͦ͠͏͔ͩͬͨΒ ࣍ճҎ߱ͷൃදऀΛืू͍ͯ͠·͢ʂ

    ɾGraph theoryͷਂ۷Γ ɾGNNsͷਂ۷Γɺ࣮૷ ɾϑϨʔϜϫʔΫ΍ϥΠϒϥϦɺσʔληοτͷ঺հ ɾ෼ੳ݁Ռͷใࠂ ɾͦͷଞͳΜͰ΋
  9. ɾGraph ɾGraph Neural Networks ɾNatural Language Processing ɾOther Applications 9

    9
  10. ɾGraph ɾGraph Neural Networks ɾNatural Language Processing ɾOther Applications 10

    10
  11. Graphͱ͸ 11 11 ϊʔυʢ௖఺ʣͱΤοδʢลʣͰ ߏ੒͞ΕΔσʔλߏ଄ ϊʔυ: Τοδ:

  12. Graphͱ͸ 12 12 ӈͷάϥϑ͸͜Μͳײ͡ʹදݱ ɹ௖఺ू߹V = {1, 2, 3, 4}

    ɹลू߹E = {{1, 2}, {1, 3}, {2, 3}, {2, 4}, {3, 4}} ɹάϥϑG = (V, E) ผͷݴ͍ํͰఆٛ͢Δͱ ɹE ⊆ [V]2 Λຬͨ͢ ɹG = (V, E) ͷू߹ͷ૊ ΛάϥϑͱݺͿ 1 2 3 4
  13. ͍ΖΜͳGraph 13 13 ޲͖͕͋Δ ϊʔυ͕multi type Τοδ͕multi type ϧʔϓ͕͋Δ

  14. GraphͰදݱͰ͖Δ΋ͷ 14 14 ϊʔυ: ਓʢஉੑ, ঁੑ, …ʣ Τοδ: ਓؒؔ܎ʢ༑ਓ, …ʣ

    Structured deep models: Deep learning on graphs and beyond karate club
  15. GraphͰදݱͰ͖Δ΋ͷ 15 15 ϊʔυ: ݪࢠʢC, H, …ʣ Τοδ: ݁߹ʢ୯݁߹, …ʣ

    Structured deep models: Deep learning on graphs and beyond
  16. GraphͰදݱͰ͖Δ΋ͷ 16 16 ϊʔυ: λϯύΫ࣭ Τοδ: PPI https://academic.oup.com/peds/article/24/9/635/1556325 Structured deep

    models: Deep learning on graphs and beyond
  17. GraphͰදݱͰ͖Δ΋ͷ 17 17 ϊʔυ: ΤϯςΟςΟʢਓ໊, ஍໊, …ʣ Τοδ: ؔ܎ʢॴଐ, ਌ࢠ,

    …ʣ Structured deep models: Deep learning on graphs and beyond
  18. GraphͰදݱͰ͖Δ΋ͷ 18 18 ݱ࣮ͷଟ͘ͷσʔλΛ άϥϑͰදݱͰ͖Δʂ

  19. GraphͰղ͖͍ͨ՝୊ 19 19 ׬ᘳͰ͸ͳ͍σʔλͷܽଛ෦෼Λิ׬ͨ͠Γɺ৽͍͠σʔλΛ෼ྨͨ͠Γ ɾϊʔυͷ෼ྨ ɾάϥϑͷ෼ྨʢFYԽֶ෺࣭ͷ෼ྨʣ ɾϦϯΫͷ༧ଌʢϊʔυಉ͕࢜ྡ઀͔൱͔ʣ ɾΤοδͷ෼ྨ Structured deep

    models: Deep learning on graphs and beyond
  20. ɾGraph ɾGraph Neural Networks ɾNatural Language Processing ɾOther Applications 20

    20
  21. GNNsͷྺ࢙ Structured deep models: Deep learning on graphs and beyond

    21
  22. GNNsͷྺ࢙ 22 https://www.slideshare.net/takahirokubo7792/graph-attention-network

  23. GNNsͷྺ࢙ᶃ ੜ஀ Structured deep models: Deep learning on graphs and

    beyond GraphΛχϡʔϥϧωοτͰѻͬͨ 23
  24. Graph Neueral Networks [Gori+ 2005] 24 24 ֤ϊʔυͷߋ৽ʹ͸ࣗ਎ͱྡ઀ϊʔυΛར༻ Structured deep

    models: Deep learning on graphs and beyond
  25. ne[n]: ϊʔυnͱྡ઀͢Δϊʔυू߹ ln: ϊʔυnͷϥϕϧ xn: ϊʔυnͷঢ়ଶ on: ϊʔυnͷग़ྗ ·ͱΊΔͱ Graph

    Neueral Networks [Gori+ 2005] 25 25 Fw͕contraction mappingʢॖईࣸ૾ʣͳΒ Fw, Gw͸ղΛ࣋ͪɺunique
  26. GNNsͷྺ࢙ᶄ Convolution Structured deep models: Deep learning on graphs and

    beyond CNNͷ৞ΈࠐΈͷ֓೦Λಋೖͯ͠ܭࢉޮ཰↑ 26 26
  27. Convolutional Neural Neworks͓͞Β͍ 27 27 2012: HintonͷAlexNet σΟʔϓϥʔχϯά͕੝Γ্͕͖͔͚ͬͨͬ CNN͸ը૾ͳͲ֨ࢠঢ়ͷσʔλߏ଄ʹద༻Մೳ Structured

    deep models: Deep learning on graphs and beyond
  28. Graph Convolutional Netoworks [Duvenaud+ 2015, Li+ 2016, Scichtkrull+ 2017] 28

    28 CNNͷ৞ΈࠐΈͷ֓೦ΛGraphʹద༻ άϥϑߏ଄͸ඇఆܕʢϊʔυͷ਺ɺ֤ϊʔυͷྡ઀ϊʔυ਺ʣ →৞ΈࠐΈͷૢ࡞Λద༻͢ΔͨΊʹ޻෉͕ඞཁ Wu et al., 2019 Euclidean non-Euclidean
  29. Graph Convolutional Netoworks [Duvenaud+ 2015, Li+ 2016, Scichtkrull+ 2017] 29

    29 CNNͷ৞ΈࠐΈͷ֓೦ΛGraphʹద༻ ΤοδΛॏΈͱͯ͠ѻͬͨ Structured deep models: Deep learning on graphs and beyond
  30. Relational Graph Convolutional Netoworks [Scichtkrull+ 2017] 30 30 relationཁૉΛ௥Ճ graph:

    G = (V, E, R) nodes: vi ∈ V edges: (vi, r, vj) ∈ E relation type: r ∈ R Schlichtkrull et al., 2017
  31. Relational Graph Convolutional Netoworks [Scichtkrull+ 2017] 31 31 hi(l): l૚໨ͷϊʔυvi

    ͷhidden state Ni r: ϊʔυvi ʹରͯؔ͠܎rͰྡ઀͢Δϊʔυू߹ ci,r: ྡ઀͢Δϊʔυͷ਺Λਖ਼نԽɺex. |Nir| ͜ΕΛ֤ϊʔυ͝ͱʹฒྻͰܭࢉɺ࣮ફతʹ͸ܭ ࢉͷޮ཰ͷͨΊʹsparse matrixΛ༻͍Δ ૚ΛॏͶΔ͜ͱͰɺෳ਺ͷϦϨʔγϣϯΛ·͙ͨ ϊʔυಉ࢜ͷؔ܎Λಋ͘ͷʹ໾ཱͭ ͋Δϊʔυʢ੺ʣʹண໨ͨ࣌͠ͷߋ৽ ֤ؔ܎ੑͷೖग़ྗʹؔΘΔྡ઀ϊʔυɾࣗݾϧʔ ϓ΋ܭࢉͯͦ͠ΕͧΕ྘ͷߦྻΛऔಘɺ concatɺReLUͰ෼ྨ Schlichtkrull et al., 2017
  32. GNNsͷྺ࢙ᶅ Attention Structured deep models: Deep learning on graphs and

    beyond attentionΛऔΓೖΕͨ
  33. Attention Mechanism͓͞Β͍ 33 33 ೖྗ͝ͱͷॏཁ౓߹͍Λߟྀͨ͠ A Beginner's Guide to Attention

    Mechanisms and Memory Networks
  34. Graph Attention Networks [Monti+ 2017, Hoshen 2017, Veličković+ 2018] 34

    34 Ͳͷϊʔυͱͷྡ઀Λॏࢹ͢Δ͔attentionͰදݱͨ͠ GCNͰaij(1/cij)͸ྡ઀ϊʔυ਺ʹґଘ͍ͯͨ͠ Graph Attention NetworksͰ͸ΑΓॏཁͳ΋ͷΛॏΈ෇͚Δ Wu et al., 2019 GCN Graph Attention Networks
  35. GNNsͷྺ࢙ᶆ άϥϑͷੜ੒ Structured deep models: Deep learning on graphs and

    beyond Version 1: Generate graph (or predict new links) between known entities Version 2: Generate graphs from scratch (single embedding vector)
  36. GraphͰղ͖͍ͨ՝୊ “ݹయత*”ͳ΋ͷ 36 36 Structured deep models: Deep learning on

    graphs and beyond ׬ᘳͰ͸ͳ͍σʔλͷܽଛ෦෼Λิ׬ͨ͠Γɺ৽͍͠σʔλΛ෼ྨͨ͠Γ *Kipfᐌ͘classical
  37. GraphͰղ͖͍ͨ՝୊ “৽͍͠”΋ͷ 37 37 (SBQI"VUPFODPEFST ྗֶత૬ޓ࡞༻Λߏ଄Λௐ΂Δ ͜ͱͳ͘ɺάϥϑ͔Βਪఆ͢Δ ҼՌؔ܎ͷਪఆ΍ λϯύΫ࣭૬ޓ࡞༻ͷղ໌ʹظ଴ Structured

    deep models: Deep learning on graphs and beyond
  38. GraphͰղ͖͍ͨ՝୊ “৽͍͠”΋ͷ 38 38 (SBQI(FOFSBUJWF/FUXPSLT .PM("/ ෼ࢠΛάϥϑͰදݱ EFTDSJNJOBUPS("/Ͱֶश SFXPSE3-Ͱֶश ෼ࢠͷੜ੒΁ͷԠ༻͕ظ଴

    Structured deep models: Deep learning on graphs and beyond
  39. ɾGraph ɾGraph Neural Networks ɾNatural Language Processing ɾOther Applications 39

    39
  40. NLP×Graph 40 40 Zhou et al., 2019

  41. ϨγϐΛάϥϑʹམͱ͠ࠐΉ ɹϊʔυ: ࡐྉ ɹΤοδ: खॱ Ԡ༻ͱͯ͠ҎԼͷ࣮ݱΛݟਾ͍͑ͯΔ ɾதؒϊʔυͷݕࡧʢᖱΊͨϕʔίϯʣ ɾෳ਺ϨγϐΛϚʔδ ɾ৽͍͠ௐཧ๏ͷ୳ࡧ 2019/02/27ͷൃදͰ෼ྔͷਖ਼نԽ

    ࣮ࣾձͷσʔλΛѻ͏͠ΜͲΈʹγϯύγʔ Machine Readable Recipe (recipe) 41 41 https://speakerdeck.com/ioki/development-of-mrr-at-cookpadtechconf2019
  42. SCIERC (scientific protocol) 42 42 Պֶ࿦จʹରͯ͠entities, relations, coreferencesΛΞϊςʔγϣϯͨ͠σʔλ ηοτΛ࡞੒ طଘͷϞσϧ͕ݸผͷλεΫΛύΠϓϥΠϯ

    తʹܨ͍Ͱͨͷʹର͠ɺmulti-task learning frameworkΛ࣮૷ͨ͠ υϝΠϯݻ༗ͷಛ௃ྔΛ༻͍ͣʹैདྷख๏Λ ্ճΔநग़ਫ਼౓Λ࣮ݱ σʔληοτ ɾ500ຊ෼ͷAbstract ɾentity: 6 types ɾrelation: 7 types Պֶత಺༰ʹಛԽͨ͠৘ใநग़Λ໨ࢦ͢ Luan et al., 2018
  43. PaperRobot (knowledge graph) 43 43 աڈͷ࿦จ͔Β knowldge graph*Λੜ੒ ɹnode: entities/concepts

    ɹedge: relations * άϥϑߏ଄knowledge base ɹʢent1, rel, ent2ʣͷtripletͰදݱ ৽͍͠Պֶతൃݟͱ͸ ৽͍͠node/relationͷൃݟͱଊ͑Δ = incremental work ೖྗ͞ΕͨλΠτϧʹԠͨ֓͡ཁ/݁࿦/ల๬Λࣗಈੜ੒͢Δ ͞Βʹੜ੒͞Εͨ࿦จ͔Β৽͍͠࿦จΛੜ੒͠ɺࣗಈͰແݶʹݚڀΛ͢Δͱ͍͏ߏ૝ 2019/5/20ʹग़ͨϗϠϗϠ࿦จ Wang et al., 2019 SCIERCͷ1st authorͷYi Luan͞Μ͕last author
  44. Learning to Represent Programs with Graphs (source code) 44 44

    ιʔείʔυͷsemanticͳ෼ੳ NLPతͳΞϓϩʔνͰ͸ಉ͡ม਺΍ؔ ਺͕཭Εͨͱ͜ΖͰ࢖ΘΕͨ࣌ͷґଘ ؔ܎ΛղܾͰ͖ͳ͔ͬͨ Gated Graph Neural NetworksΛར༻ Allamanis et al., 2018 VarNaming: จ຺͔Βม਺Λ໋໊ VarMisuse: ม਺ͷޡ༻Λݕ஌
  45. ͓͢͢Ίblogهࣄ 45 45 Graph ConvolutionΛࣗવݴޠॲཧʹԠ༻͢Δʢશ7ճʣ ٕज़ಋೖʹ͓͚ΔԾઆݕূͷϓϩηεΛΞ΢τϓοτɺͱͯ΋ษڧʹͳΔ Part7: ߟ࡯ ɾTransformerͷSelf-AttentionͷΑ͏ʹɺࣗવݴޠॲཧʹ͓͍ͯάϥϑతͳػߏ͕༗༻ͳ৔ ߹͸͋Δɻ͔͠͠ɺͦͷ͜ͱͱGraph

    Convolution͕༗ޮͳ͜ͱ͸౳ՁͰ͸ͳ͍ɻ ɾGraph Convolution͕༗ޮͳͷ͸ɺϊʔυ෼ྨ/άϥϑߏ଄෼ྨͷλεΫʹམͱ͠ࠐΊΔ έʔεɻจ຺৘ใΛ֫ಘ͍ͨ͠ͱ͍͏ϞνϕʔγϣϯͱɺGraph ConvolutionͷಘҙྖҬͱ ͸͋·Γ߹க͠ͳ͍ɻ ɾGraph ConvolutionΛࣗવݴޠॲཧͰ࢖͏ͳΒ͹ɺʮେن໛͔ͭHeterogeneousͳάϥϑ Ͱɺϊʔυ෼ྨͷ໰୊ʹؼணͰ͖Δʯέʔε͕ద͍ͯ͠ΔͱࢥΘΕΔɻ
  46. ɾGraph ɾGraph Neural Networks ɾNatural Language Processing ɾOther Applications 46

    46
  47. MoleculeNet (chemical) 47 47 molecular machine learningͷϕϯ νϚʔΫͱͳΔσʔληοτ ྔࢠྗֶɾ෺ཧԽֶɾੜ෺෺ཧֶɾ ੜཧֶͷ؍఺͔ΒूΊΒΕͨ

    700,000ͷԽ߹෺σʔλͰߏ੒ ෳ਺ͷGNNs͕σϑΥϧτͰ࢖͑Δ drug discoveryϑϨʔϜϫʔΫͷ DeepChem಺ʹͯσʔληοτͱ͠ ͯ࢖ΘΕ͍ͯΔ Wu et al., 2018
  48. BrainNetCNN (neuroscience) 48 48 ίωΫτʔϜʢਆܦճ࿏ʣΛ NNsʹಥͬࠐΜͩ ۩ମతʹ͸ૣ࢈ͷ༮ࣇͷ֦ࢄςϯιϧը૾ ʢDTIʣΛ࢖ͬͯೝ஌ೳྗͱӡಈೳྗͷ༧ ଌʹ༻͍ͨ Τοδʹྔతͳม਺Λ༩͑ɺਆܦͷ઀ଓͷ

    ڧ͞Λදݱ edge-to-edge, edge-to-node and node-to- graphͳ৞ΈࠐΈϑΟϧλʔΛར༻ Kawahara et al., 2017
  49. Other Applications 49 49 Structured deep models: Deep learning on

    graphs and beyond
  50. Other Applications 50 50 Zhou et al., 2019

  51. Datasets 51 51 Wu et al., 2019

  52. ࣮ࡍGNNsͬͯ࢖͑Δͷʁ 52 52

  53. 1-dimensional Weisfeiler-Leman graphͱಉ౳ https://www.youtube.com/watch?v=DLjmQmfRlis

  54. ϩʔύεϑΟϧλʔͱಉ౳ 54 54 https://github.com/arXivTimes/arXivTimes/issues/1232 https://twitter.com/shion_honda/status/1132146301024391169

  55. References 55 55

  56. 56 (SBQIཧ࿦ ˒͞ΜΦεεϝ%BOJFM4QJFMNBOߨٛࢿྉ ˒͞ΜΦεεϝ%BOJFM4QJFMNBOߨٛಈը (//T ˒ࢁా͓͢͢Ί,JQGͷϖʔδࢿྉ4USVDUVSFEEFFQNPEFMT%FFQMFBSOJOHPOHSBQITBOECFZPOE ˒ࢁా͓͢͢ΊSFWJFX"$PNQSFIFOTJWF4VSWFZPO(SBQI/FVSBM/FUXPSLT SFWJFX(SBQI/FVSBM/FUXPSLT"3FWJFXPG.FUIPETBOE"QQMJDBUJPOT ,JQGͷ·ͱΊ(3"1)$0/70-65*0/"-/&5803,4 JDPYGPHHSBQIDPOWPMVUJPOOMQ

    (//T"/FX.PEFMGPS-FBSOJOHJO(SBQI%PNBJOT 3($/T.PEFMJOH3FMBUJPOBM%BUBXJUI(SBQI$POWPMVUJPOBM/FUXPSLT .PEFMJOH3FMBUJPOBM%BUBXJUI(SBQI$POWPMVUJPOBM/FUXPSLTͷ·ͱΊ (//·ͱΊ  d   (SBQI"UUFOUJPO/FUXPSL References 1/2
  57. 57 /-1 .33 .BDIJOF3FBEBCMF3FDJQF ͷ։ൃ%FWFMPQNFOUPG.33!$PPLQBE5FDI$POG 4$*&3$ 1BQFS3PCPU -FBSOJOHUP3FQSFTFOU1SPHSBNTXJUI(SBQIT (SBQI$POWPMVUJPOͰࣗવݴޠॲཧΛߦ͏ 0UIFS"QQMJDBUJPOT

    .PMFDVMF/FU #SBJO/FU$// ࣮ࡍ(//Tͬͯ࢖͑Δͷʁ )PX1PXFSGVMBSF(SBQI/FVSBM/FUXPSLT  8FJTGFJMFSBOE-FNBO(P/FVSBM)JHIFSPSEFS(SBQI/FVSBM/FUXPSLT 3FWJTJUJOH(SBQI/FVSBM/FUXPSLT"MM8F)BWFJT-PX1BTT'JMUFST (SBQI/FVSBM/FUXPSL3FUSJFWB5&$)#-0( 5XJUUFS!TIJPO@IPOEB IUUQTHJUIVCDPNBS9JW5JNFTBS9JW5JNFTJTTVFT References 2/2
  58. ͍͞͝ʹ 58 58

  59. 59 59 ࣍ճҎ߱ͷൃදऀΛืू͍ͯ͠·͢ʂ ɾGraph theoryͷਂ۷Γ ɾGNNsͷαʔϕΠ, ࣮૷ ɾϑϨʔϜϫʔΫ, ϥΠϒϥϦ, σʔληοτͷ঺հ

    ɾ෼ੳ݁Ռͷใࠂ ɾͦͷଞͳΜͰ΋ ख఻͍͚ͬͯͨͩΔํ͸SlackͳΓTwitterͳΓͰ ࢁాʢroy29fukuʣ·Ͱ࿈བྷ͍ͩ͘͞ʂ ཁ๬͕͋Ε͹࣍ճҎ߱ଓ͖·͢