[
    [
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "图-解决模式识别（Pattern Recognize 问题）"
                    }
                ]
            },
            "bbox": [
                144,
                93,
                495,
                109
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Node occurance 边的关联性"
                    }
                ]
            },
            "bbox": [
                146,
                112,
                376,
                126
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "节点的属性"
                    }
                ]
            },
            "bbox": [
                146,
                130,
                238,
                143
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "边的信息"
                    }
                ]
            },
            "bbox": [
                146,
                149,
                221,
                162
            ]
        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "X _ {V} \\in \\mathbb {R} ^ {| V | \\times d}",
                "math_type": "latex",
                "image_source": {
                    "path": "images/1892e045c668f9bd05c148e60da18f1e7dfc04e4f29833416b2a854e91a002b5.jpg"
                }
            },
            "bbox": [
                151,
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                181
            ]
        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "X _ {E} \\in \\mathbb {R} ^ {| E | \\times d _ {E}}",
                "math_type": "latex",
                "image_source": {
                    "path": "images/01fda0b6beca1d355c6790b51e2776c92be237cfd5886771291019aa67c556cb.jpg"
                }
            },
            "bbox": [
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                245,
                204
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "动态图 在紧凑的表示中集成拓扑和时间信息能力，更多用于建模动态系统，如社交网络预测、推荐系统、交通预测、谣言传播等等，结合了顺序/时序数据处理和静态图学习的挑战。图被要求处理随时间变化的动态的拓扑结构（and/or）（边数）属性（节点属性边属性），为了对动态系统建模。"
                    }
                ]
            },
            "bbox": [
                144,
                223,
                853,
                293
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "对顺序数据进行处理，捕获序列不同实体之间的依赖关系。"
                    }
                ]
            },
            "bbox": [
                146,
                297,
                600,
                312
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "主要有 LSTM 的卷积架构所取代。"
                    }
                ]
            },
            "bbox": [
                146,
                315,
                403,
                330
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "基于解码器/编码器框架的序列模型，如 Transformer、依赖于注意力机制"
                    }
                ]
            },
            "bbox": [
                144,
                334,
                722,
                349
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "在静态图学习，克服图表示中缺乏节点排序所固有的置换不变性/等变性约束。"
                    }
                ]
            },
            "bbox": [
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                368
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "解决方法消息传递神经网络 MPNN"
                    }
                ]
            },
            "bbox": [
                146,
                370,
                418,
                386
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "不同的 DG"
                    }
                ]
            },
            "bbox": [
                146,
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                233,
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "离散的/连续的"
                    }
                ]
            },
            "bbox": [
                146,
                407,
                263,
                423
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "边进化/节点进化/属性进化"
                    }
                ]
            },
            "bbox": [
                146,
                426,
                357,
                441
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "同质与异质"
                    }
                ]
            },
            "bbox": [
                146,
                445,
                238,
                460
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "学习环境：直推式还是归纳式"
                    }
                ]
            },
            "bbox": [
                146,
                464,
                381,
                478
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "推断（前向预测）阶段"
                    }
                ]
            },
            "bbox": [
                146,
                482,
                327,
                497
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "通过输入X预测Y"
                    }
                ]
            },
            "bbox": [
                146,
                501,
                287,
                516
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "学习阶段（反向优化）"
                    }
                ]
            },
            "bbox": [
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                315,
                533
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "根据Y和Y‘，优化参数"
                    }
                ]
            },
            "bbox": [
                146,
                538,
                326,
                552
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "如前所述，监督学习旨在学习输入空间 X和输出空间Y之间的映射函数。X可以表示的空间。本小节现在讨论空间Y。"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "由于动态图涉及来自图和时间/顺序数据的概念，因此必须考虑这两个方面来定义空间Y。"
                    }
                ]
            },
            "bbox": [
                146,
                593,
                831,
                609
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "当学习序列数据的统计模型时，输入 X 可以由 T 个时间步长的 d 维特征表示，表示为X∈RTxd "
                    },
                    {
                        "type": "equation_inline",
                        "content": "\\boldsymbol { X } \\in \\mathbb { R } ^ { T \\times d }"
                    },
                    {
                        "type": "text",
                        "content": "。"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "输出Y的粒度可以是时间步长级别（每个时间步长一个输出，如在词性标记或更一般地序列标记中），或聚集的（一个输出用于许多输入，如在情感分类或更一般地序列分类中）。在静态图学习中，除了特征XV和XE之外，输入还具有拓扑信息。至于序列，输出 Y可以是局部的（每个节点或每条边一个标签）或全局的（每个子图或整个图一个标签）。"
                    }
                ]
            },
            "bbox": [
                144,
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                739
            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/296469f5d0a2010eb375ed7c66eed44792ebbceb0c9c733fa650c9c61c177c37.jpg"
                },
                "image_caption": [],
                "image_footnote": []
            },
            "bbox": [
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                423,
                789
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Inference "
                    }
                ]
            },
            "bbox": [
                216,
                799,
                315,
                815
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Parameter Updates "
                    }
                ]
            },
            "bbox": [
                524,
                741,
                707,
                758
            ]
        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "\\mathbf {\\Theta} ^ {\\prime} = \\operatorname {u p d a t e} (\\mathbf {\\Theta}, \\hat {\\mathbf {Y}}, \\mathbf {Y})",
                "math_type": "latex",
                "image_source": {
                    "path": "images/39c73dbbb036d3b768659fd7ac244de0a4af645f8ad357114b383906c3030594.jpg"
                }
            },
            "bbox": [
                463,
                759,
                766,
                791
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "许多最新的模型遵循编码器/解码器原理，其中可变长度的输入信号被编码成潜在表示，然后由解码器使用该潜在表示来计算下游任务的输出信号"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "这里的 Z 就是 embedding"
                    }
                ]
            },
            "bbox": [
                146,
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                354,
                888
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "再把 embedding 通过解码器得到预测"
                    }
                ]
            },
            "bbox": [
                146,
                890,
                448,
                906
            ]
        }
    ],
    [
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/e2949c5b136177889bb7cc594ee5765d36bef4e6c8b7e90fe074c101bfb8a6ea.jpg"
                },
                "image_caption": [],
                "image_footnote": []
            },
            "bbox": [
                147,
                91,
                845,
                174
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "输入和输出序列的单元可能具有不同的顺序。"
                    }
                ]
            },
            "bbox": [
                144,
                185,
                494,
                200
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "学习潜在表示（也称为嵌入）被称为表示学习。"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "当有多个节点/边的类型（项目和用户），用类型映射函数"
                    }
                ]
            },
            "bbox": [
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                239
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "GNN/GAT/K-GNN "
                    }
                ]
            },
            "bbox": [
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                294,
                273
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "DG 动态图——两种形式"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "一种离散形式的"
                    }
                ]
            },
            "bbox": [
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                275,
                312
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "DTDG "
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "只要记住每一个时间段的快照（snapshot->ti）"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "DTDG "
                    },
                    {
                        "type": "equation_inline",
                        "content": "="
                    },
                    {
                        "type": "text",
                        "content": "（G1,G2…,GT）"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "一种连续形式的"
                    }
                ]
            },
            "bbox": [
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                275,
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "CTDG 连续时间动态图"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "基于事件流的形式"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "每一次事件的变化记录下来"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "瞬时交互两个节点的（u，v）和时间 t"
                    }
                ]
            },
            "bbox": [
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                460
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Contact -Sequence ={(ui,vi,ti)} "
                    }
                ]
            },
            "bbox": [
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                394,
                480
            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Event-Based={(ui,vi,ti,deltai)} 起始(出现 )时间 ti 和持续时间 delta i，两个节点关联的边的存在的时刻"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Interval-Graph={(ui,vi,Te);Te=((t1,t1’),(t2,t2’))}，用 Te 来表示边的所有活动"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Graph stream 大规模图，用于边的添加和减少 delta i=1 add or -1deletion 标志位不考虑持续时间"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Graph Stream={（ui，vi，ti，delta i）} "
                    }
                ]
            },
            "bbox": [
                144,
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                468,
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "什么事件？"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Ti时刻下，ui和vi的边增加了/减少了"
                    }
                ]
            },
            "bbox": [
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                443,
                627
            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/c746830d302e3e44284fd48b73c0af69a11d0acf4ee6059f4189b80414d69c7f.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "Static Graphs "
                    },
                    {
                        "type": "text",
                        "content": "Weighted directed graph "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
                221,
                664,
                315,
                734
            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/6f1bb89499913ea46bf89c5766e785d288ad81eb6d1d4371993b350c787bd28d.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "Heterogeneous graph "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
                223,
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                315,
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            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/3e4e316277ba51154368e0a57961bebe492938e98fcdc466f4510639ac5629e6.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "Dynamic Graphs "
                    },
                    {
                        "type": "text",
                        "content": "DTDG (or Snapshot vision) "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
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            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/8ef90f4621dfc41510d57405f3c6bb283fb266f06ec85835cad4eb31d5ae5683.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "CTDG (or Event vision) "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
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                757,
                584,
                825
            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/0681e7b4f29f3c5eba8a879c82bd10665da1edd827bdf1c903ae625ea3f30b1c.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "(Edge-oriented) ESG "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
                601,
                678,
                885,
                722
            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/c758284426fe875cbb2097ef354f0d4a80e757498dc69b3b2a64c06ba310b2a0.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "(Node-oriented) ESG "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
                601,
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                875,
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "如何将动态图转换成等价的静态图ESG？"
                    }
                ]
            },
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                            {
                                "type": "text",
                                "content": "1、基于边的形式 节点的备份 "
                            },
                            {
                                "type": "equation_inline",
                                "content": "^ +"
                            },
                            {
                                "type": "text",
                                "content": "边的联系（节点间 "
                            },
                            {
                                "type": "equation_inline",
                                "content": "^ +"
                            },
                            {
                                "type": "text",
                                "content": "时间戳，加入了节点之间的关联性）"
                            }
                        ]
                    },
                    {
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                        "item_content": [
                            {
                                "type": "text",
                                "content": "2、基于节点的形式"
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                        "content": "GNNDelete如何删除边的关联性"
                    }
                ]
            },
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        {
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                        "content": "定义动态度："
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                                "content": "1、边和顶点都固定，fix V,E 时空图（STGCN 时空模型，既要学时间上的， 又要学空间上）"
                            }
                        ]
                    },
                    {
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                        "item_content": [
                            {
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                                "content": "2、只固定了顶点,fix V "
                            }
                        ]
                    },
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                        "item_content": [
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                                "content": "3、都变化，vary "
                            }
                        ]
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                            {
                                "type": "text",
                                "content": "4、边集不变，节点集变化，没有意义"
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                        ]
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        {
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                        "content": "输出是有粒度："
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                ],
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        {
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                        "content": "预测单一时刻的结果"
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        {
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                    {
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                        "content": "还是多个时刻的"
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                ],
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                                "content": "：时间步长级别的（ 每个时间步长一个输出）"
                            }
                        ]
                    },
                    {
                        "item_type": "text",
                        "item_content": [
                            {
                                "type": "text",
                                "content": "：聚合的，一个输出多个输入（未来五个时间的拓扑结构）"
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                        ]
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                        "content": "拓扑结构也有局部（子图）和全局的"
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                        "content": "直推式 原来的拓扑结构不变 做出预测的时候没有在训练过程中没出现过的节点归纳式 做出推断的时候训练过程中没有看到"
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                        "content": "Transductive "
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                        "content": "(1) Transductive-fixv,E Learning Inference "
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                        "content": "(2) Transductive-fixy Learning Inference "
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                        "content": "(3) Transductive-vary Learning Inference "
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                        "content": "Inductive "
                    }
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                    {
                        "type": "text",
                        "content": "（4） Inductivev"
                    }
                ]
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                        "content": "(5) InductiveDG "
                    }
                ]
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        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "离散的时间直推式学习中（DTDG,Transductive），transfix VE ：交通流量，传染病病例，犯罪数量，作物产量"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "图/全局任务：每个快照的分类 睡眠阶段分类；整个DG的预测，如骨骼的动作STG；Tarnsfix V：电信网络中连通性，会议中个人联系"
                    }
                ]
            },
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        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "离散的归纳式学习（DTDG Inductive）中 社交网络未来快照的节点分类或链接预测图集输出 基于社交网络传播树的快照对真是和假新闻分类"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "连续时间（CTDG）"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "推荐系统、社交网络"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "CTCG再其最小时间单元下不能访问全局/整个图信息，全局的时间步标签是无意义的但是全局聚合任务可以通过聚合不同时间步长的节点来实现，如连续时间内谣言检测CTDG也可以定期拍摄快照转换为DTDG"
                    }
                ]
            },
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        },
        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "动态时间下的任务"
                    }
                ]
            },
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        }
    ],
    [
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "为了评估给定任务的统计模型的性能，传统机器学学习 "
                    }
                ]
            },
            "bbox": [
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        },
        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "分类任务"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "回归任务"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "节点排名任务"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "动态任务 沿着时间轴计算静态度量"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "动态图的嵌入"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "从编码器-解码器的角度来看，深度学习统计模型首先将原始输入映射到表示为 Z的嵌入中，然后利用 Z 来预测输出[12，4]。图形可以在节点/边缘级别或（子）图形级别嵌入[13，5].节点级嵌入有利于广泛的节点相关任务，并允许保留更完整的输入信息以供稍后计算[5]以同样的方式，时间步长级嵌入比时间聚合嵌入保留更多的信息。类似地，当在顺序数据上学 习 时 [7] 。"
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        {
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        {
            "type": "equation_interline",
            "content": {
                "math_content": "Z \\in \\mathbb {R} ^ {| V | \\times | T | \\times d}, z _ {v} ^ {t} \\in \\mathbb {R} ^ {d}",
                "math_type": "latex",
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        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "对不同的动态图， 如何设计 encoder 的 settings"
                    }
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    [
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                "image_caption": [
                    {
                        "type": "text",
                        "content": "(A) Discrete, transductive "
                    }
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                        "content": "(B) Discrete, inductive "
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                        "content": "(C) Continuous, transductive "
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        },
        {
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            "content": {
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                "image_caption": [
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                        "type": "text",
                        "content": "(D) Continuous, inductive "
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "为了将动态图信息化地编码为张量或向量列表，DGNN必须捕获结构信息及其随时间的演化 。 因 此 ， 为 了 分 别 处 理 拓 扑 和 时 间 ，DG 通常被 分 解 或转换 为 等效静 态 （ 子 ） 图[74，89，75]，随机游走[113，124，123，121，122]，或者是矩阵序列[95，86，93]。"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "在文献中，通过将不同的静态图编码器 fG（·）与时态数据的fT（·）相结合，出现了许多方法。大量的图和时态数据编码器是本节中回顾的 DG编码器的基础。这些编码器在附录B和C中进行了描述。"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "在下面的小节中，我们提出了一个DGNN模型的分类，它依赖于五个类别。我们的分类，如图7所示，是基于处理时间和结构信息的策略。"
                    }
                ]
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        {
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                "list_items": [
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                        "item_type": "text",
                        "item_content": [
                            {
                                "type": "text",
                                "content": "1.通过拓扑对时间边缘进行建模并对 ESG 进行编码，表示为 TE（第 3.1 节）。"
                            }
                        ]
                    },
                    {
                        "item_type": "text",
                        "item_content": [
                            {
                                "type": "text",
                                "content": "2.对隐藏状态进行顺序编码，记为 enc（H）（第 3.2 节）。"
                            }
                        ]
                    },
                    {
                        "item_type": "text",
                        "item_content": [
                            {
                                "type": "text",
                                "content": "3.对 DGNN 参数进行顺序编码，表示为 enc（Θ）（第 3.3 节）。"
                            }
                        ]
                    },
                    {
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                        "item_content": [
                            {
                                "type": "text",
                                "content": "4.通过属性嵌入发生时间t作为ESG的边缘特征，表示为emb（t）（第3.4节）。"
                            }
                        ]
                    },
                    {
                        "item_type": "text",
                        "item_content": [
                            {
                                "type": "text",
                                "content": "5.抽样因果游走，表示为 CauseRW（第 3.5 节）。"
                            }
                        ]
                    }
                ]
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                    {
                        "type": "text",
                        "content": "1. TE "
                    }
                ]
            },
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        },
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        },
        {
            "type": "image",
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                "image_source": {
                    "path": "images/36a04b2c156c0dbfeeb1f8a5e3a2caa42895d4c195620b069cf075a54dca2717.jpg"
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        {
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            "content": {
                "image_source": {
                    "path": "images/84576c405221d1001ad1ab5a0f3de8a24f61ef9923085f789c09f31cc6a792f9.jpg"
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                        "type": "text",
                        "content": "2. Enc(H) "
                    }
                ]
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        },
        {
            "type": "image",
            "content": {
                "image_source": {
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                "paragraph_content": [
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                        "content": "3. Enc(0) "
                    }
                ]
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        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/11776d45b7f1d6ffcfced0128e76a2d7ea793afc930bd40b6c3b614f0c6b1320.jpg"
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                "image_caption": [],
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        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "4. Emb(t) "
                    }
                ]
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        },
        {
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            "content": {
                "image_source": {
                    "path": "images/28df9d27ec3d3faac8c88b3acad757af84feff54fee07c071e078c0dff6e42e6.jpg"
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "请注意，这五种方法并不是唯一的，也就是说，它们可以组合在一起并用于同一 DG。"
                    }
                ]
            },
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "1、对时序的边进行建模——转换为静态图"
                    }
                ]
            },
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        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "FixV,E 考虑了时间信息（embedding ET）"
                    }
                ]
            },
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        },
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            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/22d8dcba7544ae7f4b9a780b95130b617616df0c54a80f0a285449e5d6235839.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "Snapshots "
                    }
                ],
                "image_footnote": []
            },
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            ]
        },
        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "ASTTN "
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/8169e54de8b83dfaaa4b484f35da48c4abb52c1e0df89fb0f62c7e9903e8e394.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "STG with Er "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
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            ]
        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/6984145b6f133ae0040e209cde6ece2a90e61b23f8c1a1eedced479836a1b650.jpg"
                },
                "image_caption": [
                    {
                        "type": "text",
                        "content": "ST-GCN Module "
                    }
                ],
                "image_footnote": []
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "2、对隐藏状态进行顺序编码"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "对拓扑结构和时间戳信息进行编码"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "RST "
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "DyReG "
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Dyn-GCN "
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "把通过 f(G)编码的信息经过 LSTM 或者 GRU（Sequential endocding）进行时间序列的学习"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "Z ^ {t} = f _ {T} \\left(\\left(f _ {G} \\left(X ^ {t}\\right)\\right)\\right), o r f _ {T} \\left(X ^ {T}\\right) \\oplus f _ {G} \\left(X ^ {t}\\right)",
                "math_type": "latex",
                "image_source": {
                    "path": "images/5a524318107c7410de3f9d6c6c7dfb4c89d19c8a047e7f7cd9216910f2468991.jpg"
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            },
            "bbox": [
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        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "解码的时候也要用sequential去阶码"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "3、对于新增的节点很难预测，及没有将 fG 和 fT 结合起来"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "对应的是 transformer 直接把时间戳的信息编码进去了"
                    }
                ]
            },
            "bbox": [
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "通过（fg参数）时间步来学习时间信息"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "将时间信息的编码加入到 fg 里"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "\\Theta_ {f _ {o}} ^ {t} = L S T M \\left(\\Theta^ {t - 1} _ {f _ {o}}\\right)",
                "math_type": "latex",
                "image_source": {
                    "path": "images/6e64120448ccf32f98f8f5333b0f37188a18250a8fc5dde0d2ec35063a075a6c.jpg"
                }
            },
            "bbox": [
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        },
        {
            "type": "equation_interline",
            "content": {
                "math_content": "\\Theta^ {t} _ {f _ {G}} = G R U \\left(H ^ {t}, \\Theta^ {t - 1} _ {f _ {G}}\\right)",
                "math_type": "latex",
                "image_source": {
                    "path": "images/78d51be8fa1fc5c799d1a1c5e1de13451c969e2bbb002ac75c8cd077034d642c.jpg"
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            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "再经过编码，就没有时间上的序列性了"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "4、"
                    }
                ]
            },
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "还把时间作为嵌入信息，如何编码时间信息"
                    }
                ]
            },
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        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "Temproal point process "
                    }
                ]
            },
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            ]
        }
    ],
    [
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "在每个节点上加一个 t 的 embedding"
                    }
                ]
            },
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            ]
        },
        {
            "type": "title",
            "content": {
                "title_content": [
                    {
                        "type": "text",
                        "content": "3、随机游走的方法"
                    }
                ],
                "level": 1
            },
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        },
        {
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            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "对于异质图的方法"
                    }
                ]
            },
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "怎么设计一个 GNN"
                    }
                ]
            },
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "设计 Workflow"
                    }
                ]
            },
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "如何优化框架"
                    }
                ]
            },
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            ]
        },
        {
            "type": "title",
            "content": {
                "title_content": [
                    {
                        "type": "text",
                        "content": "时序图神经网络"
                    }
                ],
                "level": 1
            },
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            ]
        },
        {
            "type": "title",
            "content": {
                "title_content": [
                    {
                        "type": "text",
                        "content": "1、创建数据，根据快照的方式构建图"
                    }
                ],
                "level": 1
            },
            "bbox": [
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        },
        {
            "type": "image",
            "content": {
                "image_source": {
                    "path": "images/215cfded78261b39f639e96eaae2b4b9cfafc37a05f9efefaa0359da4fcafbee.jpg"
                },
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                "image_footnote": []
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "表示节点的特征，如果没有特征用 one -hot 表示"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "计算 attention 系数"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "时间注意力"
                    }
                ]
            },
            "bbox": [
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            ]
        },
        {
            "type": "paragraph",
            "content": {
                "paragraph_content": [
                    {
                        "type": "text",
                        "content": "如何计算 loss？"
                    }
                ]
            },
            "bbox": [
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            ]
        }
    ]
]