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Traversing Knowledge Graphs in Vector Space(2015)

huyi / July 2022

• 0. Abstract
  • ? 解决什么问题
  • ? recent models
  • ? recent models的问题
  • ? 这篇文章干了什么
• 1. Introduction
  • ? 模型能做到什么
• 2. Task
  • 一些定义：
  • Knowledge base completion
• 3. Compositionalization
  • 3.1 Motivating Example
  • 3.2 General technique
  • 3.3 Compositional training

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这篇文章主要讲的是一个针对path query的形式化的模型，不是很知道必要性在哪里

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0. Abstract

? 解决什么问题

answer compositional questions

? recent models

Recent models for knowledge base completion impute missing facts by embedding knowledge graphs in vector spaces 这篇文章说明了这些model可以用来answer path queries

? recent models的问题

answer path queries时，suffer from cascading errors

? 这篇文章干了什么

a new “compositional” training objective, which dramatically improves all models’ ability to answer path queries

1. Introduction

? 模型能做到什么

• compositional training enables us to answer path queries up to at least length 5
• improves upon state-of-the-art performance for knowledge base completion

2. Task

一些定义：

• path query: q有一个 anchor entity：s，然后还有一系列的转换关系$p=(r_1,…,r_k)$
• The answer or denotation of the query,$[![q]!]$: the set of all entities that can be reached from s by traversing p
• candidate answers $\mathcal{C}(q)$: 有一个$r_k$（p中最后一个relation）连到它的entity的集合
• incorrect answers $\mathcal{N}(q)$: [\mathcal{N}(q)=\mathcal{C}(q)\setminus[![q]!]]

Knowledge base completion

• Knowledge base completion (KBC)： task of predicting whether a given edge (s, r, t) belongs in the graph or not.
  • 可以看作一个path query：q = s / r，有一个candidate answer t
  显然这边的candidate跟上面说的candidate定义就不一样了

3. Compositionalization

–> compositionalize existing KBC models to answer path queries

3.1 Motivating Example

• 对每个entity，learn一个$x_e\in\mathbb{R}^d$
• 对每个relation，learn一个d*d维的矩阵$W_r$
• 评估：t是不是 query：s/r 的 answer

3.2 General technique

$\mathbb{M}$是membership operator，检验了$x_t$是不是需要求的query的answer。$\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}^d$

$\mathbb{T}$是traversal operator，$\mathbb{R}^d\rightarrow\mathbb{R}^d$

3.3 Compositional training

minimize the following max-margin objective