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题目: Integrating Deep Learning with Logic Fusion for Information Extraction

摘要:

信息抽取(Information extraction, IE)旨在从输入文本中产生结构化的信息,例如命名实体识别和关系抽取。通过特征工程或深度学习为IE提出了各种尝试。然而,他们中的大多数人并没有将任务本身所固有的复杂关系联系起来,而这一点已被证明是特别重要的。例如,两个实体之间的关系高度依赖于它们的实体类型。这些依赖关系可以看作是复杂的约束,可以有效地表示为逻辑规则。为了将这种逻辑推理能力与深度神经网络的学习能力相结合,我们提出将一阶逻辑形式的逻辑知识集成到深度学习系统中,以端到端方式联合训练。该集成框架通过逻辑规则对神经输出进行知识正则化增强,同时根据训练数据的特点更新逻辑规则的权值。我们证明了该模型在多个IE任务上的有效性和泛化性。

作者:

Sinno Jialin Pan是南洋理工大学计算机科学与工程学院院长兼副教授,研究方向是迁移学习、数据挖掘、人工智能、机器学习。

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Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characterization results in well-known subclasses of chordal graphs such as interval graphs or split graphs. A typical example that behaves computationally different in subclasses of chordal graph is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a graph $G=(V,E)$ and a set $S\subseteq V$, SFVS asks for a minimum set of vertices that intersects all cycles containing a vertex of $S$. SFVS is known to be polynomial-time solvable on interval graphs, whereas SFVS remains \NP-complete on split graphs and, consequently, on chordal graphs. Towards a better understanding of the complexity of SFVS on subclasses of chordal graphs, we exploit structural properties of a tree model in order to cope with the hardness of SFVS. Here we consider variants of the \emph{leafage} that measures the minimum number of leaves in a tree model. We show that SFVS can be solved in polynomial time for every chordal graph with bounded leafage. In particular, given a chordal graph on $n$ vertices with leafage $\ell$, we provide an algorithm for SFVS with running time $n^{O(\ell)}$. Pushing further our positive result, it is natural to consider a slight generalization of leafage, the \emph{vertex leafage}, which measures the smallest number among the maximum number of leaves of all subtrees in a tree model. However, we show that it is unlikely to obtain a similar result, as we prove that SFVS remains \NP-complete on undirected path graphs, i.e., graphs having vertex leafage at most two. Moreover, we strengthen previously-known polynomial-time algorithm for SFVS on directed path graphs that form a proper subclass of undirected path graphs and graphs of mim-width one.

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Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characterization results in well-known subclasses of chordal graphs such as interval graphs or split graphs. A typical example that behaves computationally different in subclasses of chordal graph is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a graph $G=(V,E)$ and a set $S\subseteq V$, SFVS asks for a minimum set of vertices that intersects all cycles containing a vertex of $S$. SFVS is known to be polynomial-time solvable on interval graphs, whereas SFVS remains \NP-complete on split graphs and, consequently, on chordal graphs. Towards a better understanding of the complexity of SFVS on subclasses of chordal graphs, we exploit structural properties of a tree model in order to cope with the hardness of SFVS. Here we consider variants of the \emph{leafage} that measures the minimum number of leaves in a tree model. We show that SFVS can be solved in polynomial time for every chordal graph with bounded leafage. In particular, given a chordal graph on $n$ vertices with leafage $\ell$, we provide an algorithm for SFVS with running time $n^{O(\ell)}$. Pushing further our positive result, it is natural to consider a slight generalization of leafage, the \emph{vertex leafage}, which measures the smallest number among the maximum number of leaves of all subtrees in a tree model. However, we show that it is unlikely to obtain a similar result, as we prove that SFVS remains \NP-complete on undirected path graphs, i.e., graphs having vertex leafage at most two. Moreover, we strengthen previously-known polynomial-time algorithm for SFVS on directed path graphs that form a proper subclass of undirected path graphs and graphs of mim-width one.

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