论文标题
矢量符号架构无上下文语法
Vector symbolic architectures for context-free grammars
论文作者
论文摘要
背景 /简介。向量符号体系结构（VSA）是符号数据高维表示的可行方法，例如文档，句法结构或语义框架。方法。我们提出了一个严格的数学框架，用于代表Fock空间中无上下文语法（CFG）的短语结构树和解析树，即无限二维Hilbert空间在量子场理论中使用。我们通过术语代数定义了CFG的新型正常形式。我们使用最近开发的软件工具箱（称为Fockbox），为CFG左角（LC）Parser构建的树木构建了Fock空间表示形式。结果。我们证明了FOCK空间中CFG项代数的通用定理，并通过LC Parser态的低维主成分投影说明了我们的发现。结论。我们的方法可以通过高维深神经计算来利用VSA的开发来解释人工智能（XAI）。这对于改善机器学习中VSA的认知用户界面和其他应用可能具有重要意义。
Background / introduction. Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. Methods. We present a rigorous mathematical framework for the representation of phrase structure trees and parse trees of context-free grammars (CFG) in Fock space, i.e. infinite-dimensional Hilbert space as being used in quantum field theory. We define a novel normal form for CFG by means of term algebras. Using a recently developed software toolbox, called FockBox, we construct Fock space representations for the trees built up by a CFG left-corner (LC) parser. Results. We prove a universal representation theorem for CFG term algebras in Fock space and illustrate our findings through a low-dimensional principal component projection of the LC parser states. Conclusions. Our approach could leverage the development of VSA for explainable artificial intelligence (XAI) by means of hyperdimensional deep neural computation. It could be of significance for the improvement of cognitive user interfaces and other applications of VSA in machine learning.
