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Vector Symbolic Architectures for Context-Free Grammars

  • Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. 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. 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 state. Our approach could leverage the development of VSA for explainable artificial intelligence (XAI) by means of hyperdimensional deep neural computation.

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Metadaten
Author: Peter Beim Graben, Markus Huber, Werner Meyer, Ronald RömerGND, Matthias WolffORCiD
DOI:https://doi.org/10.1007/s12559-021-09974-y
ISSN:1866-9964
Title of the source (English):Cognitive Computation
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2021
Volume/Year:14
Issue number:2
First Page:733
Last Page:748
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Kommunikationstechnik
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