Vector Symbolic Architectures for Context-Free Grammars

Autor: Peter beim Graben, Markus Huber, Werner Meyer, Ronald Römer, Matthias Wolff
Rok vydání: 2021
Předmět:
Zdroj: Cognitive Computation. 14:733-748
ISSN: 1866-9964
1866-9956
DOI: 10.1007/s12559-021-09974-y
Popis: 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.
Comment: 36 pages, 3 figures
Databáze: OpenAIRE
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