Abstract
AbstractVector 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.
Funder
Brandenburgische TU Cottbus-Senftenberg
Publisher
Springer Science and Business Media LLC
Subject
Cognitive Neuroscience,Computer Science Applications,Computer Vision and Pattern Recognition
Reference89 articles.
1. Shannon CE. Computers and automata. Proceedings of the Institute of Radio Engineering. 1953;41(10):1234–41.
2. von Uexküll J. The theory of meaning. Semiotica. 1982;4(1):25–79.
3. Fuster JM. Upper processing stages of the perception-action cycle. Trends in Cognitve Science. 2004;8(4):143–5.
4. Haykin S. Cognitive Dynamic Systems. Cambridge University Press, 2012.
5. Architectures, and Hardware;N Tishby,2011
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献