A Fock Space Toolbox and Some Applications in Computational Cognition

Wolff, Matthias; Wirsching, Günther; Huber, Markus; Graben, Peter beim; Römer, Ronald; Schmitt, Ingo

doi:10.1007/978-3-319-99579-3_77

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…2. Moreover, we present the complete Fock space LC parse generated by FockBox which is a MATLAB toolbox provided by Wolff et al [43] as its three-dimensional projection after principal component analysis (PCA [21,23,43]) in Fig. 4 as illustration.…”

Section: Resultsmentioning

confidence: 99%

Vector symbolic architectures for context-free grammars

Graben¹,

Huber²,

Meyer³

et al. 2020

Preprint

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Section: Resultsmentioning

confidence: 99%

Vector symbolic architectures for context-free grammars

Graben¹,

Huber²,

Meyer³

et al. 2020

Preprint

Self Cite

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“…A related research direction was initiated by beim Graben and colleagues [11][12][13]421]. It concerns establishing a mathematically rigorous formalism of Tensor Product Representations using the concept of a Fock space [83].…”

Section: Automata Instructions and Schemasmentioning

confidence: 99%

“…Syntactic language processing as part of phenomenological modeling was reported in [13]. An accessible and practical entry point to the area can be found in [421].…”

Section: Automata Instructions and Schemasmentioning

confidence: 99%

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

et al. 2023

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This is Part II of the two-part comprehensive survey devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations. Holographic Reduced Representations [322, 327] is an influential HDC/VSA model that is well-known in the machine learning domain and often used to refer to the whole family. However, for the sake of consistency, we use HDC/VSA to refer to the field. Part I of this survey [223] covered foundational aspects of the field, such as the historical context leading to the development of HDC/VSA, key elements of any HDC/VSA model, known HDC/VSA models, and the transformation of input data of various types into high-dimensional vectors suitable for HDC/VSA. This second part surveys existing applications, the role of HDC/VSA in cognitive computing and architectures, as well as directions for future work. Most of the applications lie within the Machine Learning/Artificial Intelligence domain, however, we also cover other applications to provide a complete picture. The survey is written to be useful for both newcomers and practitioners.

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Vector Symbolic Architectures for Context-Free Grammars

et al. 2021

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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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A Fock Space Toolbox and Some Applications in Computational Cognition

Cited by 4 publications

References 13 publications

Vector symbolic architectures for context-free grammars

Vector symbolic architectures for context-free grammars

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

Vector Symbolic Architectures for Context-Free Grammars

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