Vector symbolic architectures for context-free grammars

Graben, Peter beim; Huber, Markus Q.; Meyer, W.; Römer, Ronald; Wolff, Matthias

doi:10.48550/arxiv.2003.05171

Cited by 2 publications

(3 citation statements)

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“…There is ample work demonstrating that VSA possesses a rich computational expressiveness, from the functionality of neural networks , [Kleyko et al, 2020a], , [Frady et al, 2018b] to machine learning tasks [Recchia et al, 2015], [Rasanen and Saarinen, 2016], , [Rahimi et al, 2019] and cognitive modeling [Slipchenko and Rachkovskij, 2009], [Rachkovskij et al, 2013], [Eliasmith, 2013], [Rachkovskij and Slipchenko, 2012], [Emruli et al, 2013], [Kleyko et al, 2015]. Further, VSA can express conventional algorithms, for example, finite state automata , [Yerxa et al, 2018] and context-free grammars [beim Graben et al, 2020].…”

Section: Motivationmentioning

confidence: 99%

“…Note that the primitives for stacks and finite-state automata can be combined to create such computational models as deterministic pushdown automata or stack machines; see, e.g., [Yerxa et al, 2018] for a sketch of a stack machine operating with hypervectors. An alternative representation for pushdown automata and context-free grammars has been recently presented in [beim Graben et al, 2020].…”

Section: ) Binary Treesmentioning

confidence: 99%

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Vector Symbolic Architectures as a Computing Framework for Nanoscale Hardware

Kleyko¹,

Davies²,

Frady³

et al. 2021

Preprint

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This article reviews recent progress in the development of the computing framework Vector Symbolic Architectures (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, nanoscale hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the ring-like algebraic structure of Vector Symbolic Architectures offers simple but powerful operations on highdimensional vectors that can support all data structures and manipulations relevant in modern computing. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. This latter property opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. Vector Symbolic Architectures are Turing complete, as we show, and we see them acting as a framework for computing with distributed representations in myriad AI settings. This paper serves as a reference for computer architects by illustrating techniques and philosophy of VSAs for distributed computing and relevance to emerging computing hardware, such as neuromorphic computing.

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Section: Motivationmentioning

confidence: 99%

Section: ) Binary Treesmentioning

confidence: 99%

Vector Symbolic Architectures as a Computing Framework for Nanoscale Hardware

Kleyko¹,

Davies²,

Frady³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…Transformations of pushdown automata and context-free grammars to HVs have been presented in [beim Graben et al, 2020]. A proposal for implementing Turing machines and cellular automata was given in [Kleyko et al, 2021a].…”

Section: Deterministic Behavior With Hdc/vsamentioning

confidence: 99%

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

Kleyko,

Rachkovskij,

Osipov

et al. 2021

Preprint

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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 [Plate, 1995], [Plate, 2003] 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 area.Part I of this survey [Kleyko et al., 2021c] covered foundational aspects of the area, such as historical context leading to the development of HDC/VSA, key elements of any HDC/VSA model, known HDC/VSA models, and transforming 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 thorough picture. The survey is written to be useful for both newcomers and practitioners.

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Vector symbolic architectures for context-free grammars

Cited by 2 publications

References 40 publications

Vector Symbolic Architectures as a Computing Framework for Nanoscale Hardware

Vector Symbolic Architectures as a Computing Framework for Nanoscale Hardware

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

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