This two-part comprehensive survey is 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 distributed vector representations. Notable models in the HDC/VSA family are Tensor Product Representations, Holographic Reduced Representations, Multiply-Add-Permute, Binary Spatter Codes, and Sparse Binary Distributed Representations but there are other models too. HDC/VSA is a highly interdisciplinary field with connections to computer science, electrical engineering, artificial intelligence, mathematics, and cognitive science. This fact makes it challenging to create a thorough overview of the field. However, due to a surge of new researchers joining the field in recent years, the necessity for a comprehensive survey of the field has become extremely important. Therefore, amongst other aspects of the field, this Part I surveys important aspects such as: known computational models of HDC/VSA and transformations of various input data types to high-dimensional distributed representations. Part II of this survey [ 84 ] is devoted to applications, cognitive computing and architectures, as well as directions for future work. The survey is written to be useful for both newcomers and practitioners.

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 [ 321 , 326 ] 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 [ 222 ] 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.

Hyperdimensional (HD) computing is a promising paradigm for future intelligent electronic appliances operating at low power. This paper discusses tradeoffs of selecting parameters of binary HD representations when applied to pattern recognition tasks. Particular design choices include density of representations and strategies for mapping data from the original representation. It is demonstrated that for the considered pattern recognition tasks (using synthetic and real-world data) both sparse and dense representations behave nearly identically. This paper also discusses implementation peculiarities which may favor one type of representations over the other. Finally, the capacity of representations of various densities is discussed.

Distributed representations were often criticized as inappropriate for encoding of data with a complex structure. However Plate's holographic reduced representations and Kanerva's binary spatter codes are recent schemes that allow on-the-fly encoding of nested compositional structures by real-valued or dense binary vectors of fixed dimensionality. In this article we consider procedures of the context-dependent thinning developed for representation of complex hierarchical items in the architecture of associative-projective neural networks. These procedures provide binding of items represented by sparse binary codevectors (with low probability of 1s). Such an encoding is biologically plausible and allows a high storage capacity of distributed associative memory where the codevectors may be stored. In contrast to known binding procedures, context-dependent thinning preserves the same low density (or sparseness) of the bound codevector for a varied number of component codevectors. Besides, a bound codevector is similar not only to another one with similar component codevectors (as in other schemes) but also to the component codevectors themselves. This allows the similarity of structures to be estimated by the overlap of their codevectors, without retrieval of the component codevectors. This also allows easy retrieval of the component codevectors. Examples of algorithmic and neural network implementations of the thinning procedures are considered. We also present representation examples for various types of nested structured data (propositions using role filler and predicate arguments schemes, trees, and directed acyclic graphs) using sparse codevectors of fixed dimension. Such representations may provide a fruitful alternative to the symbolic representations of traditional artificial intelligence as well as to the localist and microfeature-based connectionist representations.