Symbolic Hyperdimensional Vector

A Symbolic Hyperdimensional Vector is very-wide vector data item that represents an information unit.

• Context:
  • It can (typically) be an Integer Vector.
  • It can (typically contain thousands of numbers.
  • It can (typically) be a fundamental element in Hyperdimensional Computing where information is represented using high-dimensional vectors.
  • It can be manipulated using algebraic operations to perform tasks such as pattern recognition, natural language processing, and data mining.
  • It can allow for the encoding of complex structures and relationships in a computationally efficient manner.
  • It can be a form of Analog Representation in computational models.
  • It can be joined with other hyperdimensional vectors to form composite representations.
  • …
• Example(s):
  • Representing words in a natural language processing task as hyperdimensional vectors, where each dimension could represent semantic or syntactic properties.
  • Encoding images as hyperdimensional vectors in a pattern recognition system, where each dimension represents different features or properties of the image.
  • Using hyperdimensional vectors in a robotic mapping system to represent the spatial environment in which the robot operates.
  • …
• Counter-Example(s):
  • Using simple numerical vectors with a low number of dimensions for data representation.
  • Representing data in a relational database as records and fields instead of hyperdimensional vectors.
  • …
• See: Hyperdimensional Computing, High-Dimensional Data, Vector (Mathematics and Physics), Analog Computing, Pattern Recognition, Natural Language Processing, Data Mining.

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References

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Hyperdimensional_computing Retrieved:2023-6-12.
  • QUOTE: ... A hyperdimensional vector (hypervector) could include thousands of numbers that represent a point in a space of thousands of dimensions. Vector Symbolic Architectures is an older name for the same broad approach."

2023

• (Kleyko et al., 2023) ⇒ D. Kleyko, D. Rachkovskij, E. Osipov, A. Rahimi. (2023). “A survey on hyperdimensional computing aka vector symbolic architectures, part ii: Applications, cognitive models, and challenges". In: ACM Computing Surveys.
  • QUOTE: ... 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 …

2021

• (Thomas et al., 2021) ⇒ A. Thomas, S. Dasgupta, T. Rosing. (2021). “A theoretical perspective on hyperdimensional computing", Journal of Artificial Intelligence Research.
  • QUOTE: ... Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be…

2020

• (Ge & Parhi, 2020) ⇒ L. Ge, K.K. Parhi. (2020). “Classification using hyperdimensional computing: A review", IEEE Circuits and Systems Magazine.
  • QUOTE: ... Hyperdimensional (HD) computing is built upon its unique data type referred to as hypervectors. The dimension of these hypervectors is typically in the range of tens of thousands…

2020

• (Karunaratne et al., 2020) ⇒ G. Karunaratne, M. Le Gallo, G. Cherubini, L. Benini. (2020). “In-memory hyperdimensional computing", Nature.
  • QUOTE: ... Hyperdimensional computing is an emerging computational framework that takes inspiration from attributes of neuronal circuits including hyperdimensionality, fully distributed…

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