Determine Associative Strength Attributes of Computational Values Represented as Points in Hyperdimensional Space Using Hypervectors

Determine Associative Strength Attributes of Computational Values Represented as Points in Hyperdimensional Space Using Hypervectors

It is possible to determine associative strength attributes among multiple computational values represented as points in hyperdimensional space using hypervectors. There are a few key aspects of hyperdimensional computing that enable this:

  • Similarity measurement: Hypervectors can be compared for similarity using distance metrics like cosine similarity or Hamming distance[1]. This allows quantifying how closely associated different hypervectors are.
  • Binding operation: The binding operation (typically element-wise multiplication) can be used to associate or bind multiple hypervectors together[1]. The strength of this binding reflects the associative strength.
  • Bundling operation: The bundling or superposition operation (typically vector addition) combines multiple hypervectors while preserving similarity to the constituents[1]. This allows representing sets or combinations of concepts.
  • Distributed representation: Information in hypervectors is distributed across all dimensions holographically. This allows complex associations to be captured.
  • High dimensionality: The high-dimensional space provides a vast capacity for representing nuanced relationships and associations.
  • Vector algebra: Operations like addition, multiplication and permutation on hypervectors enable flexible ways of combining information and computing associations[4].
  • Geometric interpretation: Hypervectors can be viewed as points in a high-dimensional geometric space, allowing geometric intuitions to be applied.

By leveraging these properties, it's possible to:

  • Encode multiple computational values as separate hypervectors
  • Combine them using binding* and bundling* operations

* For more information on binding and bundling operations in hyperdimensional computing, please see: ??Three Common Operations of Hyperdimensional Computing (HDC)

  • Measure similarities between the resulting hypervectors
  • Interpret the similarities as associative strengths

This allows capturing complex associative relationships between multiple elements in an abstract geometric construct represented by the high-dimensional space. The associative strengths emerge from the interactions and similarities of the hypervectors in this space.

Hypothetical Example

It is possible to determine associative strength attributes among multiple computational values represented as points in hyperdimensional space using hypervectors. Let's see a hypothetical example to illustrate this concept:

Suppose we are working with a hyperdimensional space of 10,000 dimensions to represent different attributes of cars. We could create hypervectors for various car features like:

  • SEDAN (representing the car type)
  • RED (representing color)
  • FAST (representing speed)
  • LUXURY (representing quality)

Each of these would be a 10,000-dimensional hypervector with pseudo-random values.

Now, let's say we want to represent a specific car - a red luxury sedan. We can combine these hypervectors using operations like binding (typically element-wise multiplication) to create a new hypervector:

CAR = SEDAN RED LUXURY

This resulting CAR hypervector represents a point in our 10,000-dimensional space.

To determine associative strengths between different cars or car attributes, we can use similarity measures like cosine similarity or Hamming distance between their respective hypervectors[1]. For example:

  • We could compare our CAR hypervector to a SPORTS_CAR hypervector to see how similar they are.
  • We could compare CAR to just the RED hypervector to see how strongly the "redness" attribute is associated with this particular car representation.

The closer these hypervectors are in the high-dimensional space (i.e., the higher their similarity measure), the stronger their associative strength.

Furthermore, we can use operations like bundling (typically vector addition) to represent sets or combinations of concepts. For instance, we could create a hypervector representing "all luxury vehicles in our database" by adding together the hypervectors of individual luxury cars.

This example demonstrates how hyperdimensional computing can capture complex associative relationships between multiple elements in an abstract geometric construct represented by the high-dimensional space. The associative strengths emerge from the interactions and similarities of the hypervectors in this space.

This is a hypothetical example, but it illustrates the principles that could be used in real-world applications of hyperdimensional computing (HDC) for tasks like classification, pattern recognition, and reasoning.

About the author:

John has authored tech content for MICROSOFT, GOOGLE (Taiwan), INTEL, HITACHI, and YAHOO! His recent work includes Research and Technical Writing for Zscale Labs?, covering highly advanced Neuro-Symbolic AI (NSAI) and Hyperdimensional Computing (HDC). John speaks intermediate Mandarin after living for 10 years in Taiwan, Singapore and China.

John now advances his knowledge through research covering AI fused with Quantum tech - with a keen interest in Toroid electromagnetic (EM) field topology for Computational Value Assignment, Adaptive Neuromorphic / Neuro-Symbolic Computing, and Hyper-Dimensional Computing (HDC) on Abstract Geometric Constructs.

John's LinkedIn: https://www.dhirubhai.net/in/john-melendez-quantum/

Citations:

https://moimani.weebly.com/brain-inspired-computing.html

https://par.nsf.gov/servlets/purl/10334215

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9363880/

https://arxiv.org/abs/2004.11204

https://www.quantamagazine.org/a-new-approach-to-computation-reimagines-artificial-intelligence-20230413/

https://www.nsf.gov/awardsearch/showAward?AWD_ID=2147640&HistoricalAwards=false

https://github.com/HyperdimensionalComputing/collection

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9775867/

https://en.wikipedia.org/wiki/Hyperdimensional_computing

https://moimani.weebly.com/brain-inspired-computing.html

https://github.com/HyperdimensionalComputing/collection

https://www.quantamagazine.org/a-new-approach-to-computation-reimagines-artificial-intelligence-20230413/

https://research.ibm.com/blog/in-memory-hyperdimensional-computing

https://en.wikipedia.org/wiki/Hyperdimensional_computing

https://www.wired.com/story/hyperdimensional-computing-reimagines-artificial-intelligence/

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