Capacity Analysis of Vector Symbolic Architectures

Understand

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them.

• The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA).
• While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open.
• We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors.