Analyzing the Capacity of Distributed Vector Representations to Encode
  Spatial Information
  Vector Symbolic Architectures belong to a family of related cognitive
modeling approaches that encode symbols and structures in high-dimensional
vectors. Similar to human subjects, whose capacity to process and store
information or concepts in short-term memory is subject to numerical
restrictions,the capacity of information that can be encoded in such vector
representations is limited and one way of modeling the numerical restrictions
to cognition. In this paper, we analyze these limits regarding information
capacity of distributed representations. We focus our analysis on simple
superposition and more complex, structured representations involving
convolutive powers to encode spatial information. In two experiments, we find
upper bounds for the number of concepts that can effectively be stored in a
single vector.
