Representing Sets as Summed Semantic Vectors
  Representing meaning in the form of high dimensional vectors is a common and
powerful tool in biologically inspired architectures. While the meaning of a
set of concepts can be summarized by taking a (possibly weighted) sum of their
associated vectors, this has generally been treated as a one-way operation. In
this paper we show how a technique built to aid sparse vector decomposition
allows in many cases the exact recovery of the inputs and weights to such a
sum, allowing a single vector to represent an entire set of vectors from a
dictionary. We characterize the number of vectors that can be recovered under
various conditions, and explore several ways such a tool can be used for
vector-based reasoning.
