Representing Sets as Summed Semantic Vectors
This work addresses a limitation in vector-based representations for AI and cognitive modeling by enabling two-way operations on summed vectors, which could enhance reasoning tasks in biologically inspired architectures.
The paper tackles the problem of recovering the original vectors and weights from a summed semantic vector, showing that exact recovery is possible in many cases using a sparse vector decomposition technique. It characterizes the number of recoverable vectors under various conditions and explores applications in vector-based reasoning.
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.