DeepAI AI Chat
Log In Sign Up

Representing Sets as Summed Semantic Vectors

by   Douglas Summers-Stay, et al.
Department of Defense

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.


page 1

page 2

page 3

page 4


From positional representation of numbers to positional representation of vectors

To represent real m-dimensional vectors, a positional vector system give...

High-Dimensional Vector Semantics

In this paper we explore the "vector semantics" problem from the perspec...

Capacity Analysis of Vector Symbolic Architectures

Hyperdimensional computing (HDC) is a biologically-inspired framework wh...

Context-theoretic Semantics for Natural Language: an Algebraic Framework

Techniques in which words are represented as vectors have proved useful ...

Deductive and Analogical Reasoning on a Semantically Embedded Knowledge Graph

Representing knowledge as high-dimensional vectors in a continuous seman...

Quantum Inspired Word Representation and Computation

Word meaning has different aspects, while the existing word representati...

Mechanism Design for Maximum Vectors

We consider the Maximum Vectors problem in a strategic setting. In the c...