Analyzing the Capacity of Distributed Vector Representations to Encode Spatial Information

TL;DR

This paper investigates the limits of how much spatial information can be encoded in high-dimensional vector representations, analyzing simple and complex encoding methods through experiments to determine capacity bounds.

Contribution

It provides a systematic analysis of the information capacity of vector symbolic architectures, especially for spatial data, highlighting upper bounds for concept storage.

Findings

Identified upper bounds for concept encoding in simple superposition.

Analyzed capacity limits of convolutive power representations.

Experimental results demonstrate practical storage constraints.

Abstract

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.