Geometric Algebra Model of Distributed Representations

TL;DR

This paper introduces a geometric algebra-based model for distributed representations, replacing convolutions with geometric products, and evaluates its recognition performance and interpretability compared to existing models.

Contribution

It presents a novel geometric algebra framework for distributed representations, offering improved interpretability and a comparative analysis of recognition accuracy.

Findings

Recognition test results show competitive accuracy.

Geometric products provide intuitive visualization of concepts.

Efficiency compares favorably with existing models.

Abstract

Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.