Distributed Representations Based on Geometric Algebra: the Continuous Model

Authors revise the concept of a distributed representation of data as well as two previously developed models: Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). A Geometric Analogue (GAc — "c" stands for continuous as opposed to its discrete version) of HRR is introduced – it employs role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space while complex data structures belong to a hierarchy of multivectors. The paper reports on a test aimed at comparison of GAc with HRR and BSC. The test is analogous to the one proposed by Tony Plate in the mid 90s. We repeat Plate’s test on GAc and compare the results with the original HRR and BSC— we concentrate on comparison of recognition percentage for the three models for comparable data size, rather than on the time taken to achieve high percentage. Results show that the best models for storing and recognizing multiple similar structures are GAc and BSC with recognition percentage highly above 90. The paper ends with remarks on perspective applications of geometric algebra to quantum algorithms.