Geometric Analogue of Holographic Reduced Representation

Details Geometric Analogue of Holographic Reduced Representation Geometric Analogue of Holographic Reduced Representation

2007-10-15

arxiv.org/abs/0710.2611v2

Journal of Mathematical Psychology 53, 389-398 (2009)

Computer Science

Artificial Intelligence

typos in eqs. (57-58) are corrected

Scientific paper

Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two different representations of $Z_2\times...\times Z_2$ (the additive group of binary $n$-tuples with addition modulo 2). As opposed to standard HRR, variable binding performed by means of geometric product allows for computing exact inverses of all nonzero vectors, a procedure even simpler than approximate inverses employed in HRR. The formal structure of the new reduced representation is analogous to cartoon computation, a geometric analogue of quantum computation.

Affiliated with

Also associated with

No associations

Rating

Geometric Analogue of Holographic Reduced Representation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric Analogue of Holographic Reduced Representation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Analogue of Holographic Reduced Representation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-125855