tap@ai.toronto.edu (Tony Plate) (05/25/91)
The following tech-report is available by ftp from the neuroprose archive at cheops.cis.ohio-state.edu. It is an expanded version of the paper "Holographic Reduced Representations: Convolution Algebra for Compositional Distributed Representations" which is to appear in the Proceedings of the 12th International Joint Conference on Artificial Intelligence (1991). Holographic Reduced Representations Tony Plate Department of Computer Science, University of Toronto Toronto, Ontario, Canada, M5S 1A4 tap@ai.utoronto.ca Technical Report CRG-TR-91-1 May 1991 Abstract A solution to the problem of representing compositional structure using distributed representations is described. The method uses circular convolution to associate items, which are represented by vectors. Arbitrary variable bindings, short sequences of various lengths, frames, and reduced representations can be compressed into a fixed width vector. These representations are items in their own right, and can be used in constructing compositional struc- tures. The noisy reconstructions given by convolution memories can be cleaned up by using a separate associative memory that has good reconstructive properties. Three appendices are attached. The first discusses some of the mathematical properties of convolution memories. The second gives a more intuitive explanation of convolution memories and explores the relationship between approximate and exact inverses to the convolution operation. The third contains examples of cal- culations of the capacities and recall probabilities for convolution memories. Here's what to do to get the file from neuroprose. unix> ftp cheops.cis.ohio-state.edu (or 128.146.8.62) Name: anonymous Password: neuron ftp> cd pub/neuroprose ftp> binary ftp> get plate.hrr.ps.Z ftp> quit unix> uncompress plate.hrr.ps.Z unix> lpr plate.hrr.ps (or however you print postscript) ---------------- Tony Plate ---------------------- tap@ai.utoronto.ca ----- Department of Computer Science, University of Toronto, 10 Kings College Road, Toronto, Ontario, CANADA M5S 1A4 ----------------------------------------------------------------------------