Geometric Analogue of Holographic Reduced Representation

  title={Geometric Analogue of Holographic Reduced Representation},
  author={Diederik Aerts and Marek Czachor and Bart De Moor},

A comparison of geometric analogues of holographic reduced representations, original holographic reduced representations and binary spatter codes

Results show that the best models for storing and recognizing multiple similar statements are GAc and Binary Spatter Codes with recognition percentage highly above 90.

Distributed Representations Based on Geometric Algebra: the Continuous Model

A Geometric Analogue of HRR is introduced – it employs role-filler binding based on geometric products and shows that the best models for storing and recognizing multiple similar structures are GAc and BSC with recognition percentage highly above 90.

Experiments on Preserving Pieces of Information in a Given Order in Holographic Reduced Representations and the Continuous Geometric Algebra Model

The property of GA c and HRR studied here is the ability to store pieces of information in a given order by means of trajectory associat ion, and results of three experiments are described.

Geometric Algebra Model of Distributed Representations

  • A. Patyk
  • Computer Science
    Geometric Algebra Computing
  • 2010
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, which shows the influence of accidental blade equality on recognition.

Preserivng pieces of information in a given order in HRR and GAc

  • Agnieszka Patyk-Lonska
  • Mathematics
    2011 Federated Conference on Computer Science and Information Systems (FedCSIS)
  • 2011
A property of GAc and HRR studied here is the ability to store pieces of information in a given order by means of trajectory association, which describes results of an experiment finding the alignment of items in a sequence without the precise knowledge of trajectory vectors.

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations

This two-part comprehensive survey is devoted to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations.

Geometric Representations for Minimalist Grammars

It is proved that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space and harmony is proposed, i.e. the distance of an intermediate processing step from the final well-formed state in represented space, as a measure of processing complexity.

Semantic Oscillations: Encoding Context and Structure in Complex Valued Holographic Vectors

  • Lance De VineP. Bruza
  • Computer Science
    AAAI Fall Symposium: Quantum Informatics for Cognitive, Social, and Semantic Processes
  • 2010
This work describes a novel and efficient approach to computing semantic spaces via the use of complex valued vector representations, and reports on the practical implementation of the proposed method and some associated experiments.

Optimal quadratic binding for relational reasoning in vector symbolic neural architectures

A new class of binding matrices based on a matrix representation of octonion algebra, an eight-dimensional extension of complex numbers, enable a more accurate unbinding than previously known methods when a small number of pairs are present and show that when there are a large number of bound pairs, a random quadratic binding performs as well as theoctonion and previously-proposed binding methods.

Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

The model can learn analogical mappings of generic two-place relationships, and the error probabilities for recall and generalization are calculated and indicate that the optimal size of the memory scales with the number of different mapping examples learned and that the sparseness of theMemory is important.



Teleportation of geometric structures in 3D

This work discusses all the elementary ingredients of the geometric version of the quantum teleportation algorithm: geometric analogs of states and controlled Pauli gates.

Holographic reduced representations

  • T. Plate
  • Computer Science
    IEEE Trans. Neural Networks
  • 1995
This paper describes a method for representing more complex compositional structure in distributed representations that uses circular convolution to associate items, which are represented by vectors.

Geometry and Meaning

What the "Geometry of Meaning" provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded.

New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation

A coordinate-free approach to the geometry of computer vision problems is discussed, believing the present formulation to be the only one in which least-squares estimates of the motion and structure are derived simultaneously using analytic derivatives.

A composite holographic associative recall model

A highly interactive model of association formation, storage, and retrieval that is applied to several well-known results, yielding several new predictions about errors in single-trial cued recall that depend on similarity relations among the to-be-remembered items, and also about the efficacy of extralist cues.

Representing word meaning and order information in a composite holographic lexicon.

A computational model that builds a holographic lexicon representing both word meaning and word order from unsupervised experience with natural language demonstrates that a broad range of psychological data can be accounted for directly from the structure of lexical representations learned in this way, without the need for complexity to be built into either the processing mechanisms or the representations.

Geometric Ordering of Concepts, Logical Disjunction, and Learning by Induction

Some of the characteristic properties of such broad non-distributive composition operations and their applications to learning algorithms and classification structures are described.

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5.

Correlation Matrix Memories

  • T. Kohonen
  • Computer Science
    IEEE Transactions on Computers
  • 1972
A new model for associative memory, based on a correlation matrix, is suggested, in which any part of the memorized information can be used as a key and the memories are selective with respect to accumulated data.

Geometric neural computing

It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs).