## 37 Citations

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

- Computer Science2011 Federated Conference on Computer Science and Information Systems (FedCSIS)
- 2011

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

- Computer ScienceInformatica
- 2011

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

- MathematicsInformatica
- 2011

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

- Computer ScienceGeometric 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

- Mathematics2011 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

- Computer ScienceACM Computing Surveys
- 2022

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

- MathematicsJ. Log. Lang. Inf.
- 2012

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

- Computer ScienceAAAI 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

- Computer ScienceArXiv
- 2022

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

- Computer ScienceCognitive Computation
- 2013

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.

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- Computer ScienceAAAI Technical Report
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