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  • Tensor-product versus geometric-product coding

    Publication

    - PHYSICAL REVIEW A - Year 2008

    Kodowanie przy pomocy iloczynów tensorowych, a kodowanie przy pomocy iloczynów geometrycznych. Formalizm jest zilustrowany przy pomocy paru przykładów.

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  • Hidden Tensor Structures

    Publication

    - ENTROPY - Year 2024

    Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration...

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  • Teleportation of geometric structures in 3D

    The simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state vectors) and 4 (for complex state vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: geometric analogs of states...

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  • Geometric analogue of holographic reduced representation

    Publication

    - Journal of Mathematical Psychology - Year 2009

    Holographic reduced representations (HRRs) are distributed representations of cognitive structuresbased on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of 1,one reinterprets the variable binding as a representation of the additive group of binary n-tupleswith addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directlyassociated with geometric structures....

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  • Geometric Algebra Model of Distributed Representations

    Publication

    - Year 2010

    Formalism based on GA is an alternative to distributed representation models developed so far-Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates...