61 research outputs found
Geometric Algebra Model of Distributed Representations
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 recognition test results
using both inner product and a clipped version of matrix representation. The
influence of accidental blade equality on recognition is also studied. Finally,
the efficiency of the GA model is compared to that of previously developed
models.Comment: 30 pages, 19 figure
Cartoon Computation: Quantum-like computing without quantum mechanics
We present a computational framework based on geometric structures. No
quantum mechanics is involved, and yet the algorithms perform tasks analogous
to quantum computation. Tensor products and entangled states are not needed --
they are replaced by sets of basic shapes. To test the formalism we solve in
geometric terms the Deutsch-Jozsa problem, historically the first example that
demonstrated the potential power of quantum computation. Each step of the
algorithm has a clear geometric interpetation and allows for a cartoon
representation.Comment: version accepted in J. Phys.A (Letter to the Editor
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