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A theory of neural computation with Clifford algebras
The present thesis introduces Clifford Algebra as a framework for neural computation. Neural computation with Clifford algebras is model-based. This principle is established by constructing CliffordExpand
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On Clifford neurons and Clifford multi-layer perceptrons
We study the framework of Clifford algebra for the design of neural architectures capable of processing different geometric entities. The benefits of this model-based computation over standardExpand
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Optimal separation of polarized signals by quaternionic neural networks
Statistical description of polarized signals is proposed in terms of proper quaternionic random processes. Within this framework, the intrinsic nature of such signals is captured well. SimulationExpand
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Optimal Learning Rates for Clifford Neurons
Neural computation in Clifford algebras, which include familiar complex numbers and quaternions as special cases, has recently become an active research field. As always, neurons are the atoms ofExpand
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Geometric Neural Networks
The representation of the external world in biological creatures appears to be defined in terms of geometry. This suggests that researchers should look for suitable mathematical systems with powerfulExpand
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On Averaging in Clifford Groups
Averaging measured data is an important issue in computer vision and robotics. Integrating the pose of an object measured with multiple cameras into a single mean pose is one such example. In manyExpand
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A Multidimensional Approach to Context-Awareness
This paper presents multidimensional context-aware principles for Enterprise Applications. The usage of information about the environment of an application, device or its user can enhance theExpand
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Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer
Phase sensitivity and thermal dephasing in coherent electron transport in quasi-one-dimensional (1D) waveguide rings of an asymmetric four-terminal geometry are studied by magnetotransportExpand
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Polarized Signal Classification by Complex and quaternionic Multi-Layer Perceptrons
For polarized signals, which arise in many application fields, a statistical framework in terms of quaternionic random processes is proposed. Based on it, the ability of real-, complex- andExpand
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On the decision boundaries of hyperbolic neurons
In this paper, the basic properties, especially decision boundary, of the hyperbolic neurons used in the hyperbolic neural networks are investigated. And also, a non-split hyperbolic sigmoidExpand
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