Optimal learning rates for clifford neurons

Authors:
Sven Buchholz;Kanta Tachibana;Eckhard M. S. Hitzer
Affiliations:
Institute of Computer Science, University of Kiel, Germany;Graduate School of Engineering, Nagoya University, Japan;Department of Applied Physics, University of Fukui, Japan
Venue:
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Year:
2007

Citing 4
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Learning in linear neural networks: a survey

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On Clifford neurons and Clifford multi-layer perceptrons

Neural Networks

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Abstract

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 of computation. The paper provides a general notion for the Hessian matrix of Clifford neurons of an arbitrary algebra. This new result on the dynamics of Clifford neurons then allows the computation of optimal learning rates. A thorough discussion of error surfaces together with simulation results for different neurons is also provided. The presented contents should give rise to very efficient second-order training methods for Clifford Multilayer perceptrons in the future.