S. Buchholz, K. Tachibana, E.S.M.Hitzer
Optimal Learning Rates for Clifford Neurons
Proceedings of International Conference on Artificial Neural Networks 2007, Springer, New York, LNCS 4668, pp. 864-873 (2007).

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 effcient second order training methods for Clifford multilayer perceptrons in the future.

[PDF] 350 kb

[Geometric Calculus Japan index]