S. Buchholz, E.S.M. Hitzer, K. Tachibana
Coordinate independent update formulas for versor Clifford neurons
Proceedings of Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys., 17-21 Sep. 2008, Nagoya, Japan, pp. 814 - 819 (2008).

Abstract: We study the optimization of neural networks with Clifford geometric algebra versor and spinor nodes. For that purpose important multivector calculus results are introduced. Such nodes are generalizations of real, complex and quaternion spinor nodes. In particular we consider nodes that can learn all proper and improper Euclidean transformations with so-called conformal versors. Thus a single node can correctly compute full 3D screws and rotoinversions with off-origin axis and offorigin points of inversion. The latter is a unique property of our proposed versor neuron. Computing inversions by ordinary real-valued networks is not easily possible due to its nonlinear nature. Simulation on learning inversions illustrating these facts are provided in the paper.

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