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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