  Quaternion valued neural networks experienced rising popularity and interest
from researchers in the last years, whereby the derivatives with respect to
quaternions needed for optimization are calculated as the sum of the partial
derivatives with respect to the real and imaginary parts. However, we can show
that product- and chain-rule does not hold with this approach. We solve this by
employing the GHRCalculus and derive quaternion backpropagation based on this.
Furthermore, we experimentally prove the functionality of the derived
quaternion backpropagation.
