Quaternion Backpropagation
This solves a fundamental mathematical issue for researchers working on quaternion neural networks, though it is incremental as it builds on existing calculus frameworks.
The paper tackled the problem of incorrect gradient calculations in quaternion-valued neural networks by using the GHRCalculus to derive a correct quaternion backpropagation method, and experimentally proved its functionality.
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.