Geoffrey Hinton's idea of "capsules", which I don't really know anything concrete about, tries to address the recognition of objects subject to rotations, etc.

Geoffrey Hinton's idea of "capsules", which I don't really know anything concrete about, tries to address the recognition of objects subject to rotations, etc. That's a topological/structural strategy within the neural network, though, so quite removed from an idea like quaternions. It's worth observing that what distinguishes complex numbers from 2-vectors like (x,y) is that there's a multiplication rule that corresponds to rotation around the origin. Similarly with quaternions. But you can also just use them as glorified vectors of 2 or 4 elements. See this https://www.technologyreview.com/s/610278/why-even-a-moths-brain-is-smarter-than-an-ai/ https://www.technologyreview.com/s/610278/why-even-a-moths-b... for a recent interesting finding on dimensionality.