Revisiting the Continuity of Rotation Representations in Neural Networks
This addresses robustness issues in neural networks for 3D rotation tasks, which is incremental as it builds on prior work on embeddings.
The paper identifies inherent pathological behaviors in Euler angles and unit quaternions for rotation representation in neural networks, showing they can produce wrong results for some inputs, and proposes an ensemble trick as an alternative solution.
In this paper, we provide some careful analysis of certain pathological behavior of Euler angles and unit quaternions encountered in previous works related to rotation representation in neural networks. In particular, we show that for certain problems, these two representations will provably produce completely wrong results for some inputs, and that this behavior is inherent in the topological property of the problem itself and is not caused by unsuitable network architectures or training procedures. We further show that previously proposed embeddings of $\mathrm{SO}(3)$ into higher dimensional Euclidean spaces aimed at fixing this behavior are not universally effective, due to possible symmetry in the input causing changes to the topology of the input space. We propose an ensemble trick as an alternative solution.