Quaternion Product Units for Deep Learning on 3D Rotation Groups
This work addresses the need for rotation robustness in deep learning for 3D data, though it appears incremental as it builds on existing quaternion and neural network methods.
The paper tackled the problem of representing data on 3D rotation groups by proposing a quaternion product unit (QPU) that uses quaternion algebra and Hamilton products to disentangle rotation-invariant and rotation-equivariant features, with experiments showing benefits for rotation-robust learning tasks.
We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We prove that the representations derived by the proposed QPU can be disentangled into "rotation-invariant" features and "rotation-equivariant" features, respectively, which supports the rationality and the efficiency of the QPU in theory. We design quaternion neural networks based on our QPUs and make our models compatible with existing deep learning models. Experiments on both synthetic and real-world data show that the proposed QPU is beneficial for the learning tasks requiring rotation robustness.