Fast Quaternion Product Units for Learning Disentangled Representations in [Formula: see text]

Area of Science:

• Computer Vision
• Machine Learning
• Geometric Deep Learning

Background:

• Real-world 3D data (point clouds, skeletons) exist on 3D rotation groups.
• Existing neural networks struggle with 3D rotation data due to Euclidean space limitations, leading to performance issues.
• This mismatch hinders effective learning on 3D geometric tasks.

Purpose of the Study:

• To propose a novel neural network component for effectively processing 3D rotation data.
• To address the limitations of Euclidean-based neural networks in handling 3D rotation groups.
• To improve the performance and robustness of deep learning models on 3D tasks.

Main Methods:

• Introduced the Quaternion Product Unit (QPU), a non-real neuron model utilizing quaternion algebra for 3D rotation data.
• Developed a fast QPU (fQPU) with reduced computational complexity (O(logN)) using tree-structured indexing and parallel computing.
• Constructed Quaternion Neural Networks (QNNs), including QMLP and QMP, leveraging the fQPU module.

Main Results:

• QPUs mathematically preserve the SO(3) structure of 3D rotation data during inference.
• QNNs disentangle representations into rotation-invariant and rotation-equivariant features.
• Experiments show QNNs outperform real-valued models, especially in rotation-robust scenarios.

Conclusions:

• The proposed QPU and resulting QNNs offer a principled approach to learning on 3D rotation groups.
• QNNs demonstrate superior performance and robustness for 3D point cloud and skeleton data processing.
• This work provides a foundation for more effective deep learning on geometric data.