Interpretable Rotation-Equivariant Quaternion Neural Networks for 3D Point Cloud Processing

Abstract

This study proposes a set of generic rules to revise existing neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs), in order to make feature representations of neural networks to be rotation-equivariant and permutation-invariant. Rotation equivariance of features means that the feature computed on a rotated input point cloud is the same as applying the same rotation transformation to the feature computed on the original input point cloud. We find that the rotation-equivariance of features is naturally satisfied, if a neural network uses quaternion features. Interestingly, we prove that such a network revision also makes gradients of features in the REQNN to be rotation-equivariant w.r.t. inputs, and the training of the REQNN to be rotation-invariant w.r.t. inputs. Besides, permutation-invariance examines whether the intermediate-layer features are invariant, when we reorder input points. We also evaluate the stability of knowledge representations of REQNNs, and the robustness of REQNNs to adversarial rotation attacks. Experiments have shown that REQNNs outperform traditional neural networks in both terms of classification accuracy and robustness on rotated testing samples.