等变映射
四元数
点云
人工神经网络
旋转(数学)
不变(物理)
稳健性(进化)
人工智能
计算机科学
算法
模式识别(心理学)
数学
纯数学
几何学
生物化学
化学
数学物理
基因
作者
Wen Zhong Shen,Zhihua Wei,Qihan Ren,Binbin Zhang,Shikun Huang,Jiaqi Fan,Quanshi Zhang
标识
DOI:10.1109/tpami.2023.3346383
摘要
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.
科研通智能强力驱动
Strongly Powered by AbleSci AI