Equivariant networks have been adopted in many 3-D learning areas. Here we identify a fundamental limitation of these networks: their ambiguity to symmetries. Equivariant networks cannot complete symmetry-dependent tasks like segmenting a left-right symmetric object into its left and right sides. We tackle this problem by adding components that resolve symmetry ambiguities while preserving rotational equivariance. We present OAVNN: Orientation Aware Vector Neuron Network, an extension of the Vector Neuron Network. OAVNN is a rotation equivariant network that is robust to planar symmetric inputs. Our network consists of three key components. 1) We introduce an algorithm to calculate symmetry detecting features. 2) We create a symmetry-sensitive orientation aware linear layer. 3) We construct an attention mechanism that relates directional information across points. We evaluate the network using left-right segmentation and find that the network quickly obtains accurate segmentations. We hope this work motivates investigations on the expressivity of equivariant networks on symmetric objects.

本文研究了等变网络在处理对称任务时的歧义性，并提出了解决方法：通过添加组件解决对称歧义问题并使其在处理平面对称性输入时具有旋转等变性，提出了一种称为OAVNN的向量神经元网络，通过左右分割任务对其进行了评估，发现网络能快速准确地完成分割任务，并希望这项工作能够推动对等变网络在对称对象上表达能力的研究。

打破对称性：解决等变神经网络中的对称歧义