Title: Towards Adaptive Symmetry Breaking in Vector Neuron Networks
Primary area: learning on graphs and other geometries & topologies
Keywords: Vector neural network; SO(3)-equivariant; symmetry; symmetry breaking; pose estimation

Abstract: Vector Neuron Networks (VNNs) have been widely adopted in various 3D tasks due to their data efficiency and strong generalization capabilities rooted in equivariance. However, the rigid equivariance constraints of VNNs limit their ability to handle the prevalent problem of symmetry breaking in the 3D world, where models may need to produce outputs with reduced symmetry from inputs with high symmetry. In this paper, we propose an adaptive equivariance paradigm within the Vector Neuron (VN) framework, comprising three key designs: (1) Architecturally, we introduce a residual architecture that transforms the rigid equivariance constraints of VNNs into soft priors, preserving their symmetry-based inductive bias while enabling symmetry breaking. (2) Methodologically, we derive an implicit equivariance regularization method that allows VNNs to dynamically adjust their equivariance constraints according to the symmetry level of input data. (3) Structurally, we design a lightweight and interpretable module that allows VNNs to regulate equivariance in a simpler and more transparent manner. Experiments on 26 categories with varying input symmetries demonstrate that our approach achieves adaptive equivariance, improving the average performance of VNNs on pose estimation tasks by a factor of 5, and by a factor of 33 on highly symmetric inputs.

TL;DR: We propose the first adaptive SO(3)-equivariant model under the vector neuron framework.