Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly present. This motivates algorithmically optimizing the architectural constraints imposed by equivariance. We propose the equivariance relaxation morphism, which preserves functionality while reparameterizing a group equivariant layer to operate with equivariance constraints on a subgroup, as well as the [G]-mixed equivariant layer, which mixes layers constrained to different groups to enable within-layer equivariance optimization. We further present evolutionary and differentiable neural architecture search (NAS) algorithms that utilize these mechanisms respectively for equivariance-aware architectural optimization. Experiments across a variety of datasets show the benefit of dynamically constrained equivariance to find effective architectures with approximate equivariance.

翻译：在神经网络培训中,将对称组的等同性作为约束因素纳入对称性组,可以改善显示这些对称性的任务的性能和一般化,但这种对称性往往不是完全的,也并非明显存在。这促使从逻辑上优化因等相异性造成的建筑限制。我们提议了等同性放松形态,保留功能,同时对群体对等性层进行重新量化,使其在分组上运行时受到不均匀性制约,以及[G]混合等同性层,将不同组的层混在一起,以便实现对等性优化。我们进一步提出进化和不同的神经结构搜索算法,这些算法分别利用这些机制实现等同性-对称性建筑优化。各种数据集的实验显示动态限制等同性能的好处,以找到具有近似不均匀性的有效结构。