Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing and place symmetry constraints on the functions a neural network can represent. The type of symmetry is typically fixed and has to be chosen in advance. Although some tasks are inherently equivariant, many tasks do not strictly follow such symmetries. In such cases, equivariance constraints can be overly restrictive. In this work, we propose a parameter-efficient relaxation of equivariance that can effectively interpolate between a (i) non-equivariant linear product, (ii) a strict-equivariant convolution, and (iii) a strictly-invariant mapping. The proposed parameterization can be thought of as a building block to allow adjustable symmetry structure in neural networks. Compared to non-equivariant or strict-equivariant baselines, we experimentally verify that soft equivariance leads to improved performance in terms of test accuracy on CIFAR-10 and CIFAR-100 image classification tasks.

翻译：在神经网络建模中,等离性提供了有益的导导偏差,在神经网络建模中,进动神经网络的翻译偏差是一个典型的典范。等离性可以通过权重共享和神经网络代表的功能的对称限制嵌入建筑中。对称类型通常是固定的,必须事先选择。虽然有些任务本质上是等异的,但许多任务并不严格遵循这种对称结构。在这种情况下,变异制约可能是过度限制性的。在这项工作中,我们提议以参数效率高的变异性放松参数,可以有效地在(一)非等离性线产品之间进行对调,(二)严格和(三)严格等异性共振和(三)严格变异性绘图。拟议的参数化可被视为允许在神经网络中调整对称结构的构件。与非等异性或严格等差基线相比,我们试验性地核查软均异性飞行导致改进的CI-10图像的精确性性。