Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased performance. To address this, this paper introduces a probabilistic method to learn the degree of equivariance in SCNNs. We parameterise the degree of equivariance as a likelihood distribution over the transformation group using Fourier coefficients, offering the option to model layer-wise and shared equivariance. These likelihood distributions are regularised to ensure an interpretable degree of equivariance across the network. Advantages include the applicability to many types of equivariant networks through the flexible framework of SCNNs and the ability to learn equivariance with respect to any subgroup of any compact group without requiring additional layers. Our experiments reveal competitive performance on datasets with mixed symmetries, with learnt likelihood distributions that are representative of the underlying degree of equivariance.

这篇论文介绍了一种概率方法，用于学习可望属性网络中等变性的程度，通过将等变性的程度参数化为傅里叶系数上的概率分布，以建模几何对称性，而无需额外的层次结构，通过模拟层级和共享的等变性，这种方法可以适用于许多类型的等变性网络，并且可以学习任何紧致群的子群的等变性，同时实验结果表明该方法在具有混合对称性的数据集上具有有竞争力的表现，并且所学习的概率分布能够准确反映底层等变性的程度。

一种学习可旋转卷积神经网络等变性程度的概率方法