  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.
