A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs
This addresses the challenge of adapting equivariant networks to real-world data with uncertain symmetries, offering a flexible approach for machine learning practitioners, though it appears incremental as it builds on existing SCNN frameworks.
The paper tackles the problem of unknown or varying symmetries in steerable CNNs, which can lead to overconstrained weights and decreased performance, by introducing a probabilistic method to learn the degree of equivariance, resulting in competitive performance on datasets with mixed symmetries.
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.