Bayesian 3D Steerable CNNs Offer Equivariance and Uncertainty Quantification

Steerable Convolutional Neural Networks (Steerable-CNNs) are highly effective in 3D vision tasks because they inherently guarantee SE(3)-equivariance, meaning their predictions are consistent regardless of rotations and translations of the input. However, their deterministic nature prevents them from quantifying uncertainty, a critical limitation in applications where confidence estimates are essential for reliable decision-making. Researchers have proposed a novel Bayesian Steerable-CNN that addresses this gap. This new framework introduces posterior distributions over the steerable basis coefficients, effectively making the kernels stochastic while rigorously preserving the exact equivariance property. The model's loss function is derived through variational inference and optimized using Bayes-by-Backpropagation, allowing for a clear decomposition of predictive uncertainty into epistemic (model uncertainty) and aleatoric (data noise) components. Empirical evaluations demonstrate that the Bayesian Steerable-CNN achieves competitive classification accuracy. Crucially, it boasts an expected calibration error of 0.0263 and outperforms its deterministic counterpart by up to 6.17% when faced with distributional shifts caused by additive Gaussian noise. Furthermore, leveraging the model's uncertainty estimates can significantly enhance its performance, yielding approximately 4% higher accuracy across 84% of the test dataset. A statistically significant negative correlation between epistemic uncertainty and prediction error confirms the semantic meaningfulness of the learned posterior variance.