Bayesian 3D Steerable CNNs: Enabling Equivariance and Uncertainty Quantification Simultaneously

The paper introduces a Bayesian Steerable Convolutional Neural Network (Steerable-CNN) that maintains SE(3)-equivariance while enabling uncertainty quantification through posterior distributions over basis coefficients. Utilizing variational inference and Bayes-by-Backpropagation, the model achieves competitive classification accuracy, with an expected calibration error of 0.0263, and demonstrates up to 6.17% improvement over deterministic models under distributional shifts. This approach allows practitioners to leverage uncertainty estimates to enhance model performance, achieving approximately 4% higher accuracy across 84% of the test dataset, thereby integrating Bayesian methods with equivariant architectures for more robust AI applications.