Group-equivariant convolutional neural networks (G-CNN) heavily rely on parameter sharing to increase CNN's data efficiency and performance. However, the parameter-sharing strategy greatly increases the computational burden for each added parameter, which hampers its application to deep neural network models. In this paper, we address these problems by proposing a non-parameter-sharing approach for group equivariant neural networks. The proposed methods adaptively aggregate a diverse range of filters by a weighted sum of stochastically augmented decomposed filters. We give theoretical proof about how the group equivariance can be achieved by our methods. Our method applies to both continuous and discrete groups, where the augmentation is implemented using Monte Carlo sampling and bootstrap resampling, respectively. Our methods also serve as an efficient extension of standard CNN. The experiments show that our method outperforms parameter-sharing group equivariant networks and enhances the performance of standard CNNs in image classification and denoising tasks, by using suitable filter bases to build efficient lightweight networks.

Neural networks promise automated prostate segmentation for the development of precise and quantifiable image-based biomarkers in modern personalized oncology.Before clinical translation, however, their stability must be ensured.In this study, we train three-dimensional Ushaped convolutional neural networks to segment prostate magnetic resonance imaging (MRI) scans and evaluate different loss formulations to improve their performance.To evaluate generalizability and reproducibility of our networks, we compare their performance in a clinically acquired test/re-test MRI data set of 26 prostate cancer patients that was previously not seen by the networks.We find our networks to be generalizable with good reproducibility with a mean Intersection over Union of 0.88.While initial results are promising, anatomical accuracy remains to be evaluated in larger, multi-center data sets.To facilitate clinical applicability, we provide an easy to use toolbox online.* This work was partially funded by the German Federal Ministry of Education and Research (BMBF) within the "BNTrAInee" (16DHBK1022) and WestAI (01IS22094E WEST