Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural network

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 continuous group convolution can be approximated 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. We demonstrate that our methods serve as an efficient extension of standard CNN. Experiments on group equivariance tests show how our methods can achieve superior performance to parameter-sharing group equivariant networks. Experiments on image classification and image denoising tasks show that in certain scenarios, with a suitable set of filter bases, our method helps improve the performance of standard CNNs and build efficient lightweight image denoising networks. The code will be available at https://github.com/ZhaoWenzhao/MCG_CNN.