Figure 8: The average values during training of the two components used in the criteria for neuron importance in the input layer: the absolute gradient of the loss with respect to the reconstructed samples and the sum of the absolute weights connected to a neuron. A.1 Implementation Details For all datasets, we used standard normalization that scales the features to have zero mean and standard deviation of one. The architecture of the autoencoder consists of one hidden layer with sigmoid activation. A linear activation is used for the output layer. We use a hidden layer of 200 neurons for all datasets.

Differently, our unsupervised multi-body task requires the model's ability to handle part-level local equivariance, Figure 1: Structure of our feature extractor based on EPN. "EPNConv" is the SE(3)-equivariant convolution proposed in the vanilla EPN network. Part-level SE(3)-equivariance is desirable for motion analysis, especially rotation estimation. Song and Y ang utilized the methodology proposed by Choy et al . All other objects were considered part of the background.

We provide optimization time ( i. e ., training time in the bracket) and inference time of our method. Our method improves the state-of-the-art results while using much fewer parameters. The surfaces are reconstructed from point clouds with low noise (a) and high noise (b). Fig 2, we show the reconstructed surfaces on point clouds with different noise levels. A partially enlarged view is provided for each shape.

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Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods.