Before revision:  Theoretical guarantees that Denise 's architecture can approximate the decomposition function, to arbitrary precision and with arbitrarily high probability, are obtained. The training scheme is also shown to convergence to a stationary point of the robust PCA's loss-function. We train Denise on a randomly generated dataset, and evaluate the performance of the DNN on synthetic and real-world covariance matrices. Denise achieves comparable results to several state-of-the-art algorithms in terms of decomposition quality, but as only one evaluation of the learned DNN is needed, Denise outperforms all existing algorithms in terms of computation time .
After revision:  Theoretical guarantees for Denise are provided. These include a novel universal approximation theorem adapted to our geometric deep learning problem, convergence to an optimal solution of the learning problem and convergence of the training scheme. Our experiments show that Denise matches state-of-the-art algorithms in terms of decomposition quality, but as only one evaluation of the learned DNN is needed, Denise outperforms all existing algorithms in terms of computation time .