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We study the recovery of training data from overparameterized autoencodermodels. Given a degraded training sample, we define the recovery of theoriginal sample as an inverse problem and formulate it as an optimization task.In our inverse problem, we use the trained autoencoder to implicitly define aregularizer for the particular training dataset that we aim to retrieve from.We develop the intricate optimization task into a practical method thatiteratively applies the trained autoencoder and relatively simple computationsthat estimate and address the unknown degradation operator. We evaluate ourmethod for blind inpainting where the goal is to recover training images fromdegradation of many missing pixels in an unknown pattern. We examine variousdeep autoencoder architectures, such as fully connected and U-Net (with variousnonlinearities and at diverse train loss values), and show that our methodsignificantly outperforms previous methods for training data recovery fromautoencoders. Importantly, our method greatly improves the recovery performancealso in settings that were previously considered highly challenging, and evenimpractical, for such retrieval.

Recovery of Training Data from Overparameterized Autoencoders: An Inverse Problem Perspective