Recovery of Training Data from Overparameterized Autoencoders: An
  Inverse Problem Perspective
Koren Abitbul Yehuda Dar
We study the recovery of training data from overparameterized autoencoder
models. Given a degraded training sample, we define the recovery of the
original sample as an inverse problem and formulate it as an optimization task.
In our inverse problem, we use the trained autoencoder to implicitly define a
regularizer for the particular training dataset that we aim to retrieve from.
We develop the intricate optimization task into a practical method that
iteratively applies the trained autoencoder and relatively simple computations
that estimate and address the unknown degradation operator. We evaluate our
method for blind inpainting where the goal is to recover training images from
degradation of many missing pixels in an unknown pattern. We examine various
deep autoencoder architectures, such as fully connected and U-Net (with various
nonlinearities and at diverse train loss values), and show that our method
significantly outperforms previous methods for training data recovery from
autoencoders. Importantly, our method greatly improves the recovery performance
also in settings that were previously considered highly challenging, and even
impractical, for such retrieval.