In recent years, neural network approaches have been widely adopted for machine learning tasks, with applications in computer vision. More recently, unsupervised generative models based on neural networks have been successfully applied to model data distributions via low-dimensional latent spaces. In this paper, we use Generative Adversarial Networks (GANs) to impose structure in compressed sensing problems, replacing the usual sparsity constraint. We propose to train the GANs in a task-aware fashion, specifically for reconstruction tasks. We also show that it is possible to train our model without using any (or much) non-compressed data. Finally, we show that the latent space of the GAN carries discriminative information and can further be regularized to generate input features for general inference tasks. We demonstrate the effectiveness of our method on a variety of reconstruction and classification problems.

While Convolutional Neural Networks (CNNs) have recently achieved impressive results on many classification tasks, it is still unclear why they perform so well and how to properly design them. In this work, we investigate the effect of the convolutional depth of a CNN on its generalization performance for binary classification problems. We prove a sufficient condition -polynomial in the depth of the CNN- on the training database size to guarantee such performance. We empirically test our theory on the problem of gender classification and explore the effect of varying the CNN depth, as well as the training distribution and set size.