Autoencoder and Partially Impossible Reconstruction Losses.

The generally unsupervised nature of autoencoder models implies that the main training metric is formulated as the error between input images and their corresponding reconstructions. Different reconstruction loss variations and latent space regularizations have been shown to improve model performances depending on the tasks to solve and to induce new desirable properties such as disentanglement. Nevertheless, measuring the success in, or enforcing properties by, the input pixel space is a challenging endeavour.

On decision regions of narrow deep neural networks.

We show that for neural network functions that have width less or equal to the input dimension all connected components of decision regions are unbounded. The result holds for continuous and strictly monotonic activation functions as well as for the ReLU activation function. This complements recent results on approximation capabilities by Hanin and Sellke (2017) and connectivity of decision regions by Nguyen et al.