In the past few years, there has been a growing interest in finding methods to train discrete weights neural networks. As a matter of fact, when it comes to implementations, discrete weights allow to reach a better efficiency, as they considerably simplify the multiply-accumulate operations, with the extreme case where weights become binary and there is no need to perform any multiplication anymore. Unfortunately, training discrete weights neural networks is complex in practice, since it basically boils down to a NPhard optimization problem. To circumvent this difficulty, many works have introduced techniques that aim at finding reasonable approximations [7, 6, 24, 13]. Among these works, in a recent paper Baldassi et al. [2] discuss the learning process in artificial neural networks with discrete weights and try to explain why these networks work so efficiently.

The robustness of classifiers has become a question of paramount importance in the past few years. Indeed, it has been shown that state-of-the-art deep learning architectures can easily be fooled with imperceptible changes to their inputs. Therefore, finding good measures of robustness of a trained classifier is a key issue in the field. In this paper, we point out that averaging the radius of robustness of samples in a validation set is a statistically weak measure. We propose instead to weight the importance of samples depending on their difficulty. We motivate the proposed score by a theoretical case study using logistic regression, where we show that the proposed score is independent of the choice of the samples it is evaluated upon. We also empirically demonstrate the ability of the proposed score to measure robustness of classifiers with little dependence on the choice of samples in more complex settings, including deep convolutional neural networks and real datasets.

Transfer learning using deep neural networks as feature extractors has become increasingly popular over the past few years. It allows to obtain state-of-the-art accuracy on datasets too small to train a deep neural network on its own, and it provides cutting edge descriptors that, combined with nonparametric learning methods, allow rapid and flexible deployment of performing solutions in computationally restricted settings. In this paper, we are interested in showing that the features extracted using deep neural networks have specific properties which can be used to improve accuracy of downstream nonparametric learning methods. Namely, we demonstrate that for some distributions where information is embedded in a few coordinates, segmenting feature vectors can lead to better accuracy. We show how this model can be applied to real datasets by performing experiments using three mainstream deep neural network feature extractors and four databases, in vision and audio.