L2-Nonexpansive Neural Network
This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of controlling Lipschitz constants to realize its full potential in maximizing robustness: our linear and convolution layers subsume those in the previous Parseval networks as a special case and allow greater degrees of freedom; aggregation, pooling, splitting and other operators are adapted in new ways, and a new loss function is proposed, all for the purpose of improving robustness. With MNIST and CIFAR-10 classifiers, we demonstrate a number of advantages. Without needing any adversarial training, the proposed classifiers exceed the state of the art in robustness against white-box L2-bounded adversarial attacks. Their outputs are quantitatively more meaningful than ordinary networks and indicate levels of confidence. They are also free of exploding gradients, among other desirable properties. …

Jeffries-Matusita Distance
Jeffries-Matusita Distance calculates the separability of a pair of probability distributions. This can be particularly meaningful for evaluating the results of Maximum Likelihood classifications. …

Area Attention
Existing attention mechanisms, are mostly item-based in that a model is designed to attend to a single item in a collection of items (the memory). Intuitively, an area in the memory that may contain multiple items can be worth attending to as a whole. We propose area attention: a way to attend to an area of the memory, where each area contains a group of items that are either spatially adjacent when the memory has a 2-dimensional structure, such as images, or temporally adjacent for 1-dimensional memory, such as natural language sentences. Importantly, the size of an area, i.e., the number of items in an area, can vary depending on the learned coherence of the adjacent items. By giving the model the option to attend to an area of items, instead of only a single item, we hope attention mechanisms can better capture the nature of the task. Area attention can work along multi-head attention for attending to multiple areas in the memory. We evaluate area attention on two tasks: neural machine translation and image captioning, and improve upon strong (state-of-the-art) baselines in both cases. These improvements are obtainable with a basic form of area attention that is parameter free. In addition to proposing the novel concept of area attention, we contribute an efficient way for computing it by leveraging the technique of summed area tables. …

Discriminator Rejection Sampling (DRS)
We propose a rejection sampling scheme using the discriminator of a GAN to approximately correct errors in the GAN generator distribution. We show that under quite strict assumptions, this will allow us to recover the data distribution exactly. We then examine where those strict assumptions break down and design a practical algorithm – called Discriminator Rejection Sampling (DRS) – that can be used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of Gaussians and on the state of the art SAGAN model. On ImageNet, we train an improved baseline that increases the best published Inception Score from 52.52 to 62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use DRS to further improve on this baseline, improving the Inception Score to 76.08 and the FID to 13.75. …