TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for training Wasserstein GANs. Recent theoretical results have shown that optimistic mirror decent (OMD) can enjoy faster regret rates in the context of zero-sum games. WGANs is exactly a context of solving a zero-sum game with simultaneous no-regret dynamics.   Moreover, we show that optimistic mirror decent addresses the limit cycling problem in training WGANs. We formally show that in the case of bi-linear zero-sum games the last iterate of OMD dynamics converges to an equilibrium, in contrast to GD dynamics which are bound to cycle. We also portray the huge qualitative difference between GD and OMD dynamics with toy examples, even when GD is modified with many adaptations proposed in the recent literature, such as gradient penalty or momentum. We apply OMD WGAN training to a bioinformatics problem of generating DNA sequences. We observe that models trained with OMD achieve consistently smaller KL divergence with respect to the true underlying distribution, than models trained with GD variants. Finally, we introduce a new algorithm, Optimistic Adam, which is an optimistic variant of Adam. We apply it to WGAN training on CIFAR10 and observe improved performance in terms of inception score as compared to Adam.

SOLUTION: We propose the use of optimistic mirror decent to address cycling problems in the training of GANs. We also introduce the Optimistic Adam algorithm

PROBLEM: In this paper we propose to view the acceptance rate of the Metropolis-Hastings algorithm as a universal objective for learning to sample from target distribution -- given either as a set of samples or in the form of unnormalized density. This point of view unifies the goals of such approaches as Markov Chain Monte Carlo (MCMC), Generative Adversarial Networks (GANs), variational inference. To reveal the connection we derive the lower bound on the acceptance rate and treat it as the objective for learning explicit and implicit samplers. The form of the lower bound allows for doubly stochastic gradient optimization in case the target distribution factorizes (i.e. over data points). We empirically validate our approach on Bayesian inference for neural networks and generative models for images.

SOLUTION: Learning to sample via lower bounding the acceptance rate of the Metropolis-Hastings algorithm

PROBLEM: We present a generic dynamic architecture that employs a problem specific differentiable forking mechanism to leverage discrete logical information about the problem data structure. We adapt and apply our model to CLEVR Visual Question Answering, giving rise to the DDRprog architecture; compared to previous approaches, our model achieves higher accuracy in half as many epochs with five times fewer learnable parameters. Our model directly models underlying question logic using a recurrent controller that jointly predicts and executes functional neural modules; it explicitly forks subprocesses to handle logical branching. While FiLM and other competitive models are static architectures with less supervision, we argue that inclusion of program labels enables learning of higher level logical operations -- our architecture achieves particularly high performance on questions requiring counting and integer comparison. We further demonstrate the generality of our approach though DDRstack -- an application of our method to reverse Polish notation expression evaluation in which the inclusion of a stack assumption allows our approach to generalize to long expressions, significantly outperforming an LSTM with ten times as many learnable parameters.

SOLUTION:
A generic dynamic architecture that employs a problem specific differentiable forking mechanism to encode hard data structure assumptions. Applied to CLEVR VQA and expression evaluation.