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.

Example Input: Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging  this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem and establish $O(\epsilon^{-4})$ complexity for finding $\epsilon$-first-order stationary point, in which the algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by~\citep{iusem2017extragradient}. Then we propose an adaptive variant of OSG named Optimistic Adagrad (OAdagrad) and reveal an \emph{improved} adaptive complexity $\widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $\widetilde{O}(\cdot)$ compresses a logarithmic factor of $\epsilon$. }, where $\alpha$ characterizes the growth rate of the cumulative stochastic gradient and $0\leq \alpha\leq 1/2$. To the best of our knowledge, this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization. Empirically, our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training. Moreover, this observation can be explained by the slow growth rate of the cumulative stochastic gradient, as observed empirically.
Example Output: This paper provides novel analysis of adaptive gradient algorithms for solving non-convex non-concave min-max problems as GANs, and explains the reason why adaptive gradient methods outperform its non-adaptive counterparts by empirical studies.

Example Input: The process of designing neural architectures requires expert knowledge and extensive trial and error.
 While automated architecture search may simplify these requirements, the recurrent neural network (RNN) architectures generated by existing methods are limited in both flexibility and components.
 We propose a domain-specific language (DSL) for use in automated architecture search which can produce novel RNNs of arbitrary depth and width.
 The DSL is flexible enough to define standard architectures such as the Gated Recurrent Unit and Long Short Term Memory and allows the introduction of non-standard RNN components such as trigonometric curves and layer normalization.   Using two different candidate generation techniques, random search with a ranking function and reinforcement learning, 
we explore the novel architectures produced by the RNN DSL for language modeling and machine translation domains.
 The resulting architectures do not follow human intuition yet perform well on their targeted tasks, suggesting the space of usable RNN architectures is far larger than previously assumed.
Example Output: We define a flexible DSL for RNN architecture generation that allows RNNs of varying size and complexity and propose a ranking function that represents RNNs as recursive neural networks, simulating their performance to decide on the most promising architectures.

Example Input: Deep learning has become the state of the art approach in many machine learning problems such as classification. It has recently been shown that deep learning is highly vulnerable to adversarial perturbations. Taking the camera systems of self-driving cars as an example, small adversarial perturbations can cause the system to  make errors in important tasks, such as classifying traffic signs or detecting pedestrians. Hence, in order to use deep learning without safety concerns a proper defense strategy is required. We propose to use ensemble methods as a defense strategy against adversarial perturbations. We find that an attack leading one model to misclassify does not imply the same for other networks performing the same task. This makes ensemble methods an attractive defense strategy against adversarial attacks. We empirically show for the MNIST and the CIFAR-10 data sets that ensemble methods not only improve the accuracy of neural networks on test data but also increase their robustness against adversarial perturbations.
Example Output:
Using ensemble methods as a defense to adversarial perturbations against deep neural networks.