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.

[Q]: 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.
[A]: 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.


[Q]: We propose NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay. In our experiments on neural networks for image classification, speech recognition, machine translation, and language modeling, it performs on par or better than well tuned SGD with momentum and Adam/AdamW. 
 Additionally, NovoGrad (1) is robust to the choice of learning rate and weight initialization, (2) works well in a large batch setting, and (3) has two times smaller memory footprint than Adam.
[A]: NovoGrad -  an adaptive SGD method with layer-wise gradient normalization and decoupled weight decay. 


[Q]: Point clouds are an important type of geometric data and have widespread use in computer graphics and vision. However, learning representations for point clouds is particularly challenging due to their nature as being an unordered collection of points irregularly distributed in 3D space. Graph convolution, a generalization of the convolution operation for data defined over graphs, has been recently shown to be very successful at extracting localized features from point clouds in supervised or semi-supervised tasks such as classification or segmentation. This paper studies the unsupervised problem of a generative model exploiting graph convolution. We focus on the generator of a GAN and define methods for graph convolution when the graph is not known in advance as it is the very output of the generator. The proposed architecture learns to generate localized features that approximate graph embeddings of the output geometry. We also study the problem of defining an upsampling layer in the graph-convolutional generator, such that it learns to exploit a self-similarity prior on the data distribution to sample more effectively.
[A]:
A GAN using graph convolution operations with dynamically computed graphs from hidden features