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.
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Question: Whereas it is believed that techniques such as Adam, batch normalization and, more recently, SeLU nonlinearities ``solve'' the exploding gradient problem, we show that this is not the case and that in a range of popular MLP architectures, exploding gradients exist and that they limit the depth to which networks can be effectively trained, both in theory and in practice. We explain why exploding gradients occur and highlight the {\it collapsing domain problem}, which can arise in architectures that avoid exploding gradients. 

 ResNets have significantly lower gradients and thus can circumvent the exploding gradient problem, enabling the effective training of much deeper networks, which we show is a consequence of a surprising mathematical property. By noticing that {\it any neural network is a residual network}, we devise the {\it residual trick}, which reveals that introducing skip connections simplifies the network mathematically, and that this simplicity may be the major cause for their success.

Answer: We show that in contras to popular wisdom, the exploding gradient problem has not been solved and that it limits the depth to which MLPs can be effectively trained. We show why gradients explode and how ResNet handles them.


Question: 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.

Answer: 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.


Question: In this work, we propose a self-supervised method to learn sentence representations with an injection of linguistic knowledge. Multiple linguistic frameworks propose diverse sentence structures from which semantic meaning might be expressed out of compositional words operations. We aim to take advantage of this linguist diversity and learn to represent sentences by contrasting these diverse views. Formally, multiple views of the same sentence are mapped to close representations. On the contrary, views from other sentences are mapped further. By contrasting different linguistic views, we aim at building embeddings which better capture semantic and which are less sensitive to the sentence outward form.


Answer:
We aim to exploit the diversity of linguistic structures to build sentence representations.