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: Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.

Answer: We systematically analyze the convergence behaviour of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates.

Question: Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further.

We present methods for training on small domains, while applying the trained models on larger domains, with consistency constraints ensuring the solutions are physically meaningful even at the boundary of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.

Answer: We present RNNs for training surrogate models of PDEs, wherein consistency constraints ensure the solutions are physically meaningful, even when the training uses much smaller domains than the trained model is applied to.

Question: Transfer learning aims to solve the data sparsity for a specific domain by applying information of another domain. Given a sequence (e.g. a natural language sentence), the transfer learning, usually enabled by recurrent neural network (RNN), represent the sequential information transfer. RNN uses a chain of repeating cells to model the sequence data. However, previous studies of neural network based transfer learning simply transfer the information across the whole layers, which are unfeasible for seq2seq and sequence labeling. Meanwhile, such layer-wise transfer learning mechanisms also lose the fine-grained cell-level information from the source domain.

In this paper, we proposed the aligned recurrent transfer, ART, to achieve cell-level information transfer. ART is in a recurrent manner that different cells share the same parameters. Besides transferring the corresponding information at the same position, ART transfers information from all collocated words in the source domain. This strategy enables ART to capture the word collocation across domains in a more flexible way. We conducted extensive experiments on both sequence labeling tasks (POS tagging, NER) and sentence classification (sentiment analysis). ART outperforms the state-of-the-arts over all experiments.

Answer:
Transfer learning for sequence via learning to align cell-level information across domains.