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: One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler generation tasks. For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially. Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space. We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.

A: Decompose the task of learning a generative model into learning disentangled latent factors for subsets of the data and then learning the joint over those latent factors.
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Q: 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.

A: 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.
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Q: This paper introduces a novel framework for learning algorithms to solve online combinatorial optimization problems. Towards this goal, we introduce a number of key ideas from traditional algorithms and complexity theory. First, we draw a new connection between primal-dual methods and reinforcement learning. Next, we introduce the concept of adversarial distributions (universal and high-entropy training sets), which are distributions that encourage the learner to find algorithms that work well in the worst case. We test our new ideas on a number of optimization problem such as the AdWords problem, the online knapsack problem, and the secretary problem. Our results indicate that the models have learned behaviours that are consistent with the traditional optimal algorithms for these problems.

A:
By combining ideas from traditional algorithms design and reinforcement learning, we introduce a novel framework for learning algorithms that solve online combinatorial optimization problems.
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