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: The available resolution in our visual world is extremely high, if not infinite. Existing CNNs can be applied in a fully convolutional way to images of arbitrary resolution, but as the size of the input increases, they can not capture contextual information. In addition, computational requirements scale linearly to the number of input pixels, and resources are allocated uniformly across the input, no matter how informative different image regions are. We attempt to address these problems by proposing a novel architecture that traverses an image pyramid in a top-down fashion, while it uses a hard attention mechanism to selectively process only the most informative image parts. We conduct experiments on MNIST and ImageNet datasets, and we show that our models can significantly outperform fully convolutional counterparts, when the resolution of the input is that big that the receptive field of the baselines can not adequately cover the objects of interest. Gains in performance come for less FLOPs, because of the selective processing that we follow. Furthermore, our attention mechanism makes our predictions more interpretable, and creates a trade-off between accuracy and complexity that can be tuned both during training and testing time.

Answer: We propose a novel architecture that traverses an image pyramid in a top-down fashion, while it visits only the most informative regions along the way.


Question: Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework – a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a novel graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while also often generating embeddings of better quality for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation.

Answer: A generic framework to scale existing graph embedding techniques to large graphs.


Question: We analyze the joint probability distribution on the lengths of the
 vectors of hidden variables in different layers of a fully connected
 deep network, when the weights and biases are chosen randomly according to
 Gaussian distributions, and the input is binary-valued.  We show
 that, if the activation function satisfies a minimal set of
 assumptions, satisfied by all activation functions that we know that
 are used in practice, then, as the width of the network gets large,
 the ``length process'' converges in probability to a length map
 that is determined as a simple function of the variances of the
 random weights and biases, and the activation function.

 We also show that this convergence may fail for activation functions 
 that violate our assumptions.

Answer:
We prove that, for activation functions satisfying some conditions, as a deep network gets wide, the lengths of the vectors of hidden variables converge to a length map.