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: Most of the existing Graph Neural Networks (GNNs) are the mere extension of the Convolutional Neural Networks (CNNs) to graphs. Generally, they consist of several steps of message passing between the nodes followed by a global indiscriminate feature pooling function. In many data-sets, however, the nodes are unlabeled or their labels provide no information about the similarity between the nodes and the locations of the nodes in the graph. Accordingly, message passing may not propagate helpful information throughout the graph. We show that this conventional approach can fail to learn to perform even simple graph classification tasks. We alleviate this serious shortcoming of the GNNs by making them a two step method. In the first of the proposed approach, a graph embedding algorithm is utilized to obtain a continuous feature vector for each node of the graph. The embedding algorithm represents the graph as a point-cloud in the embedding space. In the second step, the GNN is applied to the point-cloud representation of the graph provided by the embedding method. The GNN learns to perform the given task by inferring the topological structure of the graph encoded in the spatial distribution of the embedded vectors. In addition, we extend the proposed approach to the graph clustering problem and a new architecture for graph clustering is proposed. Moreover, the spatial representation of the graph is utilized to design a graph pooling algorithm. We turn the problem of graph down-sampling into a column sampling problem, i.e., the sampling algorithm selects a subset of the nodes whose feature vectors preserve the spatial distribution of all the feature vectors. We apply the proposed approach to several popular benchmark data-sets and it is shown that the proposed geometrical approach strongly improves the state-of-the-art result for several data-sets. For instance, for the PTC data-set, we improve the state-of-the-art result for more than 22 %.

A: The graph analysis problem is transformed into a point cloud analysis problem. 
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Q: Unsupervised bilingual dictionary induction (UBDI) is useful for unsupervised machine translation and for cross-lingual transfer of models into low-resource languages. One approach to UBDI is to align word vector spaces in different languages using Generative adversarial networks (GANs) with linear generators, achieving state-of-the-art performance for several language pairs. For some pairs, however, GAN-based induction is unstable or completely fails to align the vector spaces. We focus on cases where linear transformations provably exist, but the performance of GAN-based UBDI depends heavily on the model initialization. We show that the instability depends on the shape and density of the vector sets, but not on noise; it is the result of local optima, but neither over-parameterization nor changing the batch size or the learning rate consistently reduces instability. Nevertheless, we can stabilize GAN-based UBDI through best-of-N model selection, based on an unsupervised stopping criterion.

A: An empirical investigation of GAN-based alignment of word vector spaces, focusing on cases, where linear transformations provably exist, but training is unstable.
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Q: Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet.   Empirical and theoretical results clearly indicate that the empirical spectral density (ESD) of DNN layer matrices displays signatures of traditionally-regularized statistical models, even in the absence of exogenously specifying traditional forms of regularization, such as Dropout or Weight Norm constraints.   Building on recent results in RMT, most notably its extension to Universality classes of Heavy-Tailed matrices, we develop a theory to identify 5+1 Phases of Training, corresponding to increasing amounts of Implicit Self-Regularization.   For smaller and/or older DNNs, this Implicit Self-Regularization is like traditional Tikhonov regularization, in that there is a "size scale" separating signal from noise.   For state-of-the-art DNNs, however, we identify a novel form of Heavy-Tailed Self-Regularization, similar to the self-organization seen in the statistical physics of disordered systems.   This implicit Self-Regularization can depend strongly on the many knobs of the training process.   By exploiting the generalization gap phenomena, we demonstrate that we can cause a small model to exhibit all 5+1 phases of training simply by changing the batch size.

A:
See the abstract.  (For the revision, the paper is identical, except for a 59 page Supplementary Material, which can serve as a stand-along technical report version of the paper.)
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