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: Understanding the groundbreaking performance of Deep Neural Networks is one
 of the greatest challenges to the scientific community today. In this work, we
 introduce an information theoretic viewpoint on the behavior of deep networks
 optimization processes and their generalization abilities. By studying the Information
 Plane, the plane of the mutual information between the input variable and
 the desired label, for each hidden layer. Specifically, we show that the training of
 the network is characterized by a rapid increase in the mutual information (MI)
 between the layers and the target label, followed by a longer decrease in the MI
 between the layers and the input variable. Further, we explicitly show that these
 two fundamental information-theoretic quantities correspond to the generalization
 error of the network, as a result of introducing a new generalization bound that is
 exponential in the representation compression. The analysis focuses on typical
 patterns of large-scale problems. For this purpose, we introduce a novel analytic
 bound on the mutual information between consecutive layers in the network.
 An important consequence of our analysis is a super-linear boost in training time
 with the number of non-degenerate hidden layers, demonstrating the computational
 benefit of the hidden layers.

A: Introduce an information theoretic viewpoint on the behavior of deep networks optimization processes and their generalization abilities
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Q:   In many applications, the training data for a machine learning task is partitioned across multiple nodes, and aggregating this data may be infeasible due to storage, communication, or privacy constraints. In this work, we present Good-Enough Model Spaces (GEMS), a novel framework for learning a global satisficing (i.e. "good-enough") model within a few communication rounds by carefully combining the space of local nodes' satisficing models. In experiments on benchmark and medical datasets, our approach outperforms other baseline aggregation techniques such as ensembling or model averaging, and performs comparably to the ideal non-distributed models.


A: We present Good-Enough Model Spaces (GEMS), a framework for learning an aggregate model over distributed nodes within a small number of communication rounds.
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Q: Auto-encoders are commonly used for unsupervised representation learning and for pre-training deeper neural networks.
 When its activation function is linear and the encoding dimension (width of hidden layer) is smaller than the input dimension, it is well known that auto-encoder is optimized to learn the principal components of the data distribution (Oja1982).
 However, when the activation is nonlinear and when the width is larger than the input dimension (overcomplete), auto-encoder behaves differently from PCA, and in fact is known to perform well empirically for sparse coding problems. 

 We provide a theoretical explanation for this empirically observed phenomenon, when rectified-linear unit (ReLu) is adopted as the activation function and the hidden-layer width is set to be large.
 In this case, we show that, with significant probability, initializing the weight matrix of an auto-encoder by sampling from a spherical Gaussian distribution followed by stochastic gradient descent (SGD) training converges towards the ground-truth representation for a class of sparse dictionary learning models.
 In addition, we can show that, conditioning on convergence, the expected convergence rate is O(1/t), where t is the number of updates.
 Our analysis quantifies how increasing hidden layer width helps the training performance when random initialization is used, and how the norm of network weights influence the speed of SGD convergence.

A:
theoretical analysis of nonlinear wide autoencoder
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