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: We propose an unsupervised method for building dynamic representations of sequential data, particularly of observed interactions. The method simultaneously acquires representations of input data and its dynamics. It is based on a hierarchical generative model composed of two levels. In the first level, a model learns representations to generate observed data. In the second level, representational states encode the dynamics of the lower one. The model is designed as a Bayesian network with switching variables represented in the higher level, and which generates transition models. The method actively explores the latent space guided by its knowledge and the uncertainty about it. That is achieved by updating the latent variables from prediction error signals backpropagated to the latent space. So, no encoder or inference models are used since the generators also serve as their inverse transformations.
 The method is evaluated in two scenarios, with static images and with videos. The results show that the adaptation over time leads to better performance than with similar architectures without temporal dependencies, e.g., variational autoencoders. With videos, it is shown that the system extracts the dynamics of the data in states that highly correlate with the ground truth of the actions observed.

A: A method that build representations of sequential data and its dynamics through generative models with an active process
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Q: Learning Mahalanobis metric spaces is an important problem that has found numerous applications. Several algorithms have been designed for this problem, including Information Theoretic Metric Learning (ITML) [Davis et al. 2007] and Large Margin Nearest Neighbor (LMNN) classification [Weinberger and Saul 2009].   We consider a formulation of Mahalanobis metric learning as an optimization problem,where the objective is to minimize the number of violated similarity/dissimilarity constraints.   We show that for any fixed ambient dimension, there exists a fully polynomial time approximation scheme (FPTAS) with nearly-linear running time. This result is obtained using tools from the theory of linear programming in low dimensions. We also discuss improvements of the algorithm in practice, and present experimental results on synthetic and real-world data sets. Our algorithm is fully parallelizable and performs favorably in the presence of adversarial noise.

A:
Fully parallelizable and adversarial-noise resistant metric learning algorithm with theoretical guarantees.
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