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]: Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models: is it true that neural networks can approximate any data manifold arbitrarily well? We provide a positive answer to this question and show that under mild assumptions on the activation function one can always find a feedforward neural network that maps the latent space onto a set located within the specified Hausdorff distance from the desired data manifold. We also prove similar theorems for the case of multiclass generative models and cycle generative models, trained to map samples from one manifold to another and vice versa.
[A]: We shot that a wide class of manifolds can be generated by ReLU and sigmoid networks with arbitrary precision.

[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

[Q]: Recent research has shown that CNNs are often overly sensitive to high-frequency textural patterns. Inspired by the intuition that humans are more sensitive to the lower-frequency (larger-scale) patterns we design a regularization scheme that penalizes large differences between adjacent components within each convolutional kernel. We apply our regularization onto several popular training methods, demonstrating that the models with the proposed smooth kernels enjoy improved adversarial robustness. Further, building on recent work establishing connections between adversarial robustness and interpretability, we show that our method appears to give more perceptually-aligned gradients.
[A]:
We introduce a smoothness regularization for convolutional kernels of CNN that can help improve adversarial robustness and lead to perceptually-aligned gradients