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.

To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.
The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.

Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance.
We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty in conventional networks.

It is clear that users should own and control their data and privacy. Utility providers are also becoming more interested in guaranteeing data privacy. Therefore, users and providers can and should collaborate in privacy protecting challenges, and this paper addresses this new paradigm. We propose a framework where the user controls what characteristics of the data they want to share (utility) and what they want to keep private (secret), without necessarily asking the utility provider to change its existing machine learning algorithms. We first analyze the space of privacy-preserving representations and derive natural information-theoretic bounds on the utility-privacy trade-off when disclosing a sanitized version of the data X. We present explicit learning architectures to learn privacy-preserving representations that approach this bound in a data-driven fashion. We describe important use-case scenarios where the utility providers are willing to collaborate with the sanitization process. We study space-preserving transformations where the utility provider can use the same algorithm on original and sanitized data, a critical and novel attribute to help service providers accommodate varying privacy requirements with a single set of utility algorithms. We illustrate this framework through  the implementation of three use cases; subject-within-subject, where we tackle the problem of having a face identity detector that works only on a consenting subset of users, an important application, for example, for mobile devices activated by face recognition; gender-and-subject, where we preserve facial verification while hiding the gender attribute for users who choose to do so; and emotion-and-gender, where we hide independent variables, as is the case of hiding gender while preserving emotion detection.

Learning privacy-preserving transformations from data. A collaborative approach