instruction:
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.
question:
We conduct a mathematical analysis on the Batch normalization (BN) effect on gradient backpropagation in residual network training in this work, which is believed to play a critical role in addressing the gradient vanishing/explosion problem. Specifically, by analyzing the mean and variance behavior of the input and the gradient in the forward and backward passes through the BN and residual branches, respectively, we show that they work together to confine the gradient variance to a certain range across residual blocks in backpropagation. As a result, the gradient vanishing/explosion problem is avoided. Furthermore, we use the same analysis to discuss the tradeoff between depth and width of a residual network and demonstrate that shallower yet wider resnets have stronger learning performance than deeper yet thinner resnets.
answer:
Batch normalisation maintains gradient variance throughout training, thus stabilizing optimization.


question:
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.
answer:
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.


question:
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. Augmenting the loss by a regularization term that penalizes the deviation of the gradient norm of the critic (as a function of the network's input) from one, was proposed as an alternative that improves training. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on several data sets.
answer:

A new regularization term can improve your training of wasserstein gans