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: 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.

A: Batch normalisation maintains gradient variance throughout training, thus stabilizing optimization.
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Q: We propose a new, multi-component energy function for energy-based Generative Adversarial Networks (GANs) based on methods from the image quality assessment literature. Our approach expands on the Boundary Equilibrium Generative Adversarial Network (BEGAN) by outlining some of the short-comings of the original energy and loss functions. We address these short-comings by incorporating an l1 score, the Gradient Magnitude Similarity score, and a chrominance score into the new energy function. We then provide a set of systematic experiments that explore its hyper-parameters. We show that each of the energy function's components is able to represent a slightly different set of features, which require their own evaluation criteria to assess whether they have been adequately learned. We show that models using the new energy function are able to produce better image representations than the BEGAN model in predicted ways.

A: Image Quality Assessment Techniques Improve Training and Evaluation of Energy-Based Generative Adversarial Networks
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Q: Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models.   Adversarial training, one of the most successful empirical defenses to adversarial examples, refers to training on adversarial examples generated within a geometric constraint set. The most commonly used geometric constraint is an $L_p$-ball of radius $\epsilon$ in some norm. We introduce adversarial training with Voronoi constraints, which replaces the $L_p$-ball constraint with the Voronoi cell for each point in the training set. We show that adversarial training with Voronoi constraints produces robust models which significantly improve over the state-of-the-art on MNIST and are competitive on CIFAR-10.

A:
We replace the Lp ball constraint with the Voronoi cells of the training data to produce more robust models. 
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