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.
Example: Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in existing GPUs. MPT is typically used in combination with a technique called loss scaling, that works by scaling up the loss value up before the start of backpropagation in order to minimize the impact of numerical underflow on training. Unfortunately, existing methods make this loss scale value a hyperparameter that needs to be tuned per-model, and a single scale cannot be adapted to different layers at different training stages. We introduce a loss scaling-based training method called adaptive loss scaling that makes MPT easier and more practical to use, by removing the need to tune a model-specific loss scale hyperparameter. We achieve this by introducing layer-wise loss scale values which are automatically computed during training to deal with underflow more effectively than existing methods. We present experimental results on a variety of networks and tasks that show our approach can shorten the time to convergence and improve accuracy, compared with using the existing state-of-the-art MPT and single-precision floating point.
Example solution: We devise adaptive loss scaling to improve mixed precision training that surpass the state-of-the-art results.
Example explanation: The abstract focusses on designing an adaptive loss scaling method, hence the generated output is correct.

Problem: Neural networks could misclassify inputs that are slightly different from their training data, which indicates a small margin between their decision boundaries and the training dataset. In this work, we study the binary classification of linearly separable datasets and show that linear classifiers could also have decision boundaries that lie close to their training dataset if cross-entropy loss is used for training. In particular, we show that if the features of the training dataset lie in a low-dimensional affine subspace and the cross-entropy loss is minimized by using a gradient method, the margin between the training points and the decision boundary could be much smaller than the optimal value. This result is contrary to the conclusions of recent related works such as (Soudry et al., 2018), and we identify the reason for this contradiction. In order to improve the margin, we introduce differential training, which is a training paradigm that uses a loss function defined on pairs of points from each class. We show that the decision boundary of a linear classifier trained with differential training indeed achieves the maximum margin. The results reveal the use of cross-entropy loss as one of the hidden culprits of adversarial examples and introduces a new direction to make neural networks robust against them.
Solution: We show that minimizing the cross-entropy loss by using a gradient method could lead to a very poor margin if the features of the dataset lie on a low-dimensional subspace.