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: The lack of crisp mathematical models that capture the structure of real-world
data sets is a major obstacle to the detailed theoretical understanding of deep
neural networks. Here, we first demonstrate the effect of structured data sets
by experimentally comparing the dynamics and the performance of two-layer
networks trained on two different data sets: (i) an unstructured synthetic data
set containing random i.i.d. inputs, and (ii) a simple canonical data set such
as MNIST images. Our analysis reveals two phenomena related to the dynamics of
the networks and their ability to generalise that only appear when training on
structured data sets. Second, we introduce a generative model for data sets,
where high-dimensional inputs lie on a lower-dimensional manifold and have
labels that depend only on their position within this manifold. We call it the
*hidden manifold model* and we experimentally demonstrate that training
networks on data sets drawn from this model reproduces both the phenomena seen
during training on MNIST.
Solution: We demonstrate how structure in data sets impacts neural networks and introduce a generative model for synthetic data sets that reproduces this impact.