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: Partially observable Markov decision processes (POMDPs) are a natural model for scenarios where one has to deal with incomplete knowledge and random events.
 Applications include, but are not limited to, robotics and motion planning.
 However, many relevant properties of POMDPs are either undecidable or very expensive to compute in terms of both runtime and memory consumption.
 In our work, we develop a game-based abstraction method that is able to deliver safe bounds and tight
  approximations for important sub-classes of such properties.
 We discuss the theoretical implications and showcase the applicability of our results on a broad spectrum of benchmarks.


Solution: This paper provides a game-based abstraction scheme to compute provably sound policies for POMDPs.