Given the task definition, example input & output, solve the new input case.
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.
Output: We devise adaptive loss scaling to improve mixed precision training that surpass the state-of-the-art results.
The abstract focusses on designing an adaptive loss scaling method, hence the generated output is correct.

New input case for you: We present Merged-Averaged Classifiers via Hashing (MACH) for $K$-classification with large $K$. Compared to traditional one-vs-all classifiers that require $O(Kd)$ memory and inference cost, MACH only need $O(d\log{K})$ memory while only requiring $O(K\log{K} + d\log{K})$ operation for inference. MACH is the first generic $K$-classification algorithm, with provably theoretical guarantees, which requires $O(\log{K})$ memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification task with very small (constant) number of classes. We provide theoretical quantification of accuracy-memory tradeoff by showing the first connection between extreme classification and heavy hitters. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU (12GB), with the classification accuracy of 19.28\%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (320 GB model size) and achieves 9\% accuracy. In contrast, MACH can achieve 9\% accuracy with 480x reduction in the model size (of mere 0.6GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU.
Output:
How to Training 100,000 classes on a single GPU