Part 1. Definition
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.
Part 2. 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.
Answer: We devise adaptive loss scaling to improve mixed precision training that surpass the state-of-the-art results.
Explanation: The abstract focusses on designing an adaptive loss scaling method, hence the generated output is correct.
Part 3. Exercise
Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially efficient with respect to shallow networks, in the sense that a shallow network must grow exponentially large in order to approximate the functions represented by a deep network of polynomial size. In this work, we extend the study of expressive efficiency to the attribute of network connectivity and in particular to the effect of "overlaps" in the convolutional process, i.e., when the stride of the convolution is smaller than its filter size (receptive field).
To theoretically analyze this aspect of network's design, we focus on a well-established surrogate for ConvNets called Convolutional Arithmetic Circuits (ConvACs), and then demonstrate empirically that our results hold for standard ConvNets as well. Specifically, our analysis shows that having overlapping local receptive fields, and more broadly denser connectivity, results in an exponential increase in the expressive capacity of neural networks. Moreover, while denser connectivity can increase the expressive capacity, we show that the most common types of modern architectures already exhibit exponential increase in expressivity, without relying on fully-connected layers.
Answer:
We analyze how the degree of overlaps between the receptive fields of a convolutional network affects its expressive power.