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.

Input: Consider Input: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.

Output: The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.


Input: Consider Input: Noise injection is a fundamental tool for data augmentation, and yet there is no widely accepted procedure to incorporate it with learning frameworks. This study analyzes the effects of adding or applying different noise models of varying magnitudes to Convolutional Neural Network (CNN) architectures. Noise models that are distributed with different density functions are given common magnitude levels via Structural Similarity (SSIM) metric in order to create an appropriate ground for comparison. The basic results are conforming with the most of the common notions in machine learning, and also introduces some novel heuristics and recommendations on noise injection. The new approaches will provide better understanding on optimal learning procedures for image classification.

Output: Ideal methodology to inject noise to input data during CNN training


Input: Consider Input: The use of deep learning models as priors for compressive sensing tasks presents new potential for inexpensive seismic data acquisition. An appropriately designed Wasserstein generative adversarial network is designed based on a generative adversarial network architecture trained on several historical surveys, capable of learning the statistical properties of the seismic wavelets. The usage of validating and performance testing of compressive sensing are three steps. First, the existence of a sparse representation with different compression rates for seismic surveys is studied. Then, non-uniform samplings are studied, using the proposed methodology. Finally, recommendations for non-uniform seismic survey grid, based on the evaluation of reconstructed seismic images and metrics, is proposed. The primary goal of the proposed deep learning model is to provide the foundations of an optimal design for seismic acquisition, with less loss in imaging quality. Along these lines, a compressive sensing design of a non-uniform grid over an asset in Gulf of Mexico, versus a traditional seismic survey grid which collects data uniformly at every few feet, is suggested, leveraging the proposed method.


Output: Improved a GAN based pixel inpainting network for compressed seismic image recovery andproposed a non-uniform sampling survey recommendatio, which can be easily applied to medical and other domains for compressive sensing technique.