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.

Ex Input:
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed---both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse.

Ex Output:
We solve ill-posed inverse problems with scarce ground truth examples by estimating an ensemble of random projections of the model instead of the model itself.


Ex Input:
Abstract Stochastic gradient descent (SGD) and Adam are commonly used to optimize deep neural networks, but choosing one usually means making tradeoffs between speed, accuracy and stability. Here we present an intuition for why the tradeoffs exist as well as a method for unifying the two in a continuous way. This makes it possible to control the way models are trained in much greater detail. We show that for default parameters, the new algorithm equals or outperforms SGD and Adam across a range of models for image classification tasks and outperforms SGD for language modeling tasks.

Ex Output:
An algorithm for unifying SGD and Adam and empirical study of its performance


Ex Input:
Recognizing the relationship between two texts is an important aspect of natural language understanding (NLU), and a variety of neural network models have been proposed for solving NLU tasks. Unfortunately, recent work showed that the datasets these models are trained on often contain biases that allow models to achieve non-trivial performance without possibly learning the relationship between the two texts. We propose a framework for building robust models by using adversarial learning to encourage models to learn latent, bias-free representations. We test our approach in a Natural Language Inference (NLI) scenario, and show that our adversarially-trained models learn robust representations that ignore known dataset-specific biases. Our experiments demonstrate that our models are more robust to new NLI datasets.

Ex Output:

Adversarial learning methods encourage NLI models to ignore dataset-specific biases and help models transfer across datasets.