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:
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:
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

Ex Output:
We propose an algorithm for provably recovering parameters (convolutional and output weights) of a convolutional network with overlapping patches.


Ex Input:
Recent advances have illustrated that it is often possible to learn to solve linear inverse problems in imaging using training data that can outperform more traditional regularized least squares solutions. Along these lines, we present some extensions of the Neumann network, a recently introduced end-to-end learned architecture inspired by a truncated Neumann series expansion of the solution map to a regularized least squares problem. Here we summarize the Neumann network approach, and show that it has a form compatible with the optimal reconstruction function for a given inverse problem. We also investigate an extension of the Neumann network that incorporates a more sample efficient patch-based regularization approach.

Ex Output:

Neumann networks are an end-to-end, sample-efficient learning approach to solving linear inverse problems in imaging that are compatible with the MSE optimal approach and admit an extension to patch-based learning.