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: We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, they can be a powerful tool for unsupervised representation learning from video or graph-structured data. We cast training Spectral Inference Networks as a bilevel optimization problem, which allows for online learning of multiple eigenfunctions. We show results of training Spectral Inference Networks on problems in quantum mechanics and feature learning for videos on synthetic datasets. Our results demonstrate that Spectral Inference Networks accurately recover eigenfunctions of linear operators and can discover interpretable representations from video in a fully unsupervised manner.

Output: We show how to learn spectral decompositions of linear operators with deep learning, and use it for unsupervised learning without a generative model.

Input: Consider Input: We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.

Output: We introduce a statistical approach to assessing neural network robustness that provides an informative notion of how robust a network is, rather than just the conventional binary assertion of whether or not of property is violated.

Input: Consider Input: Depthwise separable convolutions reduce the number of parameters and computation used in convolutional operations while increasing representational efficiency.
They have been shown to be successful in image classification models, both in obtaining better models than previously possible for a given parameter count (the Xception architecture) and considerably reducing the number of parameters required to perform at a given level (the MobileNets family of architectures). Recently, convolutional sequence-to-sequence networks have been applied to machine translation tasks with good results. In this work, we study how depthwise separable convolutions can be applied to neural machine translation. We introduce a new architecture inspired by Xception and ByteNet, called SliceNet, which enables a significant reduction of the parameter count and amount of computation needed to obtain results like ByteNet, and, with a similar parameter count, achieves better results.
In addition to showing that depthwise separable convolutions perform well for machine translation, we investigate the architectural changes that they enable: we observe that thanks to depthwise separability, we can increase the length of convolution windows, removing the need for filter dilation. We also introduce a new super-separable convolution operation that further reduces the number of parameters and computational cost of the models.
Output: Depthwise separable convolutions improve neural machine translation: the more separable the better.