In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: Recurrent Neural Networks (RNNs), and specifically a variant with Long ShortTerm Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data. However, while LSTMs provide exceptional results in practice, the source of their performance and their limitations remain rather poorly understood. Using character-level language models as an interpretable testbed, we aim to bridge this gap by providing a comprehensive analysis of their representations, predictions and error types. In particular, our experiments reveal the existence of interpretable cells that keep track of long-range dependencies such as line lengths, quotes and brackets. Moreover, an extensive analysis with finite horizon n-gram models suggest that these dependencies are actively discovered and utilized by the networks. Finally, we provide detailed error analysis that suggests areas for further study.

Output: Visualizing and Understanding Recurrent Networks


Input: Consider Input: Most Software Defined Networks (SDN) traffic engineering applications use excessive and frequent global monitoring in order to find the optimal Quality-of-Service (QoS) paths for the current state of the network. In this work, we present the motivations, architecture and initial evaluation of a SDN application called Cognitive Routing Engine (CRE) which is able to find near-optimal paths for a user-specified QoS while using a very small monitoring overhead compared to global monitoring which is required to guarantee that optimal paths are found. Smaller monitoring overheads bring the advantage of smaller response time for the SDN controllers and switches. The initial evaluation of CRE on a SDN representation of the GEANT academic network shows that it is possible to find near-optimal paths with a small optimality gap of 1.65% while using 9.5 times less monitoring.

Output: Towards a Cognitive Routing Engine for Software Defined Networks


Input: Consider Input: We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms for minimizing such functions. Our results imply that these efficient algorithms are statistically stable and also generalize well. In particular, we derive fast rates which resemble the bounds that are often attained in the strongly convex setting. We specify our bounds to Principal Component Analysis and Independent Component Analysis. Our results and techniquesmay pave the way for statistical analyses of additional strict saddle problems.


Output: Fast Rates for Empirical Risk Minimization of Strict Saddle Problems