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.

[Q]: The weighted Maximum Satisfiability problem (weighted MAX-SAT) is a NP-hard problem with numerous applications arising in artificial intelligence. As an efficient tool for heuristic design, the backbone has been applied to heuristics design for many NP-hard problems. In this paper, we investigated the computational complexity for retrieving the backbone in weighted MAX-SAT and developed a new algorithm for solving this problem. We showed that it is intractable to retrieve the full backbone under the assumption that NP P . Moreover, it is intractable to retrieve a fixed fraction of the backbone as well. And then we presented a backbone guided local search (BGLS) with Walksat operator for weighted MAX-SAT. BGLS consists of two phases: the first phase samples the backbone information from local optima and the backbone phase conducts local search under the guideline of backbone. Extensive experimental results on the benchmark showed that BGLS outperforms the existing heuristics in both solution quality and runtime.
[A]: Approximating the Backbone in the Weighted Maximum Satisfiability Problem

[Q]: We study multi-turn response generation in chatbots where a response is generated according to a conversation context. Existing work has modeled the hierarchy of the context, but does not pay enough attention to the fact that words and utterances in the context are differentially important. As a result, they may lose important information in context and generate irrelevant responses. We propose a hierarchical recurrent attention network (HRAN) to model both aspects in a unified framework. In HRAN, a hierarchical attention mechanism attends to important parts within and among utterances with word level attention and utterance level attention respectively. With the word level attention, hidden vectors of a word level encoder are synthesized as utterance vectors and fed to an utterance level encoder to construct hidden representations of the context. The hidden vectors of the context are then processed by the utterance level attention and formed as context vectors for decoding the response. Empirical studies on both automatic evaluation and human judgment show that HRAN can significantly outperform state-of-the-art models for multi-turn response generation.
[A]: Hierarchical Recurrent Attention Network for Response Generation

[Q]: Training generative adversarial networks is unstable in high-dimensions when the true data distribution lies on a lower-dimensional manifold. The discriminator is then easily able to separate nearly all generated samples leaving the generator without meaningful gradients. We propose training a single generator simultaneously against an array of discriminators, each of which looks at a different random low-dimensional projection of the data. We show that individual discriminators then provide stable gradients to the generator, and that the generator learns to produce samples consistent with the full data distribution to satisfy all discriminators. We demonstrate the practical utility of this approach experimentally, and show that it is able to produce image samples with higher quality than traditional training with a single discriminator.
[A]:
Stabilizing GAN Training with Multiple Random Projections