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.

Example Input: Recently, sequence-to-sequence model by using encoder-decoder neural network has gained popularity for automatic speech recognition (ASR). The architecture commonly uses an attentional mechanism which allows the model to learn alignments between source speech sequence and target text sequence. Most attentional mechanisms used today is based on a global attention property which requires a computation of a weighted summarization of the whole input sequence generated by encoder states. However, it is computationally expensive and often produces misalignment on the longer input sequence. Furthermore, it does not fit with monotonous or left-to-right nature in speech recognition task. In this paper, we propose a novel attention mechanism that has local and monotonic properties. Various ways to control those properties are also explored. Experimental results demonstrate that encoder-decoder based ASR with local monotonic attention could achieve significant performance improvements and reduce the computational complexity in comparison with the one that used the standard global attention architecture.
Example Output: Local Monotonic Attention Mechanism for End-to-End Speech Recognition

Example Input: Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.
Example Output: Existential Rule Languages with Finite Chase: Complexity and Expressiveness

Example Input: Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g. high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.
Example Output:
Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications