You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We propose minimum risk training for end-to-end neural machine translation. Unlike conventional maximum likelihood estimation, minimum risk training is capable of optimizing model parameters directly with respect to arbitrary evaluation metrics, which are not necessarily differentiable. Experiments show that our approach achieves significant improvements over maximum likelihood estimation on a state-of-the-art neural machine translation system across various languages pairs. Transparent to architectures, our approach can be applied to more neural networks and potentially benefit more NLP tasks.

Cited Abstract(s):
[1]: ROUGE stands for Recall-Oriented Understudy for Gisting Evaluation. It includes measures to automatically determine the quality of a summary by comparing it to other (ideal) summaries created by humans. The measures count the number of overlapping units such as n-gram, word sequences, and word pairs between the computer-generated summary to be evaluated and the ideal summaries created by humans. This paper introduces four different ROUGE measures: ROUGE-N, ROUGE-L, ROUGE-W, and ROUGE-S included in the ROUGE summarization evaluation package and their evaluations. Three of them have been used in the Document Understanding Conference (DUC) 2004, a large-scale summarization evaluation sponsored by NIST.

[2]: Automatic headline generation is an important research area within text summarization and sentence compression. Recently, neural headline generation models have been proposed to take advantage of well-trained neural networks in learning sentence representations and mapping sequence to sequence. Nevertheless, traditional neural network encoder utilizes maximum likelihood estimation for parameter optimization, which essentially constraints the expected training objective within word level instead of sentence level. Moreover, the performance of model prediction significantly relies on training data distribution. To overcome these drawbacks, we employ minimum risk training strategy in this paper, which directly optimizes model parameters with respect to evaluation metrics and statistically leads to significant improvements for headline generation. Experiment results show that our approach outperforms state-of-the-art systems on both English and Chinese headline generation tasks.
More recently, our approach has been successfully applied to summarization [2] . They optimize neural networks for headline generation with respect to ROUGE [1] and also achieve significant improvements, confirming the effectiveness and applicability of our approach.