, an encoder first reads variable-length source sentences and encodes them into a sequence of vectors, then a decoder generates a target translation from the sequence of source vectors. Although NMT is an emerging machine translation approach, the translation process of a document in NMT is similar to conventional statistical machine translation (SMT), treating the document as a bag of sentences and ignoring cross-sentence dependencies.
Sentences are the constituent elements of paragraphs. harper1965studies argues that sentences possess two attributes: continuity that maintains consistency with other sentences and development that introduces new information. For any adjacent sentences of a well-formed text, they tend to have considerable degree of continuity, which is usually described and measured at two levels: cohesion at the surface level and coherence at the underlying level. These two continuity metrics are two well-known means to estalish such inter-sentence links within a text. harper1965studies finds that word recurrence, as the most common device of cohesion, occurs in 70% of adjacent sentence pairs. Xiong2015Topic show that about 60% of sentences have the same topics (coherence) as those of the documents where these sentences occur.
Such inter-sentence dependencies can and should be used to help document-level machine translation. In the literature, a variety of models have been proposed to capture these dependencies in the context of SMT, such as cache-based language and translation models [Tiedemann2010, Gong et al.2011], topic-based coherence model [Xiong and Zhang2013] and lexical cohesion model [Xiong et al.2013]. However, integrating inter-sentence information into an NMT system is still an open problem.
In this paper, we propose a simple yet effective approach to model the inter-sentence information for NMT. In order to capture the connection between two adjacent sentences, i.e. the preceding sentence and current sentence, we first use the same encoder to encode the two adjacent sentences at the same time to form a context vector a for the preceding sentence and a context vector b for current sentence. Then, we introduce a gate mechanism to combine a and b into the final context vector, which is further used to update the hidden states of the decoder. In this way, we can model the links and dependencies between adjacent sentences. To some extent, our approach models the inter-sentence relationship from the underlying semantic coherence perspective.
On the NIST Chinese-English translation tasks, our experimental results show that the proposed approach can achieve significant improvements of up to 2.0 BLEU points over the NMT baseline.
2 Related Work
In the literature, a series of document-level translation models have been proposed for conventional SMT. Just to name a few, gong2011cache propose a cache-based approach to document-level translation, which includes three caches, a dynamic cache, a static cache and a topic cache to capture various kind of document-level information. hardmeier2012document present a beam search decoding procedure for phrase-based SMT with features modeling cross-sentence dependencies. xiong2013topic propose a topic-based coherence model to produce discourse coherence for document translation. xiong2013modeling present a lexical cohesion model to capture lexical cohesion for document-level translation.
In neural language models, inter-sentence connections can be captured in a contextual model. For example, Lin2015Hierarchical propose a hierarchical recurrent neural network (HRNN) language model for document modeling, consisting of a sentence-level and word-level language model, and use the proposed model to model sentence-level coherence. In speech recognition, as input speech signals can contain thousands of frames, chan2016listen employ Bidirectional Long Short Term Memory with a pyramidal structure to capture the context of a large number of input time steps. Wang2016LARGER introduce a late fusion method to incorporate corpus-level discourse information into recurrent language modeling.
In neural conversation systems, links between multi-turn conversations are usually modeled with hierarchical neural networks. Serban2015Building use a hierarchical recurrent encoder-decoder(HRED) to model the dialogue into two-level hierarchy: a sequence of utterances and a sequence of words. The proposed model can track states over many utterances to generate context-aware multiple rounds of dialogue. Serban2016A further propose a HRED model with an additional component: a high-dimensional stochastic latent variable at every dialogue turn to sample a vaussian variable as input to the decoder.
It is natural to adapt the HRED model to document-level NMT. However, document boundaries are usually missing in bilingual training corpora, indicating that we do not have sufficient data to train the sentence-level hierarchy. In our proposed gate model, we do not need entire documents to train the NMT model. We only use pairs of two adjacent sentences to train the gate. Furthermore, each sentence in a sentence pair can be used twice: one as a preceding sentence and the other as a current sentence. Additionally, in order to reduce the number of extra parameters, we use the same encoder to encode the adjacent sentences, which can also keep the semantic consistency for the same source sentence.
3 Neural Machine Translation
In this section, we briefly describle the atttention-based NMT model proposed in [Bahdanau et al.2015].
In their framework, the encoder encodes a source sentence as a sequence of vectors with bi-directional RNNs. The forward RNN reads the source sentence from left to right and the backward RNN reads the source sentence in an inverse direction. The hidden states in the forward RNN can be computed as follows:
is a non-linear function, here defined as a gated recurrent unit (GRU)[Chung et al.2014]. Similarly, Hidden states of the backward RNN can be calculated. The forward and backward hidden states are concatenated into the final annotation vectors . The decoder is also an RNN that predicts the next word given the context vector , the hidden state and the previously generated word sequence
. The probability of the next wordis calculated as follows:
is a softmax layer,is the state of decoder RNN at time step computed as
where is a function, the same as function used in the encoder. The context vector is calculated as a weighted sum of all hidden states of the encoder as follows:
where is the weight of each hidden state
computed by the attention model,is a feedforward neural network with a single hidden layer.
We also implement an NMT system which adopts feedback attention [Wang et al.2016b, Wang et al.2016a], which will be referred to as RNNSearch in this paper. In the feedback attention, is computed as follows:
where . The hidden state of the decoder is updated as follows:
In this paper, our proposed model is implemented on the top of RNNSearch system.
4 The Inter-Sentence Gate Model
In this section, we will elaborate the proposed inter-sentence gate model, which we refer to as . Figure 1 shows the entire architecture of our NMT with the inter-sentence gate. For notational convenience, we denote two adjacent sentences as A and B: A for the preceding sentence and B for the current sentence.
We employ the same encoder to encode the adjacent sentence A and B into hidden vector representations and respectively. We then use the attention network described in Equation (4) of Section 3 to compute their context representations and .
4.2 Inter-Sentence Gate Model
When we translate the current sentence B, we have to make sure that the decoder is provided with sufficient information from sentence B, and at the same time, with helpful imformation from the preceding sentence A. In other words, we need a mechanism to control the scale of information flowing from the sentence A and sentence B to the decoder. Inspired by the success of gated units in RNN [Chung et al.2014], we propose an inter-sentence gate to control the amount of information flowing from A and B. Formally, we employ a sigmoid neural network layer and an element-wise multiplication operation, as illustrated in Figure 2. Similarly, tu2016context also propose a gating mechanism to combine source and target contexts. The gate framework assigns element-wise weights to the input signals, calculated by
is a logistic sigmoid function, and, , are the parameter matrix.
Next, we integrate the inter-sentence gate into the decoder to decide the amount of context information used in producing the decoder hidden state at each time step. In this way, we want the hidden states of the decoder to store the inter-sentence context information. The framework of updating the hidden state of the decoder at time step is illustrated in Figure 2. The decoder hidden state is computed as follows:
where is an element-wise multiplication, is the parameter matrix, and is the inter-sentence gate computed by Equation (10).
The conditional probability of the next word is calculated as follows:
where is the context vector of the current sentence B.
Our aim is to translate the current sentence B with the additional information from the preceding sentence A. We do not want to have the excessive impact of the preceding sentence on the translation output of the current sentence. Therefore, in the stage of generating the next word, we just use the context .
We carried out a series of Chinese-to-English translation experiments to evaluate the effectiveness of the proposed inter-sentence gate model on document-level NMT and conducted in-depth analyses on experiment results and translations.
5.1 Experimental Settings
We selected corpora LDC2003E14, LDC2004T07, LDC2005T06, and LDC2005T10 as our bilingual training data, where document boundaries are kept. We also used all data from the corpus LDC2004T08 (Hong Kong Hansards/Laws/News). In total, our training data contain 103,236 documents and 2.80M sentences. Averagely, each document consists of 28.4 sentences. We chose NIST05 dataset as our development set, and NIST02, NIST03, NSIT04, NIST06, NIST08 as our test sets. We used case-insensitive BLEU-4 as our evaluation metric. We compared ourwith the following two systems:
Moses [Koehn et al.2007]: an open phrase-based translation system with its default setting.
RNNSearch: our new implementation of NMT system with the feedback attention as described in Section 3.
For Moses, we used the full training data (parallel corpus) to train the model. Word alignments were produced by GIZA++ [Och and Ney2000]. We ran GIZA++ on the corpus in both directions, and merged alignments in two directions with “grow-diag-final” refinement rule [Koehn et al.2005]. We trained a 5-gram language model on the Xinhua portion of the Gigaword corpus using SRILM Toolkit with a modified Kneser-Ney smoothing.
For RNNSearch, we used the parallel corpus to train the attention-based NMT model. The encoder of RNNSearch consists of a forward (1000 hidden unit) and backward (1000 hidden unit) recurrent neural network. The maximum length of sentences that we used to train NMT in our experiments was set to 50 for both the Chinese and English sides. We used the most frequent 30K words for both Chinese and English, covering approximately 99.0% and 99.2% of the data in the two languages respectively. We replaced rare words with a special token “UNK”. We also adopted the dropout technique. Dropout is applied only on the output layer and the dropout rate was set to 0.5. All the other settings are the same as the setting up described by bahdanau2015neural. Once the NMT model was trained, we employed a beam search algorithm to find possible translations with high probabilities. We set the beam width to 10.
For the proposed model, we implemented it on the top of RNNSearch. We used tuples (x, before-x, y) as input of , where x and y are a parallel sentence pair, before-x is the previous sentence of source sentence x in the same document111 We obtain tuples (x, before-x, y) from the training corpus. During the acquisition of these tuples, we follow two constraints. First, we discard the tuple (x,before-x,y) if there is a big difference in the length of the sentence x and before-x. For example, sentence x or before-x is a date expression at the end of a document or an organization name at the beginning of a document. Second, the length of any element in a tuple (x, before-x, y) is not longer than 50. . As the first sentence of a document does not have before-x, we used the stop symbol to form the sentence s = (eos, eos, eos) as the before-x. We used a simple pre-training strategy to train our model: training the regular attention-based NMT model using our implementation of RNNSearch, and then using its parameters to initialize the parameters of the proposed model, except for those related to the operations of the inter-sentence gate.
We used the stochastic gradient descent algorithm with mini-batch and Adadelta[Zeiler2012] to train the NMT model. The mini-batch was set to 80 sentences and decay rates and of Adadelta were set to 0.95 and , respectively.
|RNNSearch + concat||21.81||18.72||19.44||16.11||16.60||9.81|
5.2 Experimental Results
Table 1 shows the results of different NMT systems measured in terms of BLEU score. From the table, we can find that our implementation RNNSearch using the feedback attention and dropout outperforms Moses by 2.65 BLEU points. The proposed model achieves an average gain of 1.33 BLEU points over RNNSearch on all test sets. And it outperforms Moses by 3.98 BLEU points.
One might use the concatenation of two neighboring source sentences as input of RNNSearch to explore the information of the preceding sentence. However, this will degenerate translation quality as shown in Table 2. The main reason is that the conventional NMT has difficulties in translating long sentences [Pougetabadie et al.2014]. Thus，we conclude that the information of preceding sentences cannot be directly explored via concatenation.
5.3 Effect of the Inter-Sentence Gate
In order to examine the effectiveness of the proposed inter-sentence gate and inter-sentence information from before-x, we also conducted three additional validation experiments in the test sets: (1) we set all before-x to NULL (the before-x sentence consists of only stop symbols). (2) we set to the fixed vector value 0 for to block the inter-sentence gate mechanism. (3) we set the context vector of before-x to a random vector, the purpose of which is to test whether the information of the preceding sentence has bad influence on the translation of the current sentence when the preceding sentence is not quite related with the current sentence, for example, a topic change happens between x and before-x. The results are shown in Table 3, from which can find that:
When we set before-x as NULL (+NULL in Table 3), the performance has an obvious decline comparing with that of , but is still better than RNNSearch in term of BLEU score. We conjecture that the reasons for this are twofold. First, in the training process, when before-x dose not exist for the first sentence of a document, we set before-x to a NULL sentence, which makes model learn the relevant capabilities. That is to say, treats all sentences in the test sets as the first sentences of documents, where some sentences are correctly handled while others not. Second, the gate mechanism assigns a pretty low rate for NULL before-x during context combination.
When we set the gate weight vector to a fixed all-zero vector (+=0 in Table 3), blocks the inter-sentence information from before-x. From the Table 3, we find a huge loss in performance. The (+=0) is even worse than RNNSearch by 2.31 BLEU points. Although the preceding sentence information is not used, this (+=0) is not exactly the baseline RNNSearch. There are two groups of parameters in : one group of parameters (new parameters) are related with the inter-sentence gate and the other group of parameters (old parameters) are from RNNSearch but have been optimized towards the maximum usage of inter-sentence information. When the inter-sentence gate is closed, old parameters are not able to guide the decoder to generate translations that best use the current sentence information. That is the reason why this result is even worse than RNNSearch.
When we set the context vector
of before-x to a random vector (+RV in Table 3), sampled from a uniform distribution between -1 and 1, the performance is worse than the baseline RNNSearch by 0.46 BLEU points. Setting theto a random vector, the information from the pseudo preceding sentence becomes meaningless, and even has a bad or uncorrelated impact on the translation of the current sentence. However, the drop of the performance is not as big as that of (+=0). This suggests that the gate mechanism is able to effectively shield these useless and counteractive information from a pseudo and random preceding sentence.
The three experiments further demonstrate that the proposed inter-sentence gate is able to detect useful information for translation and block unrelated information and reconfirm that inter-sentence information is useful for translation.
5.4 Analysis on Inter-Sentence Attention
Many studies [Bahdanau et al.2015, Luong et al.2015] on attention-based NMT have proved that attention networks are able to detect alignments between parallel sentence pairs. In our model, we use two attention networks: the first is built for the correspondences between the current source sentence and its target translation and the second for the correspondences between the preceding sentence and the target translation of the current sentence. We are interested in what correspondences the second attention network detect.
We use the entropy as the evaluation criterion to measure how attention weights distribute over words in the preceding sentence before-x for a target word in the translation of the current sentence x. If the attention distribution is even, the entropy will be large. Otherwise, the entropy is small, it suggests that the attention distribution is uneven and that the decoder pays attention to one or several particular words in the preceding sentence when generating a target word for the current sentence. The entropy is computed as follows:
We calculated entropy values in two cases:
The before-x is a NULL sentence, being composed of stop symbols.
The before-x is an ordinary sentence.
If before-x is NULL, it cannot provide useful information except for the indicator of being the first sentence of a document. The attention weight distribution over stop symbols in before-x when generating a target word is supposed to be uniform. Figure 3 exactly visualizes such a case when translating the first sentence in a document. The entropy value in Figure 3 ranges from 1.44 to 1.58 while the entire curve is quite smooth.
Figure 4 demonstrates the second case with an example (in Table 4) where some words in the preceding sentence reoccur in the current sentence. When the model generates the target translation for “非洲国家(feizhou guojia)” and “非洲(feizhou)”, the entropy significantly drops as these words have occurred both in the preceding and current sentence. This indicates that the attention network in successfully captures this word repetition (the most common lexical cohesion device) and convey such an inter-sentence relation collectively with the proposed inter-sentence gate to the prediction of target words via hidden states of the decoder.
|Before-x||进入 新 世纪 后 ， 经济 全球化 成为 非洲 国家面临 的 一个 重大 而 严峻 的 挑战 。|
|X||非洲 国家领导人 越来越 清楚 地 认识 到,非洲再也 不 能 坐失良机 , 应 奋起 寻求 应对 之 策 。|
|the leaders of the african countries have become more and more clearly aware that africa can no longer be able to UNK and take the initiative to pursue countermeasures.|
5.5 Analysis on Translation Coherence
We want to further study how the proposed inter-sentence gate model influence coherence in document translation. For this, we follow Lapata2005Automatic to measure coherence as sentence similarity. First, each sentence is represented by the mean of the distributed vectors of its words. Second, the similarity between two sentences is determined by the cosine of their means.
where , and is the vector for word .
We use Word2Vec222https://code.google.com/p/word2vec/ to obtain the distributed vectors of words and English Gigaword fourth Edition as training data to train Word2Vec. We consider that embeddings from word2vec trained on large monolingual corpus can well encode semantic information of words. We set the vectors of words to 400.
Table 5 shows the average cosine similarity of adjacent sentences in test sets. From the table, we can find that themodel produces better coherence in document translation than RNNSearch in term of cosine similarity.
In order to better reflect the performance of the model about coherence, we also provide two examples displayed in Table 6 to verify the impact of inter-sentence information on document-level NMT. In the first example, source x does not have enough context information to correctly translate word “动作(dongzuo)”. Fortunately, the before-x provides extra information: the background is about politices, which guide the decoder to select a better translation “action” for “动作(dongzuo)”. In the second example, RNNSearch generates different translations for “驻韩(zhuhan)” and “驻南韩(zhunanhan)”. generates consistent translations for these two different words but with the same meaning.
|before-x||自从 上个月 巴勒斯坦 强人 阿拉法特 去 逝 后 , 国际 社会 重新 继续 恢复 中东 和平 政策 的 推动 , 以期 早日 结束 以 巴 之间 多年 的 流血 冲突 。|
|x||中东 新闻社 说 , 官员 预测 「 准备 工作 将 会 进行 到 七月 , 然后 再 展开 政治动作 」|
|RNNSearch||the UNK news agency said that the officials forecast that “preparations will be made in july and then political moves will be taken again.”|
|the middle east news agency said, the officials forecast that “preparations will be made in july and then another political action will be taken.”|
|before-x||美军 第八 军团 司令 康贝尔 中 将 发表 声明 , 此 一 冻结 调防 军令 旨在 确保 驻 南 韩美军 实力 。|
|x||根据 南韩 与 美国 签订 的 协 防 条约 , 目前 驻 南 韩 美军 人数 约 三万七千 人 , 自 去年 十二月 北 韩 发展 核子 计 画 野心 曝光 以来 , 驻 韩美军 一直 保持 警戒 。|
|RNNSearch||according to the UNK treaty signed between south korea and the united states, the number of us troops in south korea is about UNK, and the us troops stationed in the rok since december last year have been kept alert.|
|according to the UNK treaty signed between south korea and the united states, the number of us troops stationed in south korea is about UNK. the us troops stationed in south korea have been maintaining vigilance since last december last year when north korea’s nuclear plan was exposed.|
6 Conclusion and Future Work
In this paper, we have presented a novel inter-sentence gate model for NMT to deal with document-level translation. Experimental results show that the model achieves consistent and significant improvements in translation quality over strong NMT baselines. In-depth analyses further demonstrate that the proposed model inter-sentence gate is able to capture cross-sentence dependencies and lexical cohesion devices.
The proposed inter-sentence gate model only uses source-side information to capture document-level information for translation. In the future, we would like to integrate target-side information into document-level NMT.
The present research was supported by the National Natural Science Foundation of China (Grant No. 61622209). We would like to thank three anonymous reviewers for their insightful comments.
- [Bahdanau et al.2015] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2015. Neural machine translation by jointly learning to align and translate. In Proceedings of ICLR.
- [Chan et al.2016] William Chan, Navdeep Jaitly, Quoc Le, and Oriol Vinyals. 2016. Listen, attend and spell: A neural network for large vocabulary conversational speech recognition. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 4960–4964. IEEE.
- [Cho et al.2014] Kyunghyun Cho, Bart Van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio. 2014. On the properties of neural machine translation: Encoder-decoder approaches. In Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation.
[Chung et al.2014]
Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio.
Empirical evaluation of gated recurrent neural networks on sequence
Presented in NIPS 2014 Deep Learning and Representation Learning Workshop.
[Gong et al.2011]
Zhengxian Gong, Min Zhang, and Guodong Zhou.
Cache-based document-level statistical machine translation.
Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 909–919. Association for Computational Linguistics.
- [Hardmeier et al.2012] Christian Hardmeier, Joakim Nivre, and Jörg Tiedemann. 2012. Document-wide decoding for phrase-based statistical machine translation. In Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pages 1179–1190. Association for Computational Linguistics.
- [Harper1965] Kenneth E Harper. 1965. Studies in inter-sentence connection. Technical report, DTIC Document.
- [Koehn et al.2005] Philipp Koehn, Amittai Axelrod, Alexandra Birch, Chris Callison-Burch, Miles Osborne, David Talbot, and Michael White. 2005. Edinburgh system description for the 2005 iwslt speech translation evaluation. In IWSLT, pages 68–75.
- [Koehn et al.2007] Philipp Koehn, Hieu Hoang, Alexandra Birch, Chris Callison-Burch, Marcello Federico, Nicola Bertoldi, Brooke Cowan, Wade Shen, Christine Moran, Richard Zens, et al. 2007. Moses: Open source toolkit for statistical machine translation. In Proceedings of the 45th annual meeting of the ACL on interactive poster and demonstration sessions, pages 177–180. Association for Computational Linguistics.
[Lapata and Barzilay2005]
Mirella Lapata and Regina Barzilay.
Automatic evaluation of text coherence: models and representations.
International Joint Conference on Artificial Intelligence, pages 1085–1090.
- [Lin et al.2015] Rui Lin, Shujie Liu, Muyun Yang, Mu Li, Ming Zhou, and Sheng Li. 2015. Hierarchical recurrent neural network for document modeling. In Conference on Empirical Methods in Natural Language Processing, pages 899–907.
- [Luong et al.2015] Minh-Thang Luong, Hieu Pham, and Christopher D Manning. 2015. Effective approaches to attention-based neural machine translation. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1412–1421.
- [Och and Ney2000] Franz Josef Och and Hermann Ney. 2000. Improved statistical alignment models. In Proceedings of the 38th Annual Meeting on Association for Computational Linguistics, pages 440–447. Association for Computational Linguistics.
- [Pougetabadie et al.2014] Jean Pougetabadie, Dzmitry Bahdanau, Bart Van Merrienboer, Kyunghyun Cho, and Yoshua Bengio. 2014. Overcoming the curse of sentence length for neural machine translation using automatic segmentation. Eprint Arxiv.
- [Serban et al.2015] Iulian V. Serban, Alessandro Sordoni, Yoshua Bengio, Aaron Courville, and Joelle Pineau. 2015. Building end-to-end dialogue systems using generative hierarchical neural network models. Association for the Advancement of Artificial Intelligence, (4).
- [Serban et al.2016] Iulian Vlad Serban, Alessandro Sordoni, Ryan Lowe, Laurent Charlin, Joelle Pineau, Aaron Courville, and Yoshua Bengio. 2016. A hierarchical latent variable encoder-decoder model for generating dialogues.
- [Sutskever et al.2014] Ilya Sutskever, Oriol Vinyals, and Quoc V Le. 2014. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pages 3104–3112.
- [Tiedemann2010] Jörg Tiedemann. 2010. Context adaptation in statistical machine translation using models with exponentially decaying cache. In Proceedings of the 2010 Workshop on Domain Adaptation for Natural Language Processing, pages 8–15. Association for Computational Linguistics.
- [Tu et al.2016] Zhaopeng Tu, Yang Liu, Zhengdong Lu, Xiaohua Liu, and Hang Li. 2016. Context gates for neural machine translation. arXiv preprint arXiv:1608.06043.
- [Wang and Cho2016] Tian Wang and Kyunghyun Cho. 2016. Larger-context language modelling with recurrent neural network. In Meeting of the Association for Computational Linguistics, pages 1319–1329.
- [Wang et al.2016a] Mingxuan Wang, Zhengdong Lu, Hang Li, and Qun Liu. 2016a. Memory-enhanced decoder for neural machine translation. arXiv preprint arXiv:1606.02003.
- [Wang et al.2016b] Xing Wang, Zhengdong Lu, Zhaopeng Tu, Hang Li, Deyi Xiong, and Min Zhang. 2016b. Neural machine translation advised by statistical machine translation. AAAI.
- [Xiong and Zhang2013] Deyi Xiong and Min Zhang. 2013. A topic-based coherence model for statistical machine translation. In AAAI.
- [Xiong et al.2013] Deyi Xiong, Guosheng Ben, Min Zhang, Yajuan Lv, and Qun Liu. 2013. Modeling lexical cohesion for document-level machine translation. In IJCAI.
- [Xiong et al.2015] Deyi Xiong, Min Zhang, and Xing Wang. 2015. Topic-based coherence modeling for statistical machine translation. IEEE/ACM Transactions on Audio Speech and Language Processing, 23(3):483–493.
- [Zeiler2012] Matthew D Zeiler. 2012. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.