Abstract The Neural Machine Translation (NMT) model is essentially a joint language model conditioned on both the source sentence and partial translation. Therefore, the NMT model naturally involves the mechanism of the Language Model (LM) that predicts the next token only based on partial translation. Despite its success, NMT still suffers from the hallucination problem, generating fluent but inadequate translations. The main reason is that NMT pays excessive attention to the partial translation while neglecting the source sentence to some extent, namely overconfidence of the LM. Accordingly, we define the Margin between the NMT and the LM , calculated by subtracting the predicted probability of the LM from that of the NMT model for each token. The Margin is negatively correlated to the overconfidence degree of the LM. Based on the property, we propose a Margin -based Token-level Objective (MTO) and a Margin -based Sentence-level Objective (MSO) to maximize the Margin for preventing the LM from being overconfident. Experiments on WMT14 English-to-German, WMT19 Chinese-to-English, and WMT14 English-to-French translation tasks demonstrate the effectiveness of our approach, with 1.36, 1.50, and 0.63 BLEU improvements, respectively, compared to the Transformer baseline. The human evaluation further verifies that our approaches improve translation adequacy as well as fluency. 1 1 Introduction Neural Machine Translation (NMT) has achieved great success in recent years (Sutskever et al., 2014;  Equal contribution. This work was done when Mengqi Miao was interning at Pattern Recognition Center, WeChat AI, Tencent Inc, China.  Corresponding author. 1 Code is available at https://github.com/Mlair 77/nmt adequacy Cho et al., 2014; Bahdanau et al., 2014; Luong et al., 2015; Vaswani et al., 2017; Meng and Zhang, 2019; Zhang et al., 2019a; Yan et al., 2020b), which generates accurate and fluent translation through modeling the next word conditioned on both the source sentence and partial translation. However, NMT faces the hallucination problem, i.e., translations are fluent but inadequate to the source sentences. One important reason is that the NMT model pays excessive attention to the partial translation to ensure fluency while failing to translate some segments of the source sentence (Weng et al., 2020b), which is actually the overconfidence of the Language Model (LM). In the rest of this paper, the LM mentioned refers to the LM mechanism involved in NMT. Many recent studies attempt to deal with the inadequacy problem of NMT from two main aspects. One is to improve the architecture of NMT, such as adding a coverage vector to track the attention history (Tu et al., 2016), enhancing the cross-attention module (Meng et al., 2016, 2018; Weng et al., 2020b), and dividing the source sentence into past and future parts (Zheng et al., 2019). The other aims to propose a heuristic adequacy metric or objective based on the output of NMT. Tu et al. (2017) and Kong et al. (2019) enhance the model's reconstruction ability and increase the coverage ratio of the source sentences by translations, respectively. Although some researches (Tu et al., 2017; Kong et al., 2019; Weng et al., 2020b) point out that the lack of adequacy is due to the overconfidence of the LM, unfortunately, they do not propose effective solutions to the overconfidence problem. From the perspective of preventing the overconfidence of the LM, we first define an indicator of the overconfidence degree of the LM, called the Margin between the NMT and the LM , by subtracting the predicted probability of the LM from that of the NMT model for each token. A small Margin implies that the NMT might concentrate on the partial translation and degrade into the LM, i.e., the LM is overconfident. Accordingly, we propose a M argin -based T oken-level O bjective (MTO) to maximize the Margin . Furthermore, we observe a phenomenon that if target sentences in the training data contain many words with negative Margin , they always do not correspond to the source sentences. These data are harmful to model performance. Therefore, based on the MTO, we further propose a M argin -based S entence-level O bjective (MSO) by adding a dynamic weight function to alleviate the negative effect of these dirty data. We validate the effectiveness and superiority of our approaches on the Transformer (Vaswani et al., 2017), and conduct experiments on large-scale WMT14 English-to-German, WMT19 Chinese-to-English, and WMT14 English-to-French translation tasks. Our contributions are:  We explore the connection between inadequacy translation and the overconfidence of the LM in NMT, and thus propose an indicator of the overconfidence degree, i.e., the Margin between the NMT and the LM. Furthermore, to prevent the LM from being overconfident, we propose two effective optimization objectives to maximize the Margin , i.e., the Margin-based Token-level Objective (MTO) and the Margin-based Sentence-level Objective (MSO). Experiments on WMT14 English-to-German, WMT19 Chinese-to-English, and WMT14 English-to-French show that our approaches bring in significant improvements by +1.36, +1.50, +0.63 BLEU points, respectively. Additionally, the human evaluation verifies that our approaches can improve both translation adequacy and fluency. where y <t = { y 1 , y 2 , ..., y t  1 } is the partial translation before y t . From Eq. 1, the source sentence x and partial translation y <t are considered in the meantime, suggesting that the NMT model is essentially a joint language model and the LM is instinctively involved in NMT. Based on the encoder-decoder architecture, the encoder of NMT maps the input sentence x to hidden states. At time step t , the decoder of NMT employs the output of the encoder and y <t to predict y t . The training objective of NMT is to minimize the negative log-likelihood, which is also known as the cross entropy loss function: L NMTce =  T (cid:88) t =1 log p ( y t | y <t , x ) . (2) The LM measures the probability of a target sentence similar to NMT but without knowledge of the source sentence x : P ( y ) = T (cid:89) t =1 p ( y t | y <t ) . (3) The LM can be regarded as the part of NMT decoder that is responsible for fluency, only takes y <t as input. The training objective of the LM is almost the same as NMT except for the source sentence x : L LMce =  T (cid:88) t =1 log p ( y t | y <t ) . (4) The NMT model predicts the next word y t according to the source sentence x and meanwhile ensures that y t is fluent with the partial translation y <t . However, when NMT pays excessive attention to translation fluency, some source segments may be neglected, leading to inadequacy problem. This is exactly what we aim to address in this paper. In this section, we firstly define the Margin between the NMT and the LM (Section 3.1), which reflects the overconfidence degree of the LM. Then we put forward the token-level (Section 3.2) and sentence-level (Section 3.3) optimization objectives to maximize the Margin . Finally, we elaborate our two-stage training strategy (Section 3.4). When the NMT model excessively focuses on partial translation, i.e., the LM is overconfident, the NMT model degrades into the LM, resulting in hallucinated translations. To prevent the overconfidence problem, we expect that the NMT model outperforms the LM as much as possible in predicting golden tokens. Consequently, we define the Margin between the NMT and the LM at the t -th time step by the difference of the predicted probabilities of them: ( t ) = p NMT ( y t | y <t , x )  p LM ( y t | y <t ) , (5) where p NMT denotes the predicted probability of the NMT model, i.e., p ( y t | y <t , x ) , and p LM denotes that of the LM, i.e., p ( y t | y <t ) . The Margin ( t ) is negatively correlated to the overconfidence degree of the LM, and different values of the Margin indicate different cases:  If ( t ) is big, the NMT model is apparently better than the LM, and y t is strongly related to the source sentence x . Hence the LM is not overconfident. If ( t ) is medium, the LM may be slightly overconfident and the NMT model has the potential to be enhanced. If ( t ) is small, the NMT model might degrade to the LM and not correctly translate the source sentence, i.e., the LM is overconfident. 2 Note that sometimes, the model needs to focus more on the partial translation such as the word to be predicted is a determiner in the target language. In this case, although small ( t ) does not indicate the LM is overconfident, enlarging the ( t ) can still enhance the NMT model. Based on the Margin , we firstly define the Margin loss LM and then fuse it into the cross entropy loss function to obtain the M argin -based T oken-evel Optimization O bjective (MTO). Formally, we define the Margin loss LM to maximize the Margin as follow: LM = T (cid:88) t =1 (1  p NMT ( t )) M (( t )) , (6) where we abbreviate p NMT ( y t | y <t , x ) as p NMT ( t ) . M (( t )) is a function of ( t ) , namely Margin function, which is monotonically decreasing (e.g., 1  ( t ) ). Moreover, when some words have the same ( t ) but different p NMT ( t ) , their meanings are quite different: (1) If p NMT ( t ) is big, the NMT model learns the token well and does not need to focus on the Margin too much; (2) If p NMT ( t ) is 2 In addition, if p NMT ( y t | y <t , x ) is large, less attention will be paid to this data because y t has been learned well, which will be described in detail in Section 3.2. small, the NMT model is urgently to be optimized on the token thus the weight of M (( t )) should be enlarged. Therefore, as the weight of M (( t )) , 1  p NMT ( t ) enables the model treat tokens wisely. Variations of M () . We abbreviate Margin function M (( t )) as M () hereafter. A simple and intuitive definition is the Linear function: M () = 1   , which has the same gradient for different  . However, as illustrated in Section 3.1, different  has completely various meaning and needs to be treated differently. Therefore, we propose three non-linear Margin functions M () as follows:  Cube : (1   3 ) / 2 . Quintic (fifth power): (1   5 ) / 2 . Log : 1  log ( 1   1+ ) + 0 . 5 . where  is a hyperparamater for Log . As shown in Figure 1, the four variations 3 have quite different slopes. Specifically, the three nonlinear functions are more stable around  = 0 (e.g.,   [  0 . 5 , 0 . 5] ) than Linear , especially Quintic . We will report the performance of the four M () concretely and analyze why the three non-linear M () perform better than Linear in Section 5.4. Finally, based on LM , we propose the M argin based T oken-level O bjective (MTO): LT = L NMTce +  MLM , (7) where L NMTce is the cross-entropy loss of the NMT model defined in Eq. 2 and  M is the hyperparameter for the Margin loss LM . 3 In order to keep the range of M () roughly [0,1], we set Linear function to (1  ) / 2 . Furthermore, through analyzing the Margin distribution of target sentences, we observe that the target sentences in the training data which have many tokens with negative Margin are almost halluci-nations of the source sentences (i.e., dirty data), thus will harm the model performance. Therefore, based on MTO, we further propose the M argin based S entence-level O bjective (MSO) to address this issue. Compared with the LM, the NMT model predicts the next word with more prior knowledge (i.e., the source sentence). Therefore, it is intuitive that when predicting y t , the NMT model should predict more accurately than the LM, as follow: p NMT ( y t | y <t , x ) > p LM ( y t | y <t ) . Actually, the above equation is equivalent to ( t ) > 0 . The larger ( t ) is, the more the NMT model exceeds the LM. However, there are many tokens with negative Margin through analyzing the Margin distribution. We conjecture the reason is that the target sentence is not corresponding to the source sentence in the training corpus, i.e., the target sentence is a hallucination. Actually, we also observe that if a large proportion of tokens in a target sentence have negative Margin (e.g., 50%), the sentence is probably not corresponding to the source sentence, such as the case in Figure 2. These dirty data will harm the performance of the NMT model. where # { y t  y : ( t ) < 0 } denotes the number of tokens with negative ( t ) in y , and # { y t : y t  y } is the length of the target sentence y . When R ( x , y ) is larger than a threshold k (e.g., k =50%), the target sentence may be desperately inadequate, or even completely unrelated to the source sentence, as shown in Figure 2. In order to eliminate the impact of these seriously inadequate sentences, we ignore their loss during training by the M argin -based S entence-level O bjective (MSO): LS = IR ( x , y ) <k  LT , (10) where IR ( x , y ) <k is a dynamic weight function in sentence level. The indicative function IR ( x , y ) <k equals to 1 if R ( x , y ) < k , else 0, where k is a hyperparameter. LT is MTO defined in Eq. 7. IR ( x , y ) <k is dynamic at the training stage. During training, as the model gets better, its ability to distinguish hallucinations improves thus IR ( x , y ) <k becomes more accurate. We will analyze the changes of IR ( x , y ) <k in Section 5.4. Jointly Pretraining. The language model mechanism in NMT cannot be directly evaluated, thus we train an auxiliary LM to represent it. We pretrain them together using a fusion loss function: L pre = L NMTce +  LML LMce , (11) where L NMTce and L LMce are the cross entropy loss functions of the NMT model and the LM defined in Eq. 2 and Eq. 4, respectively. LM is a hyperparameter. Specifically, we jointly train them through sharing their decoders' embedding layers and their pre-softmax linear transformation layers (Vaswani et al., 2017). There are two reasons for joint training: (1) making the auxiliary LM as consistent as possible with the language model mechanism in NMT; (2) avoiding abundant extra parameters. Finetuning. We finetune the NMT model by minimizing the MTO ( LT in Eq. 7) and MSO ( LS in Eq. 10). 4 Note that the LM is not involved at the inference stage. 4 The LM can be fixed or trained along with the NMT after pretraining. Our experimental results show that continuous training the LM and fixing the LM have analogous performance during the finetuning stage. Therefore, we only report the results of keeping the LM fixed in this paper. We conduct experiments on three large-scale NMT tasks, i.e., WMT14 English-to-German (En  De), WMT14 English-to-French (En  Fr), and WMT19 Chinese-to-English (Zh  En). Datasets. For En  De, we use 4.5M training data. Following the same setting in (Vaswani et al., 2017), we use newstest2013 as validation set and newstest2014 as test set, which contain 3000 and 3003 sentences, respectively. For En  Fr, the training dataset contains about 36M sentence pairs, and we use newstest2013 with 3000 sentences as validation set and newstest2014 with 3003 sentences as test set. For Zh  En, we use 20.5M training data and use newstest2018 as validation set and new-stest2019 as test set, which contain 3981 and 2000 sentences, respectively. For Zh  En, the number of merge operations in byte pair encoding (BPE) (Sennrich et al., 2016a) is set to 32K for both source and target languages. For En  De and En  Fr, we use a shared vocabulary generated by 32K BPEs. Evaluation. We measure the case-sensitive BLEU scores using multi-bleu.perl 5 for En  De and En  Fr. For Zh  En, case-sensitive BLEU scores are calculated by Moses mteval-v13a.pl script 6 . Moreover, we use the paired bootstrap resampling (Koehn, 2004) for significance test. We select the model which performs the best on the validation sets and report its performance on the test sets for evaluation. Model and Hyperparameters. We conduct experiments based on the Transformer (Vaswani et al., 2017) and implement our approaches with the open-source tooklit Opennmt-py (Klein et al., 2017). Following the Transformer-Base setting in (Vaswani et al., 2017), we set the hidden size to 512 and the encoder/decoder layers to 6. All three tasks are trained with 8 NVIDIA V100 GPUs, and the batch size for each GPU is 4096 tokens. The beam size is 5 and the length penalty is 0.6. Adam optimizer (Kingma and Ba, 2014) is used in all the models. The LM architecture is the decoder of the Transformer excluding the cross-attention layers, sharing the embedding layer and the pre-softmax 5 https://github.com/moses-smt/mosesde coder/blob/master/scripts/generic/multi-bleu.perl 6 https://github.com/moses-smt/mosesde coder/blob/mast-er/scripts/generic/mteval-v13a.pl linear transformation with the NMT model. For En  De, Zh  En, and En  Fr, the number of training steps is 150K for jointly pretraining stage and 150K for finetuning 7 . During pretraining, we set  LM to 0.01 for all three tasks 8 . Experimental results shown in Appendix A indicate that the LM has converged after pretraining for all the three tasks. During finetuning, the Margin function M () in Section 3.2 is set to Quintic , and we will analyze the four M () in Section 5.4. M in Eq. 7 is set to 5, 8, and 8 on En  De, En  Fr and Zh  En, respectively. For MSO, the threshold k in Eq. 10 is set to 30% for En  De and Zh  En, 40% for En  Fr. The two hyperparameters (i.e.,  M and k ) are searched on validation sets, and the selection details are shown in Appendix B. The baseline model (i.e., vanilla Transformer) is trained for 300k steps for En  De, En  Fr and Zh  En. Moreover, we use a joint training model as our secondary baseline, namely NMT+LM, by jointly training the NMT model and the LM throughout the training stage with 300K steps. The training steps of all the models are consistent, thus the experiment results are strictly comparable. We first evaluate the main performance of our approaches (Section 5.1 and 5.2). Then, the human evaluation further confirms the improvements of translation adequacy and fluency (Section 5.3). Finally, we analyze the positive impact of our models on the distribution of Margin and explore how each fragment of our method works (Section 5.4). The results on WMT14 English-to-German (En  De) are summarized in Table 1. We list the results from (Vaswani et al., 2017) and several related competitive NMT systems by various methods, such as Minimum Risk Training (MRT) objective (Shen et al., 2016), Simple Fusion of NMT and LM (Stahlberg et al., 2018), optimizing adequacy metrics (Kong et al., 2019; Feng et al., 2019) and improving the Transformer architecture (Yang et al., 2018; Zheng et al., 2019; Yang et al., 2019; Weng et al., 2020b; Yan et al., 2020a). We re-7 The LM does not need to be state-of-the-art. The previous study of (Baziotis et al., 2020) has shown that a more powerful LM does not lead to further improvements to NMT. 8 The experimental results show that the model is insensitive to  LM . Therefore we make  LM consistent for all the three tasks. Similarly, we re-implement the Simple Fusion (Stahlberg et al., 2018) model. 9 Finally, the results of the joint training model NMT+LM, and models with our MTO and MSO objectives are reported. Compared with the baseline, NMT+LM yields +0.75 BLEU improvement. Based on NMT+LM, our MTO achieves further improvement with +0.50 BLEU scores, indicating that preventing the LM from being overconfident could significantly enhance model performance. Moreover, MSO performs better than MTO by +0.11 BLEU scores, which implies that the dirty data in the training dataset indeed harm the model performance, and the dynamic weight function IR ( x , y ) <k in Eq. 10 could reduce the negative impact. In conclusion, our approaches improve up to +1.36 BLEU scores on En  De compared with the Transformer baseline and substantially outperforms the existing NMT systems. The results demonstrate the effectiveness and superiority of our approaches. The results on WMT14 English-to-French (En  Fr) and WMT19 Chinese-to-English (Zh  En) are shown in Table 2. We also list the results of (Vaswani et al., 2017) and our reimplemented Transformer as the baselines. On En  Fr, our reimplemented result is higher than the result of (Vaswani et al., 2017), since we update 300K steps while Vaswani et al. (2017) only update 100K steps. Many studies obtain similar results to ours (e.g., 41.1 BLEU scores from (Ott et al., 2019)). Compared with the baseline, NMT+LM yields +0.07 and +0.15 BLEU improvements on En  Fr and Zh  En, respectively. The improvement of NMT+LM on En  De in Table 1 (i.e., +0.75) is greater than these two datasets. We conjecture the reason is that the amount of training data of En  De is much smaller than that of En  Fr and Zh  En, thus NMT+LM is more likely to improve the model performance on En  De. Compared with NMT+LM, our MTO achieves further improvements with +0.42 and +1.04 BLEU scores on En  Fr and Zh  En, respectively, which demonstrates the performance improvement is mainly due to our Margin -based objective rather than joint training. Moreover, based on MTO, our MSO further yields +0.14 and +0.31 BLEU improvements. In summary, our approaches improve up to +0.63 and +1.50 BLEU scores on En  Fr and Zh  En compared with the baselines, respectively, which demonstrates the effectiveness and generalizability of our approaches. We conduct the human evaluation for translations in terms of adequacy and fluency. Firstly, we ran-Model Adequacy Fluency Ave. domly sample 100 sentences from the test set of WMT19 Zh  En. Then we invite three annotators to evaluate the translation adequacy and fluency. Five scales have been set up, i.e., 1, 2, 3, 4, 5. For adequacy, 1 means totally irrelevant to the source sentence, and 5 means equal to the source sentence semantically. For fluency, 1 represents not fluent and incomprehensible; 5 represents very native. Finally, we take the average of the scores from the three annotators as the final score. The results of the baseline and our approaches are shown in Table 3. Compared with the NMT baseline, NMT+LM, MTO and MSO improve adequacy with 0.08, 0.22, and 0.37 scores, respectively. Most improvements come from our Margin -based methods MTO and MSO, and MSO performs the best. For fluency, NMT+LM achieves 0.2 improvement compared with NMT. Based on NMT+LM, MTO and MSO yield further improvements with 0.01 and 0.05 scores, respectively. Human evaluation indicates that our MTO and MSO approaches remarkably improve translation adequacy and slightly enhance translation fluency. Margin between the NMT and the LM. Firstly, we analyze the distribution of the Margin between the NMT and the LM (i.e.,  in Eq. 5). As shown in Figure 3, for the joint training model NMT+LM, although most of the Margin s are positive, there are still many tokens with negative Margin and a large amount of Margin s around 0. This indicates that the LM is probably overconfident for many tokens, and addressing the overconfidence problem is meaningful for NMT. By comparison, the Margin distribution of MSO is dramatically different with NMT+LM: the tokens with Margin around 0 are significantly reduced, and the tokens with Margin in [0 . 75 , 1 . 0] are increased apparently. More precisely, we list the percentage of tokens with negative Margin and the average Margin for each model in Table 4. Compared with NMT+LM, MTO and MSO reduce the percentage of negative Margin by 2.28 and 1.56 points, respectively. We notice MSO performs slightly worse than MTO, because MSO neglects the hallucinations during training. As there are many tokens with negative Margin in hallucinations, the ability of MSO to reduce the proportion of  < 0 is weakened. We further analyze effects of MTO and MSO on the average of Margin . Both MTO and MSO improve the average of the Margin by 33% (from 0.33 to 0.44). In conclusion, MTO and MSO both indeed increase the Margin between the NMT and the LM. Variations of M () . We compare the performance of the four Margin functions M () defined in Section 3.2. We list the BLEU scores of the Transformer baseline, NMT+LM and our MTO approach with the four M () in Table 5. All the four variations bring improvements over NMT and NMT+LM. The results of Log with different  are similar to Linear , while far lower than Cube and Quintic . And Quintic performs the best among all the four variations. We speculate the reason is that Function BLEU  NMT (Transformer) 25.75 ref + LM 25.90 +0.15 + Linear 26.13 +0.38 + Cube 26.45 +0.60 + Quintic 26.94 +1.19 + Log (  = 5 ) 26.12 +0.37 + Log (  = 10 ) 26.07 +0.32 + Log (  = 20 ) 26.24 +0.49 Table 5: Case-sensitive BLEU scores (%) on Zh  En test set of MTO with several variations of M () . Effects of the Weight of M () . In MTO, we propose the weight 1  p NMT ( t ) of the Margin function M () in Eq. 6. To validate the importance of it, we remove the weight and the Margin loss degrades to LM = (cid:80) Tt =1 M (( t )) . The results are listed in Table 6. Compared with NMT+LM, MTO without weight performs worse with 0.25 and 0.05 BLEU decreases on the validation set and test set, respectively. Compared with MTO with weight, it decreases 0.73 and 1.09 BLEU scores on the validation set and test set, respectively. This demonstrates that the weight 1  p NMT ( t ) is indispensable for our approach. Changes of IR ( x , y ) <k During Training. In MSO, we propose a dynamic weight function IR ( x , y ) <k in Eq. 10. Figure 4 shows the changes of IR ( x , y ) <k in MSO and the BLEU scores of MSO and MTO during finetuning. As the training continues, our model gets more competent, and the proportion of sentences judged to be dirty data by our model increases rapidly at first and then 23.0 23.2 23.4 23.6 23.8 24.0 24.2 24.4 24.6 24.8 25.0 0.056 0.058 0.060 0.062 0.064 0.066 0.068 0.070 0.072 155K 175K 195K 215K 235K 255K 275K 295K BLEUP r o p o r t i o n Training steps Propotion of I=0 MTOMSO Figure 4: Changes of the proportion of IR ( x , y ) < 30% = 0 on Zh  En during finetuning for MSO, and BLEU scores (%) on the validation set of Zh  En for MTO and MSO. flattens out, which is consistent with the trend of BLEU of MSO. Moreover, by adding the dynamic weight function, MSO outperforms MTO at most steps. Case Study. To better illustrate the translation quality of our approach, we show several translation examples in Appendix C. Our approach grasps more segments of the source sentences, which are mistranslated or neglected by the Transformer. Translation Adequacy of NMT. NMT suffers from the hallucination and inadequacy problem for a long time (Tu et al., 2016; Muller et al., 2020; Wang and Sennrich, 2020; Lee et al., 2019). Many studies improve the architecture of NMT to alleviate the inadequacy issue, including tracking translation adequacy by coverage vectors (Tu et al., 2016; Mi et al., 2016), modeling a global representation of source side (Weng et al., 2020a), dividing the source sentence into past and future parts (Zheng et al., 2019), and multi-task learning to improve encoder and cross-attention modules in decoder (Meng et al., 2016, 2018; Weng et al., 2020b). They inductively increase the translation adequacy, while our approaches directly maximize the Margin between the NMT and the LM to prevent the LM from being overconfident. Other studies enhance the translation adequacy by adequacy metrics or additional optimization objectives. Tu et al. (2017) minimize the difference between the original source sentence and the reconstruction source sentence of NMT. Kong et al. (2019) propose a coverage ratio of the source sentence by the model translation. Feng et al. (2019) evaluate the fluency and adequacy of translations with an evaluation module. However, the metrics or objectives in the above approaches may not wholly represent adequacy. On the contrary, our approaches are derived from the criteria of the NMT model and the LM, thus credible. Language Model Augmented NMT. Language Models are always used to provide more information to improve NMT. For low-resource tasks, the LM trained on extra monolingual data can rerank the translations by fusion (Gulcehre et al., 2015; Sriram et al., 2017; Stahlberg et al., 2018), enhance NMT's representations (Clinchant et al., 2019; Zhu et al., 2020), and provide prior knowledge for NMT (Baziotis et al., 2020). For data augmentation, LMs are used to replace words in sentences (Kobayashi, 2018; Wu et al., 2018; Gao et al., 2019). Differently, we mainly focus on the Margin between the NMT and the LM, and no additional data is required. Stahlberg et al. (2018) propose the Simple Fusion approach to model the difference between NMT and LM. Differently, it is trained to optimize the residual probability, positively correlated to p NMT /p LM which is hard to optimize and the LM is still required in inference, slowing down the inference speed largely. Data Selection in NMT. Data selection and data filter methods have been widely used in NMT. To balance data domains or enhance the data quality generated by back-translation (Sennrich et al., 2016b), many approaches have been proposed, such as utilizing language models (Moore and Lewis, 2010; van der Wees et al., 2017; Zhang et al., 2020), translation models (Junczys-Dowmunt, 2018; Wang et al., 2019a), and curriculum learning (Zhang et al., 2019b; Wang et al., 2019b). Different from the above methods, our MSO dynamically combines language models with translation models for data selection during training, making full use of the models. We alleviate the problem of inadequacy translation from the perspective of preventing the LM from being overconfident. Specifically, we firstly propose an indicator of the overconfidence degree of the LM in NMT, i.e., Margin between the NMT and the LM. Then we propose Margin -based Token-level and Sentence-level objectives to maximize the Margin . Experimental results on three large-scale translation tasks demonstrate the effectiveness and superiority of our approaches. The human evaluation further verifies that our methods can improve translation adequacy and fluency. The research work descried in this paper has been supported by the National Nature Science Foundation of China (No. 12026606). The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper.
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