Abstract Token-level adaptive training approaches can alleviate the token imbalance problem and thus improve neural machine translation, through re-weighting the losses of different target tokens based on specific statistical metrics ( e.g., token frequency or mutual information). Given that standard translation models make predictions on the condition of previous target contexts, we argue that the above statistical metrics ignore target context information and may assign inappropriate weights to target tokens. While one possible solution is to directly take target contexts into these statistical metrics, the target-context-aware statistical computing is extremely expensive, and the corresponding storage overhead is unrealistic. To solve the above issues, we propose a target-context-aware metric, named conditional bilingual mutual information (CBMI), which makes it feasible to supplement target context information for statistical metrics. Particularly, our CBMI can be formalized as the log quotient of the translation model probability and language model probability by decomposing the conditional joint distribution. Thus CBMI can be efficiently calculated during model training without any pre-specific statistical calculations and large storage overhead. Furthermore, we propose an effective adaptive training approach based on both the tokenand sentence-level CBMI. Experimental results on WMT14 English-German and WMT19 Chinese-English tasks show our approach can significantly outperform the Transformer baseline and other related methods. Neural machine translation (NMT) (Bahdanau et al., 2014; Gehring et al., 2017; Vaswani et al., 2017; Meng and Zhang, 2019; Liu et al., 2021a,b) has made remarkable achievements in recent years. Generally, NMT models are trained to maximize the likelihood of the next target token given ground-truth tokens as inputs (Johansen and Juselius, 1990; Goodfellow et al., 2016). Due to the token imbalance phenomenon in natural language (Zipf, 1949), for an NMT model, the learning difficulties of different target tokens may be various. However, the vanilla NMT model equally weights the training losses of different target tokens, irrespective of their difficulties. Recently, various adaptive training approaches (Gu et al., 2020; Xu et al., 2021) have been proposed to alleviate the above problem for NMT. Generally, these approaches re-weight the losses of different target tokens based on specific statistical metrics. For example, Gu et al. (2020) take the token frequency as an indicator and encourage the NMT model to focus more on low-frequency tokens. Xu et al. (2021) further propose the bilingual mutual information (BMI) to measure the word mapping diversity between bilinguals, and down-weight the tokens with relatively lower BMI values. tions in these adaptive training approaches. Given that the standard translation model autoregressively makes predictions on the condition of previous target contexts, we argue that the statistical metrics used in the above approaches ignore target context information and may assign inaccurate weights for target tokens. Specifically, although existing statistical metrics can reflect complex characteristics of target tokens ( e.g., mapping diversity), they fail to model how these properties vary across different target contexts. Secondly, for the identical target tokens in different positions of a target sentence ( e.g., two  traffic ' tokens in the Figure 1), they may be mapped from different source-side tokens, but such target-context-free metrics cannot distinguish the above different mappings. In summary, it is necessary to incorporate target context information into the above statistical metrics. One possible solution is to directly take target context information into account and conduct target-context-aware statistical calculations. But in this way, the calculation cost and storage overhead will become huge and unrealistic 1 . Therefore, it is non-trivial to design a suitable target-context-aware statistical metric for adaptive training in the field of NMT. In this paper, we aim to address the above issues in adaptive training methods. Firstly, we propose a novel target-context-aware metric, named C onditional B ilingual M utual I nformation (CBMI), to measure the importance of different target tokens by their dependence on the source sentence. Specifically, we calculate CBMI by the mutual information between a target token and its source sentence on the condition of its target contexts. With the aid of target-context-aware calculations, CBMI can easily model the various characteristics of target tokens under different target contexts, and of course can distinguish identical target tokens with different source mappings. Regarding the computational efficiency, through decomposing the conditional joint distribution in the aforementioned mutual information, our CBMI can be formalized as the log quotient of the translation model probability and language model probability 2 . Therefore, CBMI can be efficiently calculated dur-1 Take the vanilla BMI (Xu et al., 2021) as an example, to process the raw WMT14 En-De training data (about 1.5GB), it takes about 12 CPU hours and 2GB disk storage to save the BMI values. To make matters worse, the cost will increase dozens of times in target-context-aware statistical calculations. 2 The detailed derivation process is shown in Equation (7). Please note that the language model is only used during training and thus does not affect the inference speed. ing model training without any pre-specific statistical calculations and huge storage overhead, which makes it feasible to supplement target context information for statistical metrics. Subsequently, we design an adaptive training approach based on both the tokenand sentence-level CBMI, which dynamically re-weights the training losses of the corresponding target tokens. We evaluate our approach on the WMT14 English-German and WMT19 Chinese-English translation tasks. Experimental results on both datasets demonstrate that our approach can significantly outperform the Transformer baseline and other adaptive training methods. Further analyses reveal that CBMI can also reflect the adequacy of translation, and our CBMI-based adaptive training can improve translation adequacy meanwhile maintain fluency. The main contributions of this paper can be summarized as follows:  We propose a novel target-context-aware metric, named CBMI, which can reflect the importance of target tokens for NMT models. Theoretical analysis and experimental results show that CBMI is computationally efficient, which makes it feasible to complement target context information in statistical metrics. We further propose an adaptive training approach based on both the tokenand sentence-level CMBI, which dynamically re-weights the training losses of target tokens. Further analyses show that CBMI can also reflect the adequacy of translation, and CBMI-based adaptive training can improve translation adequacy meanwhile maintain fluency 3 . An NMT model is designed to translate a source sentence with M tokens x = { x 1 , x 2 , . . . , x M } into a target sentence with N tokens y = { y 1 , y 2 , . . . , y N } by predicting the probability of each target token: where j is the index of each time step, y <j is the target-side previous context for y j , and  is the model parameter. During training, NMT models are generally optimized with the cross-entropy (CE) loss: LCE (  ) =  N (cid:88) j =1 log p ( y j | y <j , x ;  ) (2) During inference, NMT models predict the probabilities of target tokens in an auto-regressive mode and generate hypotheses using heuristic search algorithms like beam search (Reddy, 1977). Token-level adaptive training aims to alleviate the token imbalance problem for NMT models by re-weighting the training losses of target tokens. How to design a suitable weight adjustment strategy matters, which is we aim to improve in this paper. Formally, for the j -th target token and its adaptive weight w j , the standard cross-entropy loss in Equation (2) is expanded to the following formula: L ada (  ) =  N (cid:88) j =1 w j log p ( y j | y <j , x ;  ) (3) 2.3 Mutual Information for NMT Mutual information (MI) is a general metric in information theory (Shannon, 1948), which measures the mutual dependence between two random variables a and b as follows 4 : MI( a ; b ) = log (cid:18) p ( a, b ) p ( a )  p ( b ) (cid:19) (4) Xu et al. (2021) propose token-level bilingual mutual information (BMI) to measure the word mapping diversity between bilinguals and further conduct BMI-based adaptive training for NMT. The BMI is formulated as: BMI( x ; y j ) = | x | (cid:88) i =1 log (cid:18) f ( x i , y j ) f ( x i )  f ( y j ) (cid:19) (5) where f (  ) is an word frequency counter. Although BMI can reflect the bilingual mapping properties to some extent, it cannot correspondingly vary with the target context. However, simply introducing target-context-aware calculations into BMI would make the above statistical calculations unrealistic. In this section, we first introduce the definition of CBMI (Section 3.1). Then, we illustrate how to adjust the weights for the training losses of target tokens based on the tokenand the sentence-level CBMI (Section 3.2). Figure 2 shows the overall training process of our approach. As mentioned above, it is necessary to incorporate target context information into the statistical metrics ( e.g., BMI) for adaptive training. However, it is impractical to directly conduct target-context-aware statistical computations due to the expensive computational costs and storage overhead. In this paper, we propose a new target-context-aware metric, named conditional bilingual mutual information (CBMI), to solve the above issues. Specifically, CBMI is calculated by the mutual information between each target token and its source sentence under the condition of previous target context. Formally, the CBMI of a target token y j and its source sentence x is calculated as follow: CBMI( x ; y j ) = MI ( x ; y j | y <j ) = log (cid:18) p ( y j , x | y <j ) p ( y j | y <j )  p ( x | y <j ) (cid:19) (6) The original CBMI definition presented in the above equation still struggles in computation, thus we further simplify it by decomposing the condi-2379 tional joint distribution: CBMI( x ; y j ) = log (cid:18) p ( y j , x | y <j ) p ( y j | y <j )  p ( x | y <j ) (cid:19) = log (cid:18) p ( y j | x , y <j )  p ( x | y <j ) p ( y j | y <j )  p ( x | y <j ) (cid:19) = log (cid:18) p ( y j | x , y <j ) p ( y j | y <j ) (cid:19) = log (cid:18) p NMT ( y j ) p LM ( y j ) (cid:19) (7) where p NMT ( y j ) is the probability output by the NMT model, and p LM ( y j ) is the probability output by an additional target-side language model (LM). In this way, we formalize the complex target-context-aware calculation in Equation (6) as the log quotient of the NMT probability and LM probability. Based on the simplified Equation (7), CBMI can be computed in real time during the model training, thus enabling both target-context-aware and efficient computations. Considering the massive computation required by existing methods to perform the target-context-aware calculation, the LM in our CBMI only brings a modest computational cost in training and finally leads to better performance. We will give a detailed comparison of the calculation cost and storage overhead between our CBMI and existing approaches in Section 5.2. According to the definition, CBMI measures the mutual dependence between a target token and its corresponding source sentence on the condition of its context. Namely, target tokens with larger CBMI value rely more on the source-side information and less on the target historical translations, which is exactly in line with the goal of the adequacy translation model. Given that current NMT models tend to generate fluent but inadequate translations (Weng et al., 2020; Miao et al., 2021), we speculate that making the NMT models pay more attention to target tokens with larger CBMI values can improve translation adequacy and thus improve translation performance. Furthermore, we observe a phenomenon that if target sentences contain many words with small CBMI values, they generally do not match well with the corresponding source sentences. To alleviate the negative effect of these poorly matched sentence pairs, we average all the token-level CBMI values in a target sentence into a sentence-level CBMI and incorporate it into our approach. Consequently, we propose to dynamically adjust the training weight of each target token based on both the tokenand sentence-level CBMI. For clarity, we use t to mark the token-level' intermediate variables and s to mark the sentence-level' ones in the following formulas. Token-Level CBMI. The token-level CBMI can reflect the importance of target tokens for improving translation adequacy ( i.e. , dependency of the source side information). Thus we amplify the weights of target tokens with larger token-level CBMI to make the NMT model pay more attention to them. Particularly, to reduce the variances and stabilize the distribution of the token-level CBMI in each target sentence, we firstly conduct intra-sentence normalization for the token-level CBMI CBMI t ( x ; y j ) : CBMI tnorm ( x ; y j ) = (CBMI t ( x ; y j )   t ) / t (8) where  t ,  t represent the mean values and the standard deviations of CBMI t ( x ; y j ) in each target sentence. Then we scale the normalized CBMI value CBMI tnorm ( x ; y j ) to obtain the token-level training weight for y j : w tj = max { 0 , scale t  CBMI tnorm ( x ; y j )+1 } (9) where scale t is a hyperparameter that controls the effect of CBMI tnorm ( x ; y j ) . Sentence-level CBMI. We average all the token-level CBMI values in a target sentence to form the sentence-level CBMI, which can further reflect the matching degree between the bilingual sentences in a sentence pair. To alleviate the negative effect of poorly matched sentence pairs and encourage the NMT model focus on well-matched sentences pairs, we up-weight the sentence pairs with larger sentence-level CBMI values and downweight those sentence pairs with smaller sentence-level CBMI values. Specifically, the sentence-level CBMI between the source sentence x and the target sentence y can be derived from Equation (4) and represented as the arithmetic average of token-level CBMI values 5 : 5 We divide the original sentence CBMI with its corresponding sentence length to reduce its variance. CBMI s ( x ; y ) = 1 | y | log (cid:18) p ( x , y ) p ( x )  p ( y ) (cid:19) = 1 | y | log (cid:18) p ( y | x ) p ( y ) (cid:19) = 1 | y | log (cid:32)(cid:81) j p ( y j | x , y <j ) (cid:81) j p ( y j | y <j ) (cid:33) = 1 | y | (cid:88) j log (cid:18) p ( y j | x , y <j ) p ( y j | y <j ) (cid:19) = 1 | y | (cid:88) j CBMI t ( x ; y j ) (10) Similarly, we conduct inter-sentence normalization for CBMI s ( x ; y ) : where  s ,  s represent the mean values and the standard deviations of CBMI s ( x ; y ) in each mini-batch during training. Subsequently, we also scale CBMI snorm ( x ; y ) in Equation (11) with another hyperparameter scale s to obtain the sentence-level training weight: w s = max { 0 , scale s  CBMI snorm ( x ; y ) + 1 } (12) Final Loss Weight. In our adaptive training approach, for the target token y j , its final loss weight w j in Equation (3) is the multiplication of the above two weights in Equation (9) and (12): w j = w tj  w s (13) 4 Experiments 4.1 Datasets We conduct experiments on two large-scale WMT tasks, i.e., the WMT14 English to German (En-De) and WMT19 Chinese to English (Zh-En). For the En-De task, the training set contains 4.5M sentence pairs. The validation set and test set are new-stest2013 and newstest2014, respectively. For the Zh-En task, the training set totally contains 20M sentence pairs and the validation set and test set are newstest2018 and newstest2019, respectively. Following previous work, we share the vocabulary for the En-De task and segment words into subwords using byte pair encoding (BPE) (Sennrich et al., 2016) with 32k merge operations for both datasets. Training. We implement baselines and our approach under Transformer base and Transformer big settings based on the open-source toolkit fairseq (Ott et al., 2019) with mixed precision (Ott et al., 2018). We train all the translation models with the cross-entropy loss for 100k steps, and further finetune them with different adaptive training objectives for another 200k steps on both tasks. The target-side language model is a Transformer decoder without the cross-attention modules, which is trained synchronously with the translation model. The training data for the language model is the target-side monolingual data from the NMT training set. All the experiments are conducted on 8 NVIDIA Tesla V100 GPUs, and each batch on each GPU contains approximately 4096 tokens. We use Adam optimizer (Kingma and Ba, 2014) with 4000 warmup steps to optimize models. More training details are listed in Appendix B. In our experiments, we have not been able to bring further improvement to our approach through simply enhancing the language model. Our conjecture is that stronger language models will generate sharper distribution, and will increase the variances of CBMI values when used as the denominator, resulting in detriment for NMT model training. We will leave this for the future work. Evaluation. During inference, we set beam size to 4 and length penalty to 0.6 for both tasks. We use multibleu.perl to calculate case-sensitive BLEU for WMT14 En-De and SacreBLEU 6 to calculate case-sensitive BLEU for WMT19 Zh-En. We use the paired bootstrap resampling methods (Koehn, 2004) for the statistical significance test. In this section, we introduce the hyperparameter settings of our approach according to the performance on the validation set of the WMT14 En-De dataset, and we share the same hyperparameter settings with the WMT19 Zh-En dataset. Scale Setting. The two hyperparameter scale t and scale s in Equation (9) and Equation (12) determine the effects of token-level and sentence-level CBMI. To investigate the effects of the two CBMI in different granularities, we firstly fix scale t to a moderate value, i.e. , 0.1, and tune scale s from 0.0 to 0.3 with the step of 0.05. The detailed results are shown in Figure 3. We observe that models perform better with larger scale s , which conforms with our conjecture in Section 3.2 that well-matched sentence pairs contribute more to NMT models. Then 6 SacreBLEU hash: BLEU+case.mixed+numrefs.1 +smooth.exp+tok.13a+version.1.5.1. we fix scale s to 0.3 and tune scale t in a similar way. We find it better to keep scale t in a small range and too large value is harmful for models. We conjecture that over-focus on the high-CBMI tokens brings another imbalance for training and may hurt the models. Thus we set scale t to 0.1 in our following experiments. We implement our approach based on the Transformer (Vaswani et al., 2017) and compare it with some mainstream adaptive training methods (de-tailed hyperparameter settings are provided in Appendix C). Transformer. We follow the standard base/big model configurations (Vaswani et al., 2017) to implement our baseline systems. Freq-Exponential. Gu et al. (2020) use monolingual token frequency to design an exponential weight function for token-level adaptive training: w j = A  e  T  Count ( y j ) + 1 where A and T are two hyperparameters to adjusting the distribution of weights. Freq-Chi-Square. Gu et al. (2020) use the chi-square distribution to filter out extremely low frequency target tokens: w j = A  Count ( y j ) 2 e  T  Count ( y j ) + 1 where A and T play the same roles as above. BMI-adaptive. Xu et al. (2021) calculate BMI (in Equation (5)) during the data pre-processing stage and scale it for adaptive loss weights. Focal Loss. Lin et al. (2017) propose the focal loss for objective detection tasks to solve the class imbalance problem. Here we introduce it into NMT. where  and  are hyperparameters to adjust the loss weight and p is the NMT predicted probability. Anti-Focal Loss. Raunak et al. (2020) design an anti-focal loss function to solve the long-tailed problem in NMT by incorporating the inductive bias of inference into training. Self-Paced Learning. Wan et al. (2020) calculate model confidence via Monte Carlo dropout sampling (Gal and Ghahramani, 2016) to measure the token difficulty and use it to re-weight the training losses of tokens. Simple Fusion. Stahlberg et al. (2018) propose two simple strategies (i.e., PRENORM and POSTNORM ) to fuse the NMT probabilities with the LM probablities and directly optimize the fusion during the NMT training process 7 . LM Prior. Baziotis et al. (2020) propose to distill the prior knowledge from LMs trained on rich-resource monolingual data to low-resource NMT models 8 : L lmp = LNMT +   LKL ( p LM || p NMT ;  ) (17) where  weights the distillation term and  is the softmax temperature (Hinton et al., 2015). 7 The results in Table 1 are the higher ones between the two strategies. 8 We did not use extra monolingual data for the LMs in Simple Fusion' and LM Prior' in our implementation for fair comparison. The overall results on two WMT tasks based on the Transformer base and Transformer big configurations are shown in Table 1. Under the Transformer base setting, CBMI-based adaptive training can respectively improve +0.91 and +0.85 BLEU scores on En-De and Zh-En tasks compared to the Transformer baseline. Compared to the most related yet target-context-free strategy BMI-adaptive', our CBMI-based adaptive training strategy can respectively yield significant improvements up to +0.46 and +0.44 BLEU scores on En-De and Zh-En, which demonstrate the significance of the target context for token assessment in token-level adaptive training. Compared with the best performing baseline Self-Paced Learning', our approach still outperforms it by +0.32 and +0.46 BLEU scores on the two tasks. Our conjecture is that CBMI not only reflects the model competence used in Self-Paced Learning' but also further incorporates the linguistic statistical information from the target-side LM, thus reflects more explicit translation property ( i.e., adequacy). However, other LM enhanced methods ( e.g., Simple Fusion' and LM Prior') bring limited improvement or even degradation to the NMT models when there is no extra data for the LMs, which further proves the utilization of the LM in our approach is more effective. Under the Transformer big setting, where the performances of existing methods are limited, our method can still bring the improvement of +0.81 and +0.82 BLEU scores on the En-De and Zh-En, which demonstrates the superiority of CBMI under stronger baselines. In this section, we provide in-depth analyses on the effectiveness of our CBMI and conduct experiments on the validation set of WMT14 En-De with the Transformer base model. We take the Transformer base as baseline, and then apply adaptive training based on the token-level CBMI, the sentence-level CBMI, and both of them, respectively. Results are listed in Table 2. We observe certain improvements (+0.29 and +0.44 BLEU scores) when separately applying the token-and sentence-level CBMI based approaches. It suggests that our CBMI can measure the token importance from different granularities, and up-weight 2383 Model BLEU Transformer base 26.24 + token-level CBMI 26.53 (+0.29) + sentence-level CBMI 26.68 (+0.44) + token& sentence-level CBMI 26.78 (+0.54) Table 2: BLEU scores (%) of CBMI at different granularities on the validation set of WMT14 En-De. the important tokens or sentence pairs can improve translation quality. Furthermore, the combination of both the tokenand sentence-level CBMI brings further improvement (+0.55 BLEU scores), which illustrates that the CBMI in different granularities are complementary and have cumulative gains. In this section, we compare our CBMI-based approach with the BMI-based adaptive training in terms of the number of trainable parameters, the CPU computational costs of pre-processing, the GPU computational costs of training, and disk cost for storing intermediate variables. As shown in Table 3, the vanilla BMI-based approach requires additional 12 CPU hours to obtain the BMI values during the pre-processing stage, and about 2.0 GB of disk space to store these BMI values. To make matters worse, the costs of CPU calculation and disk storage will increase dozens of times (approx-imately equal to the average length of target sentences) when conducting the target-context-aware calculations for BMI. In contrast, our CBMI-based approach gets rid of the CPU computational costs, and thus has no additional storage overhead. Although we introduce an additional LM to calculate the CBMI values, it only brings a slight increase of model parameters and GPU calculation cost during model training. Particularly, our proposed method simply modifies the training loss of NMT, and thus has no effect on the inference speed. In short, our CBMI can be efficiently calculated during model training without any pre-specific statistical calculations and storage overhead, which makes it feasible to supplement target context information for statistical metrics. To verify whether our CBMI measurement is indeed highly related to the translation adequacy of NMT models, as we conjectured in Section 3.2, we conduct the human evaluation in terms of adequacy and fluency. We randomly sample 100 sentences Method Pre-process #Params Train Disk (hour) (M) (hour) (GB) Transformer base 0 65 10 0 + BMI 12 65 11 2.0 + target context  12  N 65   2.0  N + CBMI 0 101 12 0 Table 3: The costs of calculation and storage of the BMIand CBMI-based approaches on the WMT14 EnDe (100k training steps). from the test set of WMT19 Zh-En and invite three annotators to evaluate the translation adequacy and fluency. Scores for both indexes are limited in [1,5]. For adequacy, 1' represents irrelevant to the source sentence and 5' represents semantically equal. For fluency, 1' means unintelligible and 5' means fluent and native. We finally average the scores from three annotators and list the results in Table 4. We observe that our approach significantly promotes the translation adequacy of the Transformer base baseline, and meanwhile slightly promotes the translation fluency. It indicates that the CBMI measurement is highly related to the adequacy of NMT models, and focusing more on the tokens with high CBMI can improve translation adequacy, and thus improve translation performance. Given that CBMI reflects the dependency between a target token and its source sentence on the condition of its target context, in this section, we explore whether CBMI can serve as an indicator for selecting an appropriate prior distribution to improve the NMT model. Prior distributions have been proved for their ability to provide additional knowledge for models (Baziotis et al., 2020; Li et al., 2020). Thus we try three generated distributions as prior distributions for NMT models, i.e. , the translation model distribution (TM prior), the language model distribution (LM prior), and the softmax normalized CBMI distribution (CBMI prior). these distributions according to different tokens and surprisingly observe that the accuracies are highly related to the CBMI values of tokens. As shown in Figure 4, the most accurate prior for target tokens with different CBMI values is not always consistent. Based on this observation, we further design a CBMI-based prior selection strategy to choose the best prior distribution for each token. The details of the selection strategy are seen in Appendix D. As shown in Table 5, all these prior distributions can provide helpful guidance and enhance the baseline model. More importantly, the CBMI-based prior selection strategy can achieve a better performance compared with the single prior, demonstrating that CBMI also serves as an appropriate indicator for the translation prior selection. We will explore the more sophisticated CBMI-based prior selection strategy in the future work. the information in language models is a common solution to improve NMT models. In low-resource scenarios, LMs trained on extra monolingual data are usually more informative and thus used to fuse with NMT prediction (Gulcehre et al., 2015, 2017; Sriram et al., 2017; Stahlberg et al., 2018), provide prior knowledge for NMT models (Baziotis et al., 2020) and enhance representations of NMT (Clinchant et al., 2019; Zhu et al., 2020). In data augmentation methods, LMs are also widely used to generate contextual substitutions of words in sentences (Kobayashi, 2018; Wu et al., 2018; Gao et al., 2019). Differently, all the aforementioned methods rely on the LMs that are trained on extra data, while the LM in our method does not require extra data and also has no influence on the inference speed. In this paper, we propose a target-context-aware metric for target tokens, named conditional bilingual mutual information (CBMI). Compared with previous statistical metrics, our CBMI only increases limited computational costs to incorporate the target context and provides a more suitable assessment for tokens. Furthermore, based on the tokenand sentence-level CBMI, we design a CBMI-based adaptive training strategy to amply the contributions of the important tokens. Experimental results on two WMT tasks demonstrate the effectiveness of our proposed approach. Further analyses show that CBMI can improve translation adequacy and serve as an appropriate indicator for the translation prior selection. The research work descried in this paper has been supported by the National Key R&D Program of China (2020AAA0108001) and the National Nature Science Foundation of China (No. 61976016, 61976015, and 61876198). The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper.
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