arxiv:1911.13182v1 [cs.cl] 29 nov 2019

An Iterative Polishing Framework based on Quality Aware Masked LanguageModel for Chinese Poetry Generation

Liming Deng,1 Jie Wang,1 Hangming Liang,1 Hui Chen,1Zhiqiang Xie,3∗ Bojin Zhuang,1 Shaojun Wang,1 Jing Xiao2

1Ping An Technology2Ping An Insurance (Group) Company of China3University of Science and Technology of China

[email protected], [email protected]

Abstract

Owing to its unique literal and aesthetical characteristics, au-tomatic generation of Chinese poetry is still challenging inArtificial Intelligence, which can hardly be straightforwardlyrealized by end-to-end methods. In this paper, we propose anovel iterative polishing framework for highly qualified Chi-nese poetry generation. In the first stage, an encoder-decoderstructure is utilized to generate a poem draft. Afterwards,our proposed Quality-Aware Masked Language Model (QA-MLM) is employed to polish the draft towards higher qualityin terms of linguistics and literalness. Based on a multi-tasklearning scheme, QA-MLM is able to determine whether pol-ishing is needed based on the poem draft. Furthermore, QA-MLM is able to localize improper characters of the poemdraft and substitute with newly predicted ones accordingly.Benefited from the masked language model structure, QA-MLM incorporates global context information into the pol-ishing process, which can obtain more appropriate polishingresults than the unidirectional sequential decoding. Moreover,the iterative polishing process will be terminated automati-cally when QA-MLM regards the processed poem as a qual-ified one. Both human and automatic evaluation have beenconducted, and the results demonstrate that our approachis effective to improve the performance of encoder-decoderstructure.

IntroductionChinese Poetry, originated from people’s production andlife, has a long history. The poetry is developed from fewcharacters, vague rules to some fixed characters and lineswith stable rules and forms. The rules like tonal pattern,rhyme scheme lead to poems easy to be read and remem-bered. The great poems, which touch millions of people atheart across the space and time, should unify the conciseform, refined language and rich content together to guaran-tee the long-term prosperity. Writing great poems are noteasy, which require strong desire for poets to express theirfeelings, views or thoughts and then to choose charactersand build sentence carefully.

Poets are always regarded as genius with great talents andwell trained in writing poems. It is hard to write a poem

∗This work was done when Zhiqiang Xie was at Ping An Tech-nology

for ordinary people, let alone to computers. Although manyworks (Gervas 2001; Ghazvininejad et al. 2016; Yi et al.2018; Li et al. 2018) have been conducted for automatic po-etry generation and poetic rules and forms can be learnedpartially, the large gaps remain in the meaningfulness andcoherence of generated poems.

In this paper, we focus on the automatic Chinese poetrygeneration and aim to fill these gaps. We notice that poetswould first write a poem draft and then polish the draft manytimes to a perfect one. There is a popular story about pol-ishing poem by Dao Jia, a famous poet in Tang Dynasty,who influences many later poets in polishing their poemsintensively. Motivated by the writing poem process of po-ets, we aim to imitate this process and improve the coher-ence and meaningfulness of primitive poems. However, it ischallenging for computer algorithms to automatically polishthe poem draft to an excellent one. The computer algorithmsare unable to choose the characters and sentences like poetswith intuition and comprehensive understanding of the char-acters, which are only good at calculating the probability ofcharacters and picking up ones with maximum probabilityfrom vocabulary. There are three key issues to be addressedfor the polishing framework.

• Whether the text need to be polished, and when should westop the iterative polishing process?

• Which characters in the text are improper and need to bereplaced with better ones?

• How to obtain the better ones?

To address these key issues and further improve the qual-ity of generated poem, we propose a Quality-Aware MaskedLanguage Model (QA-MLM) to implement an iterative pol-ishing process. To the best of our knowledge, this is the firstwork to solve the three key issues in polishing frameworkwith one elegant model.

Our idea originates from the BERT (Devlin et al. 2018)with two-task learning schema, and we modify the tasks toaware of text quality and further obtain appropriate charac-ters to replace the low quality characters in the text. Withthese two tasks, we can polish the generated poem draft it-eratively, and the polishing process will be terminated auto-matically. The main contributions of this paper are summa-

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rized as follows:• Our proposed model QA-MLM, a novel application of

BERT for poem refinement, which can judge the qualityof poem and polish the bad characters in the poem iter-atively. The polish process will be terminated automati-cally until the polished poem is regarded as a qualifiedone by our model.

• The QA-MLM model can obtain high quality charactersby incorporating both left and right context information,and overcomes the weakness of the unidirectional decod-ing that only consider one side context information for thenext character prediction.

• A two-stage poem generation has been proposed tostrengthen the meaningfulness and coherence of gener-ated poems. On the first stage, the encoder-decoder struc-ture has been utilized to generate the poem draft. Specif-ically, the pre-trained BERT and the transformer de-coder has been utilized for poem draft generation. Thepoem draft is further polished by our proposed QA-MLMmodel on the second stage.

Related WorkAutomatic poetry generation has been investigated fordecades. The early work focus on improving the grammat-ical rules and complying with poetic forms with template-based methods (Gervas 2001; Wu, Tosa, and Nakatsu 2009)and evolution algorithms (Manurung 2004; Zhou, You, andDing 2010). The statistical machine translation methods(He, Zhou, and Jiang 2012) and text summarization meth-ods (Yan et al. 2013) have also been utilized for generatingmore natural and flexible poems.

As neural network demonstrates powerful ability for nat-ural language representation (Bengio et al. 2003; Goldberg2017), different neural network structures have been uti-lized for poem generation and shown great advances. Themain structures are developed from vanilla recurrent neu-ral network (Zhang and Lapata 2014) to bi-directional longshort term memory network and bi-directional gated recur-rent unit network (Wang et al. 2016; Yi, Li, and Sun 2017).The poem generation is widely interpreted as a sequence-to-sequence problem, which utilize the encoder-decoder frame-work to encode the previous sequence and generate the latersequence with the decoder (Wang, Luo, and Wang 2016;Yi, Li, and Sun 2017). To strengthen the relation betweenthe encoder and decoder, the attention mechanism has beenincorporated for poem generation (Wang, Luo, and Wang2016; Zhang et al. 2017; Yi, Li, and Sun 2017). Besides,some tricks like working memory mechanism and salient-clue mechanism (Yi et al. 2018; Yi, Li, and Sun 2018) havebeen proposed to improve the coherence in meanings andtopics for poem generation. Recently, the conditional varia-tional autoencoder (C-VAE) has been utilized to generate thepoem (Yang et al. 2017; Li et al. 2018). The C-VAE can ob-tain high quality poem with topic coherence to some extent.Some bad cases are also reported by (Li et al. 2018).

All the previous methods are generating the poem directlywithout any refinement. The most similar work to our pa-per is i,poet (Yan 2016), which has implemented an polish-

ing framework via encoding the writing intents repetitivelyto rewrite the poem. This work empirically polishes all thecharacters that generated at previous iterative step, and as-sumes that the further encoding of the writing intents wouldenhance the theme consistency. Another similar work is theDeliberation Network (Xia et al. 2017), which has utilized asecond decoder to generate the final sequence with the addi-tional input of sequence that generated by the first decoder.Followed by the Deliberation Network, a more recent work(Zhang et al. 2019) has employed transformer decoder toimplement the two-decoder polishing process for text sum-marization. All these methods fail to sense the text qualityand regard rewriting the whole sequence as polishing pro-cess, which are inefficiency and may replace qualified char-acters with low-quality ones. Besides, the polishing processin these methods are heavily coupled with the initial draftgeneration process, which refers to not only the generateddrafts but also the additional information that has been uti-lized in the draft generation. Therefore, these polishing pro-cess cannot be utilized to polish the text drafts that generatedseparately by other models.

By contrast, our proposed QA-MLM model is differentto the previous works significantly and implements the iter-atively polishing process like humans. Our model can firstaware of the text quality and decide whether the text needto be polished. Furthermore, our model can aware of thelow-quality characters and pick them up to be polished withboth left and right context information. Since our model cansense the text quality, the iterative polish step will be ter-minated automatically once the polished text has been re-garded as qualified. Our model only polishes a small part oflow-quality characters instead of rewriting the whole text.The polishing process implemented by our model is inde-pendent to the draft generation process, which can polishthe draft generated by other separate model. In this paper,we apply our proposed QA-MLM model for Chinese po-etry polishing, which can significantly improve the qualityof poem particular in terms of meaningfulness and coher-ence. We will introduce our approach in the following sec-tions.

Model DesignOverviewWe focus on the generation and polishing of quatrain, whichis a famous kind of Chinese classic poetry with strict con-straints of poetic rules and forms. In general, the quatrain iswith four poem lines, the number of characters for each lineis equal, which is either five or seven. The tone level andrhythm are constrained with specific patterns (Wang 2002).We follow the text-to-text generation paradigm (Wang et al.2016; Li et al. 2018) and generate the poem line by line.The first poem line is generated by keywords or topic words,and the following lines are generated by the preceding linesor their combinations. The key task turns into designing aproper model to generate the following lines with given key-words or preceding lines.

Inspired by the real procedure of writing poems for po-ets, we generate the poem lines with two stages. The poem

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Poem draft generation

Iterative polishing

Figure 1: An overview of our poem generation approach,including poem draft generation and iterative polishing pro-cess. 1© Predict the character position with worst quality,2© Mask the worst quality character, 3© Predict the masked

character and update it into the text accordingly, 4© Repeatthe previous steps until no character needs to be polished.

draft lines are first generated with encoder-decoder frame-work and then polished with our proposed QA-MLM. Theoverall structure of our approach can be shown in Figure 1.

Input Representation

Our input representation is similar to the embedding meth-ods in BERT (Devlin et al. 2018). In addition to sum the to-ken, segment and position embeddings as the representation,we also add the tonal and rhythm embeddings into the inputrepresentation. The tone of each character is either Ping (thelevel tone) or Ze (the downward tone) (Wang 2002). We en-code the tone with three categories due to some tokens likecomma without any tone. The rhythm of last character foreach poem line will be encoded and we utilize the ThirteenRhyme. 1 With the tone and rhythm are embedded into therepresentation, we can improve the poeticness of generatedpoem significantly without sacrifice much of the poem qual-ity. The visualization of our input representation is given inFigure 2.

1Classify the final vowels into thirteen categories according tothe rhyme table.

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TokenEmbeddings

SegmentEmbeddings

PositionEmbeddings

ToneEmbeddings

RhymeEmbeddings

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Figure 2: The input representation. The input embeddingsis the sum of the token embeddings, segmentation embed-dings, position embeddings and tone embeddings as wellas rhyme embeddings. The EN and ER represent the tokenwithout tone or no need to embed the rhyme respectively.

Poem Draft GenerationThe poem draft can be generated via encoder-decoder struc-ture. This structure learns the relation between the target se-quence t = {t1, t2, ..., tn} and the source sequence s ={s1, s2, ..., sm}. The generation probability P (t|s; Θ) canbe obtained by Equation (1), where the Θ is model parame-ters and learned from the sequence pairs (s, t) ∈ (S,T). Wemaximize the objective function in Equation (2).

P (t|s; Θ) =

n∏j=1

P (tj |t<j , s; Θ) (1)

Lcharacter =∑

(s,t)∈(S,T)

logP (t|s; Θ) (2)

As shown in Figure 3, the BERT is utilized as the encoderto represent the source sequence s with vector h, and therepresentation vector h is then fed to a two-layer transformerdecoder to generate the target sequence t (Devlin et al. 2018;Zhang et al. 2019). The source sequence can be a keywordor poem lines, and the target sequence is the poem line thatwe want to generate. All or part of previous sequence havebeen utilized as source sequence by previous works (Wanget al. 2016; Yi, Li, and Sun 2017). After carefully consid-ering the relevance among poem lines and without makingthe generation system complicated, we build three differentmodels with the same structure for each poem line genera-tion, namely: key2one, one2one, and two2one.

The key2one model is utilized to generate the first poemline with the input of keyword. The one2one model is em-ployed to generate the second poem line and the fourth poemline due to the similar relevance with their preceding poemlines. As for generating the third poem line, we considerboth the first and second poem lines via the two2one model.The whole poem draft generation process can be visualizedin the upper part of Figure 1.

Iterative PolishingThere is an obvious deficiency for the aforementionedencoder-decoder method (Xia et al. 2017). During the de-

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…

Figure 3: The sequence-to-sequence generation with BERT and Transformer decoder.

coding, the character generated sequentially is affected bythe previous characters and ignores the influence of subse-quent characters, as demonstrated in Equation (1). There-fore, an iterative polishing framework which can utilize bothprevious and subsequent context information to polish cen-ter character is critical to obtain a semantic consistency andcoherence poem.

We propose a quality aware masked language model (QA-MLM) to implement the iterative polishing process. Thequality aware reflects the model capability of distinguish-ing the character quality and deciding which character needto be polished. Besides, our model can decide whether thetext need to be polished and when should we stop the iter-ative polishing process. The masked language model is tomask the low quality character first and then predict anothercharacter by referring the two-side context information. Thepredicted character is assumed to be with better semanticconsistency and coherence due to the consideration of boththe previous and subsequent information. Inspired by (De-vlin et al. 2018), we train the QA-MLM with two predic-tion tasks and apply it to polish the generated poem draft, asdescribed in the following subsections.

Prediction Tasks In order to provide reasonable solutionsto the aforementioned three key issues in polishing frame-work, we design a quality prediction task and a masked lan-guage model task based on BERT (Devlin et al. 2018). Un-like the BERT, which learns from multi-task for context rep-resentation, our proposed QA-MLM predicts the positionsof low quality characters and then replaces the low qual-ity characters with newly predicted ones for text refinement.The structure of QA-MLM can be visualized in Figure 4.The quality prediction task is to predict the character posi-tions that the characters are with low quality. We regard theoriginal poem lines from poetry corpus are the gold stan-dards, and any changing of the original poem lines wouldhurt the quality of the poem. Therefore, we randomly re-place the characters in original poem line with random to-kens. We denote sg as the original poem line, and the scas the changed poem line. The positions that have beenreplaced can be denoted as p = [pi1, pi2, ..., pir], whereir < n, and the real characters that have been replacedare si = [si1, si2, ..., sir]. The number of replaced posi-tions r reflects the learning capacity of the QA-MLM thathow many mismatched characters can be learned. A larger rallows a more powerful model for polishing the bad poem

BERT

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E[CLS] E1 Ei En

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Position prediction

BERT

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E[CLS] E1 Ei En

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Token prediction



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Mask character

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Quality Aware

Masked Language Model

Figure 4: The structure of quality aware masked languagemodel.

lines intensively. However, the large r would lead to thechanged poem lines very bad and increases the training dif-ficult. It should be careful to choose an appropriate r con-sidering both the model capacity and learning quality.

In this work, each poem line is randomly replaced 2 ac-cording to the following rules:• 60% of the time: replace one character with ran-

dom token, eg., the original poem line sg =[s1, s2, s3, s4, s5, s6, s7] (n = 7, for example) is changedto sc = [s1, s2, si1, s4, s5, s6, s7] and the position la-bel is p = 3, then the masked poem line is sm =[s1, s2, [MASK], s4, s5, s6, s7].

2Refers to both the positions and the tokens are randomly se-lected

• 20% of the time: replace two characters withrandom tokens, eg., the original poem linesg = [s1, s2, s3, s4, s5, s6, s7] is changed tosc = [s1, si1, s3, s4, s5, si2, s7] and the positionlabel is p = [2, 6], then the masked poem line issm = [s1, [MASK], s3, s4, s5, [MASK], s7].

• 20% of the time: keep the poem line unchanged, in thissituation we set the position label as 0, namely sg = scand p = 0, there is no need to mask the poem line sc andno need to polish poem line sc, which infers pend = 0.

Learning and Inference We can jointly learning theaforementioned two tasks to train QA-MLM by minimiz-ing the following loss functions:

Lossq = −∑sc∈Sc

ir∑j=i1

logP (pj = pj |sc; Θ) (3)

Lossm = −∑

(sm,sg)∈(Sm,Sg)

ir∑j=i1

logP (sm,j = sg,j |sm, 6=j ; Θ) (4)Losstotal =Lossm + λLossq (5)

After learning our proposed QA-MLM over the constructedpoem corpus (Sg,Sc,Sm), we can utilize the QA-MLM topolish the poem draft. At the beginning of polishing process,the QA-MLM predicts the character position that with worstcharacter quality. If the predicted position pi is equal to pend(in our setting pend = 0), which means that all characters inthe draft are qualified enough and no more any polishing,otherwise the character identified with the worst quality willbe masked in the draft, and the masked draft will be fur-ther utilized for a better character prediction via QA-MLMmodel. The predicted character is regarded as more appro-priate than the masked character due to the incorporationof two-side context information during the prediction. Thus,we replace the masked character in sequence draft with thepredicted character, and one polishing step is finished. By re-peating the above polishing step, the sequence draft can beiteratively polished many times until the end indicator pendis predicted. At this time, the iterative polishing process willbe terminated automatically, and the sequence draft has beenpolished completely. The iterative polishing process can beshown in Algorithm 1.

Algorithm 1 : Iterative Polishing with QA-MLM1: Perform iterative polishing on sequence draft sd =

[s1,s2,...,si,...,sn]2: Predict bad character position pi = QA(sd)3: while pi 6= pend do4: si ← [MASK] , sd = [s1,s2,...,[MASK],...,sn]5: Predict the new character si = MLM(sd)6: sd← [s1,s2,...,si,...,sn]7: pi←QA(sd)

8: return polished sd

The sequence draft can be a poem line or several poemlines and even a whole poem, our approach is capable of pol-

ishing all of them. In this work, we polish the whole poemtogether, which incorporates the whole context informationfor inappropriate character prediction, and the inappropriatecharacters will be replaced with highly qualified charactersto obtain semantic consistency and coherence.

Experiments and EvaluationsExperimental SetupIn this paper, we concentrate on the generation of Chinesequatrain with seven fixed characters for each line. Our po-etry corpus is consist of poems from Tang Dynasty, SongDynasty, Yuan Dynasty, Ming Dynasty and Qing Dynasty.About 130,525 poems with total 905,790 number of poemlines are filtered from the poetry corpus. Each filtered poemcontain four or multiple of four poem lines, and each poemline with seven characters. These poems are randomly splitinto three part for model training (90%), validation (5%)and testing (5%). Three models (key2one, one2one, andtwo2one) trained by different sequence-to-sequence pairsare utilized to generate the poem draft lines.

The BERT is selected as the encoder with 12 layers andinitialized with the parameters pre-trained by (Devlin et al.2018). The 2-layer transformer decoder is selected for thepoem generation. After the poem draft has been generated,the QA-MLM is proposed for the polishing. The aware ofpoem quality is implemented by the quality task to predictthe position character that with worst semantic quality. In ad-dition to the current total 28 positions for the seven-characterquatrain, an end position pend = 0 is added to indicate theend of iterative polishing. The character located by the qual-ity prediction task will be masked and then replaced withnewly predicted one by masked language model task. Thequality prediction task and the masked language model taskare based on the 12-layer BERT and learned jointly.

The conventional RNN encoder-decoder structure with at-tention mechanism (AS2S) (Wang et al. 2016) and a morerecent work CVAE-D (Li et al. 2018) are selected as thebaselines for poem draft generation. Besides, we also im-plement a more powerful encoder-decoder structure withpre-trained BERT and transformer decoder (B&T) for poemdraft generation. The poem drafts are generated with the in-put of keywords or writing intents, and we follow the key-words extraction method adopted by AS2S (Wang et al.2016), which cuts the poem lines into several word segmen-tations by Jieba (Sun 2012) and then utilizes the TextRank(Mihalcea and Tarau 2004) method to select keyword withthe highest score. The poems generated by the aforemen-tioned three models are further polished with the proposedQA-MLM. Both the automatical evaluation criteria and hu-man evaluations have been conducted. The following sub-section will introduce the detail about the evaluations.

Evaluation MetricsIt is difficult for computer to estimate the quality of poem.Therefore, we utilize both automatic evaluation metrics andhuman judgements for model comparisons. The automaticevaluation metrics including BLEU (Papineni et al. 2002),

Table 1: The BLEU score results on different generated poem line with same extracted keyword or previous poem lines. BL-1and BL-2 are the BLEU scores on unigrams and bigrams.

Model key→ 1 1→ 2 1&2→ 3 3→ 4 AverageBL-1 BL-2 BL-1 BL-2 BL-1 BL-2 BL-1 BL-2 BL-1 BL-2

AS2S 0.072 0.047 0.016 0.005 0.019 0.006 0.021 0.007 0.032 0.016AS2S-P 0.074 0.047 0.026 0.009 0.030 0.010 0.036 0.012 0.042 0.020CVAE-D 0.109 0.059 0.013 0.005 0.015 0.005 0.019 0.006 0.039 0.019

CVAE-D-P 0.105 0.057 0.015 0.005 0.016 0.006 0.021 0.007 0.039 0.019B&T 0.102 0.050 0.028 0.010 0.036 0.014 0.035 0.013 0.050 0.022

B&T-P 0.100 0.050 0.028 0.009 0.034 0.013 0.033 0.012 0.049 0.021

Table 2: The evaluation results. Sim12 refers to the similarity between first poem line and second poem line; Sim34 refers tothe similarity between the third poem line and the fourth poem line; Sim2L refers to the similarity between first two poem linesand the last two poem lines; TA. and RA. are the tone level predicted accuracy and the rhythm predicted accuracy respectively;Con., Flu., Mea., and Poe. represent the Consistency, Fluency, Meaningfulness and Poeticness respectively.

Model Automatic Evaluation Human EvaluationSim12 Sim34 Sim2L TA. RA. Con. Flu. Mea. Poe.

AS2S 0.479 0.487 0.648 0.539 0.121 2.46 2.37 2.35 2.28AS2S-P 0.484 0.495 0.650 0.517 0.124 2.64 2.63 2.59 2.59CVAE-D 0.494 0.500 0.651 0.521 0.086 2.62 2.50 2.55 2.42

CVAE-D-P 0.499 0.507 0.653 0.524 0.091 2.75 2.72 2.74 2.64B&T 0.500 0.516 0.640 0.976 0.956 3.01 2.99 3.06 2.88

B&T-P 0.502 0.519 0.642 0.962 0.841 3.14 3.19 3.24 3.09

Similarity (Wieting et al. 2015), tone accuracy and rhythmaccuracy are adopted in this paper.

The BLEU is designed for machine translation and alsowidely adopted by many previous works (Zhang and Lap-ata 2014; Li et al. 2018) in poem generation. The BLEU isto measure the overlapping of characters between the gener-ated sentence and the referred sentence. Unlike the machinetranslation, the generated sentence can be significantly dif-ferent from the referred sentence but also regarded as highquality by human judgements. The poem generation is morerelated to creativity and the generated poem may far awayfrom the referred poem, which may lead to the comparisonof BLEU score is trivial. Therefore, we compare the BLEUscore on one sentence instead of the whole poem. Each sen-tence is generated by different approaches with the samekeyword or sentence input.

The Similarity is aimed to automatically measure the co-herency or consistency among poem lines. The embeddingof characters can partially reflect the similarities and we ac-cumulate the embeddings of all the characters for each poemline for sentence-level embeddings (Wieting et al. 2015).Then, the similarity between two poem lines can be calcu-lated by the cosine function on the sentence-level embed-dings.

The Tone Accuracy and Rhythm Accuracy are also em-ployed for the evaluation. The tone accuracy is the percent-age that the tone level (Ping or Ze) is predicted correct to allthe generated samples, and the rhythm accuracy is similarabout the last character of each poem line that the rhyme ispredicted correct.

The Human Evaluation is inevitable for poem evalua-

tion, which is more reliable and credible than the automaticevaluation metrics. Twenty well educated annotators are in-vited to evaluate the generated poems in four dimensions,namely Consistency, Fluency, Meaningfulness and Poetic-ness (Zhang and Lapata 2014; Li et al. 2018). Each dimen-sion is rated using the 1 to 5 scale to represent from badquality to excellent. Each model generates one thousand po-ems and the poems are divided equally into twenty pieces.To reduce the individual scoring bias, the poems rated byeach participant are from all models, but the participant hasno information about the model that each poem belongs to.Therefore, we can obtain 6000 (20× 6× 50) poem ratings.

Results and DiscussionsThe BLEU scores are compared in Table 1. The comparedmodels are shown in the first column of the table, wherethe suffix -P indicates that the poems generated by previ-ous models have been polished by QA-MLM. The key-words and poem lines are extracted from test dataset withone thousand poems. In general, the BLEU scores of CVAE-D are higher than AS2S but lower than B&T, which par-tially reflects the generation performance of these models.The polishing process improves the BLEU scores for AS2Smodel while has no obvious improvement or even a bit hurtof BLEU scores for CVAE-D and B&T. This is probablydue to the creativity and diversity properties in poem gener-ation. The quality of generated poem is not proportional tothe BLEU score when the BLEU score is comparative high.The BLEU score should be referred conservative during thequality evaluation for poetry generation.

The other automatic evaluation results and human score

,In the lonely spring breeze, birds are violently

fluttering their wings,

��The autumn wind blows the rain with delicate fragrance,

overflowing the courtyard lightly.

�� ᦩ ԅYou’d like to know the old things

in order to come back late�

ᰜOnly the flowers and the happiness of fishing.

,In the lonely spring breeze, birds are violently

fluttering their wings,

The autumn wind blows the rain with delicate fragrance, overflowing the courtyard lightly.

�� Ꭳ

You’d like to know the news from homeland while come back late �

ռOnly the flowers and their fragrance remaining�

Figure 5: The example of poem draft and the polished poem. The left poem is the poem draft generated by B&T and the rightpoem is the poem iteratively polished by QA-MLM. The iterative polishing is automatically terminated after 3 polish steps.

results can be found in Table 2. These evaluation results arealso based on one thousand poems from test dataset. Thekeywords are extracted from these poems and utilized togenerate poem drafts by AS2S, CVAE-D and B&T. All thepoem drafts generated by this three encoder-decoder struc-ture models have been further polished by our proposed QA-MLM model. We can find that the polish procedure im-proves the scores of Similarity criteria on all the comparedencoder-decoder structure models, which demonstrates theeffectiveness of our proposed QA-MLM for the improve-ment of sematic coherence and theme consistency. The tonelevel and rhythm for AS2S and CVAE-D models seem ran-domly. By contrast, the accuracy of tone level and rhythmfor B&T are significantly higher than the other two base-lines, which demonstrates the embedding-based method iseffective to control the tone level and rhythm. The polishingframework on the B&T hurts a bit accuracy of tone leveland rhythm, which sacrifices the tone level and rhythm con-straints to obtain better semantic meaning and coherence.

The human evaluations are consistent with the automaticevaluation metrics. As for the poem draft generators, theCVAE-D outperforms the AS2S on all the quality aspectsevaluated by our annotators, which is consistent with theresults from (Li et al. 2018). However, the poem genera-tion performance of B&T is better than CVAE-D, which isprobability due to the powerful text representation ability ofBERT or transformer.

Above all, our proposed QA-MLM can further improvethe qualities (consistency, fluency, meaningfulness and poet-icness ) of poems generated by all the three aforementionedencoder-decoder structure models, which demonstrates thatthe quality prediction task is effective to locate the bad char-acters and the masked language model task is also effec-tive to obtain better predictions when referring to the globalcontext information. Therefore, the unidirectional sequentialdecoding deficiency of the encoder-decoder structure can belargely saved by our proposed QA-MLM for poetry refine-ment.

Although the improvements brought by the QA-MLM in

automatic evaluation metrics seem trivial, the improvementsare significant in the human evaluation results. It is easy tounderstand that the polishing process only update a smallpart of characters, and the improvements will be averagedon all the characters for automatic evaluation metrics. How-ever, human can understand and notice the significant differ-ence of the changed characters to the whole poem context.Even one character changed would lead to a big improve-ment for poetry quality. We can notice the difference fromthe example in Figure 5.

ConclusionIn this paper, we present an iterative polishing frameworkfor Chinese poetry generation by imitating the real poemwriting process. Following the famous encoder-decoderparadigm, a pre-trained BERT encoder and a transformerdecoder are combined to generate poem drafts. Then, poempolishing is accomplished by a multifunctional QA-MLM,which can improve poem quality in terms of semantics, syn-tactics and literary. Based on the multi-task learning, thetrained QA-MLM is able to aware of the poem quality andlocate improper characters. Besides, the QA-MLM is capa-ble of predicting better ones to replace the improper charac-ters by synthesizing the all-round poem context information.Moreover, the QA-MLM will automatically terminate theiterative polishing process when the polished draft is classi-fied as qualified.

Both automatic evaluation and human scores demonstratethat our proposed approach is effective in Chinese poetrygeneration. Our model can automatically modify prelim-inary poems to elegant ones while keeping their originalintents. Even though our proposed QA-MLM polishingframework is concentrated on Chinese poetry generation inthis work, this new text refinement approach can be extendedto other natural language generation areas.

AcknowledgmentsWe thank Haoshen Fan, Weijing Huang, Mingkuo Ji andShaopeng Ma for helpful discussions.

References[Bengio et al. 2003] Bengio, Y.; Ducharme, R.; Vincent, P.;and Jauvin, C. 2003. A neural probabilistic language model.Journal of machine learning research 3(Feb):1137–1155.

[Devlin et al. 2018] Devlin, J.; Chang, M.-W.; Lee, K.; andToutanova, K. 2018. Bert: Pre-training of deep bidirectionaltransformers for language understanding. arXiv preprintarXiv:1810.04805.

[Gervas 2001] Gervas, P. 2001. An expert system for thecomposition of formal spanish poetry. Knowledge-BasedSystems 14(3-4):181–188.

[Ghazvininejad et al. 2016] Ghazvininejad, M.; Shi, X.;Choi, Y.; and Knight, K. 2016. Generating topical poetry. InProceedings of the 2016 Conference on Empirical Methodsin Natural Language Processing, 1183–1191.

[Goldberg 2017] Goldberg, Y. 2017. Neural network meth-ods for natural language processing. Synthesis Lectures onHuman Language Technologies 10(1):1–309.

[He, Zhou, and Jiang 2012] He, J.; Zhou, M.; and Jiang, L.2012. Generating chinese classical poems with statisticalmachine translation models. In AAAI.

[Li et al. 2018] Li, J.; Song, Y.; Zhang, H.; Chen, D.; Shi, S.;Zhao, D.; and Yan, R. 2018. Generating classical chinese po-ems via conditional variational autoencoder and adversarialtraining. In Proceedings of the 2018 Conference on Empiri-cal Methods in Natural Language Processing, 3890–3900.

[Manurung 2004] Manurung, H. 2004. An evolutionary al-gorithm approach to poetry generation.

[Mihalcea and Tarau 2004] Mihalcea, R., and Tarau, P. 2004.Textrank: Bringing order into text. In Proceedings of the2004 conference on empirical methods in natural languageprocessing, 404–411.

[Papineni et al. 2002] Papineni, K.; Roukos, S.; Ward, T.;and Zhu, W. J. 2002. Bleu: a method for automatic eval-uation of machine translation. In Proc Meeting of the Asso-ciation for Computational Linguistics.

[Sun 2012] Sun, J. 2012. jiebachinese word segmentationtool.

[Wang et al. 2016] Wang, Z.; He, W.; Wu, H.; Wu, H.; Li,W.; Wang, H.; and Chen, E. 2016. Chinese poetry gener-ation with planning based neural network. arXiv preprintarXiv:1610.09889.

[Wang, Luo, and Wang 2016] Wang, Q.; Luo, T.; and Wang,D. 2016. Can machine generate traditional chinese poetry?a feigenbaum test. In International Conference on BrainInspired Cognitive Systems, 34–46. Springer.

[Wang 2002] Wang, L. 2002. A summary of rhyming con-straints of chinese poems.

[Wieting et al. 2015] Wieting, J.; Bansal, M.; Gimpel, K.;and Livescu, K. 2015. Towards universal paraphrastic sen-tence embeddings. arXiv preprint arXiv:1511.08198.

[Wu, Tosa, and Nakatsu 2009] Wu, X.; Tosa, N.; andNakatsu, R. 2009. New hitch haiku: An interactive renkupoem composition supporting tool applied for sightseeingnavigation system. In Natkin, S., and Dupire, J., eds.,

Entertainment Computing – ICEC 2009, 191–196. Berlin,Heidelberg: Springer Berlin Heidelberg.

[Xia et al. 2017] Xia, Y.; Tian, F.; Wu, L.; Lin, J.; Qin, T.;Yu, N.; and Liu, T.-Y. 2017. Deliberation networks: Se-quence generation beyond one-pass decoding. In Advancesin Neural Information Processing Systems, 1784–1794.

[Yan et al. 2013] Yan, R.; Jiang, H.; Lapata, M.; Lin, S.-D.;Lv, X.; and Li, X. 2013. i, poet: Automatic chinese poetrycomposition through a generative summarization frameworkunder constrained optimization. In IJCAI, 2197–2203.

[Yan 2016] Yan, R. 2016. i, poet: Automatic poetry compo-sition through recurrent neural networks with iterative pol-ishing schema. In IJCAI, 2238–2244.

[Yang et al. 2017] Yang, X.; Lin, X.; Suo, S.; and Li, M.2017. Generating thematic chinese poetry with conditionalvariational autoencoder. CoRR.

[Yi et al. 2018] Yi, X.; Sun, M.; Li, R.; and Yang, Z. 2018.Chinese poetry generation with a working memory model.arXiv preprint arXiv:1809.04306.

[Yi, Li, and Sun 2017] Yi, X.; Li, R.; and Sun, M. 2017.Generating chinese classical poems with rnn encoder-decoder. In Chinese Computational Linguistics and Natu-ral Language Processing Based on Naturally Annotated BigData. Springer. 211–223.

[Yi, Li, and Sun 2018] Yi, X.; Li, R.; and Sun, M. 2018. Chi-nese poetry generation with a salient-clue mechanism. arXivpreprint arXiv:1809.04313.

[Zhang and Lapata 2014] Zhang, X., and Lapata, M. 2014.Chinese poetry generation with recurrent neural networks.In Proceedings of the 2014 Conference on Empirical Meth-ods in Natural Language Processing (EMNLP), 670–680.

[Zhang et al. 2017] Zhang, J.; Feng, Y.; Wang, D.; Wang, Y.;Abel, A.; Zhang, S.; and Zhang, A. 2017. Flexible and cre-ative chinese poetry generation using neural memory. arXivpreprint arXiv:1705.03773.

[Zhang et al. 2019] Zhang, H.; Gong, Y.; Yan, Y.; Duan, N.;Xu, J.; Wang, J.; Gong, M.; and Zhou, M. 2019. Pretraining-based natural language generation for text summarization.arXiv preprint arXiv:1902.09243.

[Zhou, You, and Ding 2010] Zhou, C.-L.; You, W.; andDing, X. 2010. Genetic algorithm and its implementation ofautomatic generation of chinese songci. Journal of Software21(3):427–437.

arxiv:1911.13182v1 [cs.cl] 29 nov 2019

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