SlowGuess/ACL_2020_OCR huggingface dataset:
$$
\begin{array}{l} P (y _ {t} \mid \boldsymbol {z} _ {t}) = p _ {\mathrm {g a t e}} P _ {\mathrm {g e n}} (y _ {t} \mid \boldsymbol {z} _ {t}) \\ + \left(1 - p _ {\text {g a t e}}\right) \sum_ {j = 1: o _ {j} = y _ {t}} ^ {M} P _ {\text {c o p y}} \left(o _ {j} \mid \boldsymbol {z} _ {t}\right), \\ \end{array}
$$
where it is assumed that the triples in the memory have the same subject and thus only objects need to be copied.
4.3 Model Learning
The conditional probability of sequence of actions  $\pmb{a} = (a_{1}, a_{2}, \dots, a_{T})$  given the set of triples  $\mathcal{T}$  and
the sequence of input words  $\pmb{x}$  can be written as
$$
P (\boldsymbol {a} \mid \mathcal {T}, \boldsymbol {x}) = \prod_ {t = 1} ^ {T} P (a _ {t} \mid \boldsymbol {z} _ {t})
$$
where  $P(a_{t} \mid z_{t})$  is the conditional probability of action  $a_{t}$  given state  $z_{t}$  at time  $t$  and  $T$  denotes the number of actions.
The conditional probability of sequence of generated words  $\pmb{y} = (y_{1}, y_{2}, \dots, y_{T})$  given the sequence of actions  $\pmb{a}$  can be written as
$$
P (\boldsymbol {y} \mid \boldsymbol {a}) = \prod_ {t = 1} ^ {T} P (y _ {t} \mid a _ {t})
$$
where  $P(y_{t} \mid a_{t})$  is the conditional probability of generated word  $y_{t}$  given action  $a_{t}$  at time  $t$ , which is calculated as
$$
P (y _ {t} \mid a _ {t}) = \left\{ \begin{array}{l l} P (y _ {t} \mid \boldsymbol {z _ {t}}) & \text {i f a _ {t} = G e n} \\ 1 & \text {o t h e r w i s e} \end{array} \right.
$$
Note that not all positions have a generated word. In such a case,  $y_{t}$  is simply a null word.
The learning of the model is carried out via supervised learning. The objective of learning is to minimize the negative log-likelihood of  $P(\mathbf{a} \mid \mathcal{T}, \mathbf{x})$  and  $P(\mathbf{y} \mid \mathbf{a})$
$$
\mathcal {L} (\boldsymbol {\theta}) = - \sum_ {t = 1} ^ {T} \left\{\log P \left(a _ {t} \mid \boldsymbol {z} _ {t}\right) + \log P \left(y _ {t} \mid a _ {t}\right) \right\}
$$
where  $\theta$  denotes the parameters.
A training instance consists of a pair of draft text and revised text, as well as a set of triples, denoted as  $x$ ,  $y$ , and  $\mathcal{T}$  respectively. For each instance, our method derives a sequence of actions denoted as  $\pmb{a}$ , in a similar way as that in (Dong et al., 2019). It first finds the longest common subsequence between  $x$  and  $y$ , and then selects an action of Keep, Drop, or Gen at each position, according to how  $y$  is obtained from  $x$  and  $\mathcal{T}$  (cf., Tab. 4). Action Gen is preferred over action Drop when both are valid.
(a) Table-to-Text
(b) Text-to-Text
Figure 2: Model architectures of the baselines. All models employ attention and copy mechanism.
(c) ENCEDEDITOR
4.4 Time Complexity
The time complexity of inference in FACTEDITOR is  $\mathcal{O}(NM)$ , where  $N$  is the number of words in the buffer, and  $M$  is the number of triples. Scanning of data in the buffer is of complexity  $\mathcal{O}(N)$ . The generation of action needs the execution of attention, which is of complexity  $\mathcal{O}(M)$ . Usually,  $N$  is much larger than  $M$ .
4.5 Baseline
We consider a baseline method using the encoder-decoder architecture, which takes the set of triples and the draft text as input and generates a revised text. We refer to the method as EncDecEDITOR. The encoder of EncDecEDITOR is the same as that of FACTEDITOR. The decoder is the standard attention and copy model, which creates and utilizes a context vector and predicts the next word at each time.
The time complexity of inference in EncDecEDITOR is  $\mathcal{O}(N^2 +NM)$  (cf., Britz et al. (2017)). Note that in fact-based text editing, usually  $N$  is very large. That means that EncDecEDITOR is less efficient than FACTEDITOR.
We conduct experiments to make comparison between FACTEDITOR and the baselines using the two datasets WEBEDIT and ROTOEDIT.
The main baseline is the encoder-decoder model ENCDECEDITOR, as explained above. We further consider three baselines, No-Editing, Table-to-Text, and Text-to-Text. In No-Editing, the draft text is directly used. In Table-to-Text, a revised text is generated from the triples using encoder-decoder. In Text-to-Text, a revised text is created from the draft text using the encoder-decoder model. Figure 2 gives illustrations of the baselines.
We evaluate the results of revised texts by the models from the viewpoint of fluency and fidelity.
We utilize ExactMatch (EM), BLEU (Papineni et al., 2002) and SARI (Xu et al., 2016) scores as evaluation metrics for fluency. We also utilize precision, recall, and F1 score as evaluation metrics for fidelity. For WEBEDIT, we extract the entities from the generated text and the reference text and then calculate the precision, recall, and F1 scores. For ROTOEDIT, we use the information extraction tool provided by Wiseman et al. (2017) for calculation of the scores.
For the embeddings of subject and object for both datasets and the embedding of the predicate for ROTOEDIT, we simply use the embedding lookup table. For the embedding of the predicate for WEBEDIT, we first tokenize the predicate, lookup the embeddings of lower-cased words from the table, and use averaged embedding to deal with the OOV problem (Moryossef et al., 2019).
We tune the hyperparameters based on the BLEU score on a development set. For WEBEDIT, we set the sizes of embeddings, buffers, and triples to 300, and set the size of the stream to 600. For ROTOEDIT, we set the size of embeddings to 100 and set the sizes of buffers, triples, and stream to 200. The initial learning rate is 2e-3, and AMSGrad is used for automatically adjusting the learning rate (Reddi et al., 2018). Our implementation makes use of AllenNLP (Gardner et al., 2018).
Quantitative evaluation
We present the performances of our proposed model FACTEDITOR and the baselines on fact-based text editing in Table 5. One can draw several conclusions from the results.
First, our proposed model, FACTEDITOR, achieves significantly better performances than the main baseline, ENCODEDITOR, in terms of almost all measures. In particular, FACTEDITOR
5We use a modified version of SARI where  $\beta$  equals 1.0, available at https://github.com/tensorflow/tensor2tensor/blob/master/tensor2tensor/util/sari hook.py
Model	FLUENCY	FIDELITY
BLEU	SARI	KEEP	ADD	DELETE	EM	P%	R%	F1%
Baselines
No-Editing	66.67	31.51	78.62	3.91	12.02.	0.	84.49	76.34	80.21
Table-to-Text	33.75	43.83	51.44	27.86	52.19	5.78	98.23	83.72	90.40
Text-to-Text	63.61	58.73	82.62	25.77	67.80	6.22	81.93	77.16	79.48
Fact-based text editing
ENCDECEDITOR	71.03	69.59	89.49	43.82	75.48	20.96	98.06	87.56	92.51
FACTEDITOR	75.68	72.20	91.84	47.69	77.07	24.80	96.88	89.74	93.17
(a)WEBEDIT
Model	FLUENCY	FIDELITY
BLEU	SARI	KEEP	ADD	DELETE	EM	P%	R%	F1%
Baselines
No-Editing	74.95	39.59	95.72	0.05	23.01	0.	92.92	65.02	76.51
Table-to-Text	24.87	23.30	39.12	14.78	16.00	0.	48.01	24.28	32.33
Text-to-Text	78.07	60.25	97.29	13.04	70.43	0.02	63.62	41.08	49.92
Fact-based text editing
ENCODEDITOR	83.36	71.46	97.69	44.02	72.69	2.49	78.80	52.21	62.81
FACTEDITOR	84.43	74.72	98.41	41.50	84.24	2.65	78.84	52.30	63.39
obtains significant gains in DELETE scores on both WEBEDIT and ROTOEDIT.
Second, the fact-based text editing models (FACTEDITOR and ENCDECEDITOR) significantly improve upon the other models in terms of fluency scores, and achieve similar performances in terms of fidelity scores.
Third, compared to No-Editing, Table-to-Text has higher fidelity scores, but lower fluency scores. Text-to-Text has almost the same fluency scores, but lower fidelity scores on ROTOEDIT.
Qualitative evaluation
We also manually evaluate 50 randomly sampled revised texts for WEBEDIT. We check whether the revised texts given by FACTEDITOR and ENCEDECEDITOR include all the facts. We categorize the factual errors made by the two models. Table 6 shows the results. One can see that FACTEDITOR covers more facts than ENCEDECEDITOR and has less factual errors than ENCEDECEDITOR.
FACTEDITOR has a larger number of correct editing (CQT) than ENCODEDITOR for fact-based text editing. In contrast, ENCODEDITOR often includes a larger number of unnecessary rephrasings (UPARA) than FACTEDITOR.
(b) ROTOEDIT
Table 5: Performances of FACTEDITOR and baselines on two datasets in terms of Fluency and Fidelity. EM stands for exact match.
Covered facts	Factual errors
CQT	UPARA	RPT	MS	USUP	DREL
ENCODEDITOR	14	7	16	21	3	12
FACTEDITOR	24	4	9	19	1	3
Table 6: Evaluation results on 50 randomly sampled revised texts in WEBEDIT in terms of numbers of correct editing (CQT), unnecessary paraphrasing (UPARA), repetition (RPT), missing facts (Ms), unsupported facts (USUP) and different relations (DREL)
There are four types of factual errors: fact repetitions (RPT), fact missings (Ms), fact unsupported (USUP), and relation difference (DREL). Both FACTEDITOR and ENCODEDITOR often fail to insert missing facts (Ms), but rarely insert unsupported facts (USUP). ENCODEDITOR often generates the same facts multiple times (RPT) or facts in different relations (DREL). In contrast, FACTEDITOR can seldomly make such errors.
Table 7 shows an example of results given by ENCDECEDITOR and FACTEDITOR. The revised texts of both ENCDECEDITOR and FACTEDITOR appear to be fluent, but that of FACTEDITOR has higher fidelity than that of ENCDECEDITOR. ENCDECEDITOR cannot effectively eliminate the
Set of triples	{(Ardmore_Airport, runwayLength, 1411.0),
(Ardmore_Airport, 3rd_runway_SurfaceType, Poaceae),
(Ardmore_Airport, operatingOrganisation, Civil_Aviation_Authority_of_New_Zealand),
(Ardmore_Airport, elevationAboveTheSeaLevel, 34.0),
(Ardmore_Airport, runwayName, 03R/21L)}
Draft text	Ardmore_Airport, ICAO Location Identifier UTAA . Ardmore_Airport 3rd runway is made of Poaceae and Ardmore_Airport . 03R/21L is 1411.0 m long and Ardmore_Airport is 34.0 above sea level .
Revised text	Ardmore_Airport is operated by Civil_Aviation_Authority_of_New_Zealand . Ardmore_Airport 3rd runway is made of Poaceae and Ardmore_Airport name is 03R/21L . 03R/21L is 1411.0 m long and Ardmore_Airport is 34.0 above sea level .
ENCDECEDITOR	Ardmore_Airport, ICAO Location Identifier UTAA , is operated by Civil_Aviation_Authority_of_New_Zealand . Ardmore_Airport 3rd runway is made of Poaceae and Ardmore_Airport . 03R/21L is 1411.0 m long and Ardmore_Airport is 34.0 m long .
FACTEDITOR	Ardmore_Airport is operated by Civil_Aviation_Authority_of_New_Zealand . Ardmore_Airport 3rd runway is made of Poaceae and Ardmore_Airport . 03R/21L is 1411.0 m long and Ardmore_Airport is 34.0 above sea level .
Table 7: Example of generated revised texts given by ENCDECEDITOR and FACTEDITOR on WEBEDIT. Entities in green appear in both the set of triples and the draft text. Entities in orange only appear in the draft text. Entities in blue should appear in the revised text but do not appear in the draft text.
WEBEDIT	ROTOEDIT
Table-to-Text	4,083	1,834
Text-to-Text	2,751	581
ENCODEDITOR	2,487	505
FACTEDITOR	3,295	1,412
Table 8: Runtime analysis (# of words/second). Table-to-Text always shows the fastest performance (Bold-faced). FACTEDITOR shows the second fastest runtime performance (Underlined).
description about an unsupported fact (in orange) appearing in the draft text. In contrast, FACTEDITOR can deal with the problem well. In addition, ENCODEDITOR conducts an unnecessary substitution in the draft text (underlined). FACTEDITOR tends to avoid such unnecessary editing.
Runtime analysis
We conduct runtime analysis on FACTEDITOR and the baselines in terms of number of processed words per second, on both WEBEDIT and ROTOEDIT. Table 8 gives the results when the batch size is 128 for all methods. Table-to-Text is the fastest, followed by FACTEDITOR. FACTEDITOR is always faster than ENCODEDITOR, apparently because it has a lower time complexity, as explained in Section 4. The texts in WEBEDIT are relatively short, and thus FACTEDITOR and ENCODEDITOR have similar runtime speeds. In contrast, the texts in ROTOEDIT are relatively long, and thus FACTEDITOR executes approximately two times faster than ENCODEDITOR.
In this paper, we have defined a new task referred to as fact-based text editing and made two contributions to research on the problem. First, we have proposed a data construction method for fact-based text editing and created two datasets. Second, we have proposed a model for fact-based text editing, named FACTEDITOR, which performs the task by generating a sequence of actions. Experimental results show that the proposed model FACTEDITOR performs better and faster than the baselines, including an encoder-decoder model.
We would like to thank the reviewers for their insightful comments.
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