1 CUBBITT model

Our CUBBITT translation system follows the Transformer architecture (Fig. 1, Supplementary Fig. 1) introduced in Vaswani et al.18. Transformer has an encoder-decoder structure where the encoder maps an input sequence of tokens (words or subword units) to a sequence of continuous deep representations z. Given z, the decoder generates an output sequence of tokens one element at a time. The decoder is autoregressive, i.e., consuming the previously generated symbols as additional input when generating the next token.

The encoder is composed of a stack of identical layers, with each layer having two sublayers. The first is a multi-head self-attention mechanism, and the second is a simple, position-wise fully connected feed-forward network. We employ a residual connection around each of the two sublayers, followed by layer normalization. The decoder is also composed of a stack of identical layers. In addition to the two sublayers from the encoder, the decoder inserts a third sublayer, which performs multi-head attention over the output of the encoder stack. Similar to the encoder, we employ residual connections around each of the sublayers, followed by layer normalization.

The self-attention layer in the encoder and decoder performs multi-head dot-product attention, each head mapping matrices of queries (Q), keys (K), and values (V) to an output vector, which is a weighted sum of the values V:

$${mathrm{Attention}}left( {Q,K,V} right) = {mathrm{softmax}}left( {frac{{QK^T}}{{sqrt {d_k} }}} right)V,$$


where Q ({Bbb R}^{n times d_k}), K ({Bbb R}^{n times d_k}), V ({Bbb R}^{n times d_v}), n is the sentence length, dv is the dimension of values, and dk is the dimension of the queries and keys. Attention weights are computed as a compatibility of the corresponding key and query and represent the relationship between deep representations of subwords in the input sentence (for encoder self-attention), output sentence (for decoder self-attention), or between the input and output sentence (for encoder-decoder attention). In encoder and decoder self-attention, all queries, keys and values come from the output of the previous layer, whereas is the encoder-decoder attention, keys and values come from the encoder’s topmost layer and queries come from the decoder’s previous layer. In the decoder, we modify the self-attention to prevent it from attending to following positions (i.e., rightward from the current position) by adding a mask, because the following positions will not be known in inference time.

2 English–Czech training data

Our training data are constrained to the data allowed in the WMT 2018 News translation shared task17 ( Parallel (authentic) data are: CzEng 1.7, Europarl v7, News Commentary v11 and CommonCrawl. Monolingual data for backtranslation are: English (EN) and Czech (CS) NewsCrawl articles. Data sizes (after filtering, see below) are reported in Supplementary Table 1.

While all our monolingual data are news articles, only less than 1% of our parallel data are news (summing News Commentary v12 and the news portion of CzEng 1.7). The biggest sources of our parallel data are: movie subtitles (63% of sentences), EU legislation (16% of sentences), and Fiction (9% of sentences)27. Unfortunately, no finer-grained metadata specifying the exact training-data domains (such as politics, business, and sport) are available.

We filtered out ca. 3% of sentences in the monolingual data by restricting the length to 500 characters and in case of Czech NewsCrawl also by keeping only sentences containing at least one accented character (using a regular expression m/[ěščřžýáíéúůd’t’ň]/i). This simple heuristic is surprisingly effective for Czech; it filters out not only sentences in other languages than Czech, but also various non-linguistic content, such as lists of football or stock-market results.

We divided the Czech NewsCrawl (synthetic data) into two parts: years 2007–2016 (58,231 k sentences) and year 2017 (7152 k sentences). When training block-BT, we simply concatenated four blocks of training data: authentic, synthetic 2007–2016, authentic and synthetic 2017. The sentences within these four blocks were randomly shuffled; we only do not shuffle across the data blocks. When training mix-BT, we used exactly the same training sentences, but we shuffled them fully. This means we upsampled the authentic training data two times. The actual ratio of authentic and synthetic data (as measured by the number of subword tokens) in the mix-BT training data was approximately 1.2:1.

3 English–Czech development and test data

WMT shared task on news translation provides a new test-set (with ~3000 sentences) each year collected from recent news articles (WMT = Workshop on statistical Machine Translation. In 2016, WMT was renamed to Conference on Machine Translation, but keeping the legacy abbreviation WMT. For more information see the WMT 2018 website The reference translations are created by professional translation agencies. All of the translations are done directly, and not via an intermediate language. Test sets from previous years are allowed to be used as development data in WMT shared tasks.

We used WMT13 (short name for WMT newstest2013) as the primary development set in our experiments (e.g., Figure 2a). We used WMT17 as a test-set for measuring BLEU scores in Fig. 2c. We used WMT18 (more precisely, its subset WMT18-orig-en, see below) as our final manual-evaluation test-set. Data sizes are reported in Supplementary Table 2.

In WMT test sets since 2014, half of the sentences for a language pair X-EN originate from English news servers (e.g., and the other half from X-language news servers. All WMT test sets include the server name for each document in metadata, so we were able to split our dev and test sets into two parts: originally Czech (orig-cs, for Czech-domain articles, i.e., documents with docid containing “.cz”) and originally English (orig-en, for non-Czech-domain articles. The WMT13-orig-en part of our WMT13 development set contains not only originally English articles, but also articles written originally in French, Spanish, German and Russian. However, the Czech reference translations were translated from English. In WMT18-orig-en, all the articles were originally written in English.).

According to Bojar et al.17, the Czech references in WMT18 were translated from English “by the professional level of service of, preserving 1–1 segment translation and aiming for literal translation where possible. Each language combination included two different translators: the first translator took care of the translation, the second translator was asked to evaluate a representative part of the work to give a score to the first translator. All translators translate towards their mother tongue only and need to provide a proof or their education or professional experience, or to take a test; they are continuously evaluated to understand how they perform on the long term. The domain knowledge of the translators is ensured by matching translators and the documents using T-Rank,”

Toral et al.22 furthermore warned about post-edited MT used as human references. However, confirmed that MT was completely deactivated during the process of creating WMT18 reference translations (personal communication).

4 English–French data

The English–French parallel training data were downloaded from WMT2014 ( The monolingual data were downloaded from WMT 2018 (making sure there is no overlap with the development and test data). We filtered the data for being English/French using the langid toolkit ( Data sizes after filtering are reported in Supplementary Table 3. When training English–French block-BT, we concatenated the French NewsCrawl2008–2014 (synthetic data) and authentic data, with no upsampling. When training French–English block-BT, we split the English NewsCrawl into three parts: 2011–2013, 2014–2015, and 2016–2017 and interleaved with three copies of the authentic training data, i.e., upsampling the authentic data three times. We always trained mix-BT on a fully shuffled version of the data used for the respective block-BT training.

Development and test data are reported in Supplementary Table 4.

5 English–Polish data

The English–Polish training and development data were downloaded from WMT2020 ( We filtered the data for being English/Polish using the FastText toolkit ( Data sizes after filtering are reported in Supplementary Table 5. When training English–Polish block-BT, we upsampled the authentic data two times and concatenated with the Polish NewsCrawl2008–2019 (synthetic data) upsampled six times. When training Polish–English block-BT, we upsampled the authentic data two times and concatenated with English NewsCrawl2018 (synthetic data, with no upsampling). We always trained mix-BT on a fully shuffled version of the data used for the respective block-BT training.

Development and test data are reported in Supplementary Table 6.

6 CUBBITT training: BLEU score

BLEU28 is a popular automatic measure for MT evaluation and we use it for hyperparameter tuning. Similarly to most other automatic MT measures, BLEU estimates the similarity between the system translation and the reference translation. BLEU is based on n-gram (unigrams up to 4-grams) precision of the system translation relative to the reference translation and a brevity penalty to penalize too short translations. We report BLEU scaled to 0–100 as is usual in most papers (although BLEU was originally defined as 0–1 by Papineni et al.28); the higher BLEU value, the better translation. We use the SacreBLEU implementation29 with signature BLEU+case.mixed+lang.en-cs+numrefs.1+smooth.exp+tok.13a.

7 CUBBITT training: hyperparameters

We use the Transformer “big” model from the Tensor2Tensor framework v1.6.018. We followed the training setup and tips of Popel and Bojar30 and Popel et al.31, training our models with the Adafactor optimizer32 instead of the default Adam optimizer. We use the following hyperparameters: learning_rate_schedule = rsqrt_decay, batch_size = 2900, learning_rate_warmup_steps = 8000, max_length = 150, layer_prepostprocess_dropout = 0, optimizer = Adafactor. For decoding, we use alpha = 1.0, beam_size = 4.

8 CUBBITT training: checkpoint averaging

A popular way of improving the translation quality in NMT is ensembling, where several independent models are trained and during inference (decoding, translation) each target token (word) is chosen according to an averaged probability distribution (using argmax in the case of greedy decoding) and used for further decisions in the autoregressive decoder of each model.

However, ensembling is expensive both in training and inference time. The training time can be decreased by using checkpoint ensembles33, where N last checkpoints of a single training run are used instead of N independently trained models. Checkpoint ensembles are usually worse than independent ensembles33, but allow to use more models in the ensemble thanks to shorter training time. The inference time can be decreased by using checkpoint averaging, where the weights (learned parameters of the network) in the N last checkpoints are element-wise averaged, creating a single averaged model.

Checkpoint averaging has been first used in NMT by Junczys-Dowmunt et al.34, who report that averaging four checkpoints is “not much worse than the actual ensemble” of the same four checkpoints and it is better than ensembles of two checkpoints. Averaging ten checkpoints “even slightly outperforms the real four-model ensemble”.

Checkpoint averaging has been popular in recent NMT systems because it has almost no additional cost (averaging takes only several minutes), the results of averaged models have lower variance in BLEU and are usually at least slightly better than models without averaging30.

In our experiments, we store checkpoints each hour and average the last 8 checkpoints.

9 CUBBITT training: Iterated backtranslation

For our initial experiments with backtranslation, we reused an existing CS → EN system UEdin (Nematus software trained by a team from the University of Edinburgh and submitted to WMT 201635). This system itself was trained using backtranslation. We decided to iterate the backtranslation process further by using our EN → CS Transformer to translate English monolingual data and use that for training a higher quality CS → EN Transformer, which was in turn used for translating Czech monolingual data and training our final EN → CS Transformer system called CUBBITT. Supplementary Fig. 2 illustrates this process and provides details about the training data and backtranslation variants (mix-BT in MT1 and block-BT in MT2–4) used.

Each training we did (MT3–5 in Supplementary Fig. 2) took ca. eight days on a single machine with eight GTX 1080 Ti GPUs. Translating the monolingual data with UEdin2016 (MT0) took ca. two weeks and with our Transformer models (MT1–3) it took ca. 5 days.

10 CUBBITT training: translationese tuning

It has been observed that text translated from language X into Y has different properties (such as lexical choice or syntactic structure) compared to text originally written in language Y36. Term translationese is used in translation studies (translatology) for this phenomenon (and sometimes also for the translated language itself).

We noticed that when training on synthetic data, the model performs much better on the WMT13-orig-cs dev set than on the WMT13-orig-en dev set. When trained on authentic data, it is the other way round. Intuitively, this makes sense: The target side of our synthetic data are original Czech sentences from Czech newspapers, similarly to the WMT13-orig-cs dataset. In our authentic parallel data, over 90% of sentences were originally written in English about non-Czech topics and translated into Czech (by human translators), similarly to the WMT13-orig-en dataset. There are two closely related phenomena: a question of domain (topics) in the training data and a question of so-called translationese effect, i.e., which side of the parallel training data (and test data) is the original and which is the translation.

Based on these observations, we prepared an orig-cs-tuned model and an orig-en-tuned model. Both models were trained in the same way; they differ only in the number of training steps. For the orig-cs-tuned model, we selected a checkpoint with the best performance on WMT13-orig-cs (Czech-origin portion of WMT newstest2013), which was at 774k steps. Similarly, for the orig-en-tuned model, we selected the checkpoint with the best performance on WMT13-orig-en, which was at 788k steps. Note that both the models were trained jointly in one experiment, just selecting checkpoints at two different moments. The WMT18-orig-en test-set was translated using the orig-en-tuned model and the WMT18-orig-cs part was translated using the orig-cs-tuned model.

11 CUBBITT training: regex postediting

We applied two simple post-processings to the translations, using regular expressions. First, we converted quotation symbols in the translations to the correct-Czech lower and upper quotes („ and “) using two regexes: s/(ˆ|[({[])(“|,,|”|“)/$1„/g and s/(“|”)($|[,.?!:;)}]])/“$2/g. Second, we deleted phrases repeated more than twice (immediately following each other); we kept just the first occurrence. We considered phrases of one up to four words. This postprocessing affected less than 1% sentences in the dev set.

12 CUBBITT training: English–French and English–Polish

We trained English→French, French→English, English→Polish and Polish→English versions of CUBBITT, following the abovementioned English–Czech setup, but using the training data described in Supplementary Tables 3 and 5 and the training diagram in Supplementary Fig. 3. All systems (including M1 and M2) were trained with Tensor2Tensor Transformer (no Nematus was involved). Iterated backtranslation was tried only for French→English. No translationese tuning was used (because we report just the BLEU training curve, but no experiments where the final checkpoint selection is needed). No regex post-diting was used.

13 Reanalysis of context-unaware evaluation in WMT18

We first reanalyzed results from the context-unaware evaluation of WMT 2018 English–Czech News Translation Task, provided to us by the WMT organizers ( The data shown in Fig. 3a were processed in the same way as by the WMT organizers: scores with BAD and REF types were first removed, a grouped score was computed as an average score for every triple language pair (“Pair”), MT system (“SystemID”), and sentence (“SegmentID”) was computed, and the systems were sorted by their average score. In Fig. 3a, we show distribution of the grouped scores for each of the MT systems, using paired two-tailed sign test to compare significance of differences of the subsequent systems.

We next assessed whether the results could be confounded by the original language of the source. Specifically, one half of the test-set sentences in WMT18 were originally English sentences translated to Czech by a professional agency, while the other half were English translations of originally Czech sentences. However, both types of sentences were used together for evaluation of both translation directions in the competition. Since the direction of translation could affect the evaluation, we first re-evaluated the MT systems in WMT18 by splitting the test-set according to the original language in which the source sentences were written.

Although the absolute values of source direct assessment were lower for all systems and reference translation in originally English source sentences compared to originally Czech sentences, CUBBITT significantly outperformed the human reference and other MT systems in both test sets (Supplementary Fig. 4). We checked that this was true also when comparing z-score normalized scores and using unpaired one-tail Mann–Whitney U test, as by the WMT organizers.

Any further evaluation in our study was performed only on documents with the source side as the original text, i.e., with originally English sentences in the English→Czech evaluations.

14 Context-aware evaluation: methodology

Three groups of paid evaluators were recruited: six professional translators, three translation theoreticians, and seven other evaluators (non-professionals). All 16 evaluators were native Czech speakers with excellent knowledge of the English language. The professional translators were required to have at least 8 years of professional translation experience and they were contacted via The Union of Interpreters and Translators ( The translation theoreticians were from The Institute of Translation Studies, Charles University’s Faculty of Arts ( Guidelines presented to the evaluators are given in Supplementary Methods 1.1.

For each source sentence, evaluators compared two translations: Translation T1 (the left column of the annotation interface) vs Translation T2 (the right column of the annotation interface). Within one document (news article), Translation T1 was always a reference and Translation T2 was always CUBBITT, or vice versa (i.e., each column within one document being purely reference translation or purely CUBBITT). However, evaluators did not know which system is which, nor that one of them is a human translation and the other one is a translation by MT system. The order of reference and CUBBITT was random in each document. Each evaluator encountered reference being Translation T1 in approximately one half of the documents.

Evaluators scored 10 consecutive sentences (or the entire document if shorter than 10 sentences) from a random section of the document (the same section was used in both T1 and T2 and by all evaluators scoring this document), but they had access to the source side of the entire document (Supplementary Fig. 5).

Every document was scored by at least two evaluators (2.55 ± 0.64 evaluators on average). The documents were assigned to evaluators in such a way that every evaluator scored nine different nonspam documents and most pairs of evaluators had at least one document in common. This maximized the diversity of annotator pairs in the computation of interannotator agreement. In total, 135 (53 unique) documents and 1304 (512 unique) sentences were evaluated by the 15 evaluators who passed quality control (see below).

15 Context-aware evaluation: quality control

The quality control check of evaluators was performed using a spam document, similarly as in Läubli et al.23 and Kittur et al.37. In MT translations of the spam document, the middle words (i.e., except the first and last words in the sentence) were randomly shuffled in each of the middle six sentences of the document (i.e., the first and last two sentences were kept intact). We ascertained that the resulting spam translations made no sense.

The criterion for evaluators to pass the quality control was to score at least 90% of reference sentences better than all spam sentences (in each category: adequacy, fluency, overall). One non-professional evaluator did not pass the quality control, giving three spam sentences a higher score than 10% of the reference sentences. We excluded the evaluator from the analysis of the results (but the key results reported in this study would hold even when including the evaluator).

16 context-aware evaluation: interannotator agreement

We used two methods to compute interannotator agreement (IAA) on the paired scores (CUBBITT—reference difference) in adequacy, fluency, and overall quality for the 15 evaluators. First, for every evaluator, we computed Pearson and Spearman correlation of his/her scores on individual sentences with a consensus of scores from all other evaluators. This consensus was computed for every sentence as the mean of evaluations by other evaluators who scored this sentence. This correlation was significant after Benjamini–Hochberg correction for multiple testing for all evaluators in adequacy and fluency and overall quality. The median and interquartile range of the Spearman r of the 15 evaluators were 0.42 (0.33–0.49) for adequacy, 0.49 (0.35–0.55) for fluency, and 0.49 (0.43–0.54) for overall quality. The median and interquartile range of the Pearson r of the 15 evaluators were 0.42 (0.32–0.49) for adequacy, 0.47 (0.39–0.55) for fluency, and 0.46 (0.40–0.50) for overall quality.

Second, we computed Kappa in the same way as in WMT 2012–201638, separately for adequacy, fluency, and overall quality (Supplementary Table 7).

17 Context-aware evaluation: statistical analysis

First, we computed the average score for every sentence from all evaluators who scored the sentence within the group (non-professionals, professionals, translation theoreticians for Fig. 3 and Supplementary Fig. 7B) or within the entire cohort (for Supplementary Fig. 7A). The difference between human reference and CUBBITT translations was assessed using paired two-tailed sign test (Matlab function sign test) and P values below 0.05 were considered statistically significant.

In the analysis of relative contribution of adequacy and fluency in the overall score (Supplementary Fig. 6), we fitted a linear model through scores in all sentences, separately for human reference translations and CUBBITT translations for every evaluator, using matlab function fitlm(tableScores,‘overall~adequacy+fluency’,‘RobustOpts’,‘on’, ‘Intercept’, false).

18 Context-aware evaluation: analysis of document types

For analysis of document types (Supplementary Fig. 11), we grouped the 53 documents (news articles) into seven classes: business (including economics), crime, entertainment (including art, film, one article about architecture), politics, scitech (science and technology), sport, and world. Then we compared the relative difference of human reference minus CUBBITT translation scores on the document-level scores and sentence-level scores and used sign test to assess the difference between the two translations.

19 Evaluation of error types in context-aware evaluation

Three non-professionals and three professional translator evaluators performed a follow-up evaluation of error types, after they finished the basic context-aware evaluation. Nine columns were added into the annotation sheets next to their evaluations of quality (adequacy, fluency, and overall quality) of each of the two translations. The evaluators were asked to classify all translation errors into one of eight error types and to identify sentences with an error due to cross-sentence context (see guidelines). In total, 54 (42 unique) documents and 523 (405 unique) sentences were evaluated by the six evaluators. Guidelines presented to the evaluators are given in Supplementary Methods 1.2.

Similarly to Section 5.4, we compute IAA Kappa scores for each error type, based on the CUBBITT—Reference difference (Supplementary Table 8).

When carrying out statistical analysis, we first grouped the scores of sentences with multiple evaluations by computing the average number of errors per sentence and error type from the scores of all evaluators who scored this sentence. Next, we compared the percentage of sentences with at least one error (Fig. 4a) and the number of errors per sentence (Supplementary Fig. 9), using sign test to compare the difference between human reference and CUBITT translations.

20 Evaluation of five MT systems

Five professional-translator evaluators performed this follow-up evaluation after they finished the previous evaluations. For each source sentence, the evaluators compared five translations by five MT systems: Google Translate from 2018, UEdin from 2018, Transformer trained with one iteration of mix-BT (as MT2 in Supplementary Fig. 2, but with mix-BT instead of block-BT), Transformer trained with one iteration of block-BT (MT2 in Supplementary Fig. 2), and the final CUBBITT system. Within one document, the order of the five systems was fixed, but it was randomized between documents. Evaluators were not given any details about the five translations (such as whether they are human or MT translations or by which MT systems). Every evaluator was assigned only documents that he/she has not yet evaluated in the basic quality + error types evaluations. Guidelines presented to the evaluators are given in Supplementary Methods 1.3.

Evaluators scored 10 consecutive sentences (or the entire document if this was shorter than 10 sentences) from a random section of the document (the same for all five translations), but had access to the source side of the entire document. Every evaluator scored nine different documents. In total, 45 (33 unique) documents and 431 (336 unique) sentences were evaluated by the five evaluators.

When measuring interannotator agreement, in addition to reporting IAA Kappa scores for the evaluation of all five systems (as usual in WMT) in Supplementary Table 9, we also provide IAA Kappa scores for each pair of systems in Supplementary Fig. 12. This confirms the expectation that a higher interannotator agreement is achieved in comparisons of pairs of systems with a large difference in quality.

When carrying out statistical analysis, we first grouped the scores of sentences with multiple evaluations by computing the fluency and adequacy score per sentence and translation from the scores of all evaluators who scored this sentence. Next, we sorted the MT systems by the mean score, using sign test to compare the difference between the consecutive systems (for Fig. 4b). Evaluation of the entire test-set (all originally English sentences) using BLEU for comparison is shown in Supplementary Fig. 13.

21 Translation turing test

Participants of the Translation Turing test were unpaid volunteers. The participants were randomly assigned into four non-overlapping groups: A1, A2, B1, B2. Groups A1 and A2 were presented translations by both human reference and CUBBITT. Groups B1 and B2 were presented translations by both human reference and Google Translate (obtained from on 13 August 2018). The source sentences in the four groups were identical. Guidelines presented to the evaluators are given in Supplementary Methods 1.4.

The evaluated sentences were taken from originally English part of the WMT18 evaluation test-set (i.e., WMT18-orig-en) and shuffled in a random order. For each source sentence, it was randomly assigned whether Reference translation will be presented to group A1 or A2; the other group was presented this sentence with the translation by CUBBITT. Similarly, for each source sentence, it was randomly assigned whether Reference translation will be presented to group B1 or B2; the other group was presented this sentence with the translation by Google Translate. Every participant was therefore presented human and machine translations approximately in a 1:1 ratio (but this information was intentionally concealed from them).

Each participant encountered each source sentence at most once (i.e., with only one translation), but each source sentence was evaluated for all the three systems. (Reference was evaluated twice, once in the A groups, once in the B groups.) Each participant was presented with 100 sentences. Only participants with more than 90 sentences evaluated were included in our study.

The Translation Turing test was performed as the first evaluation in this study (but after the WMT18 competition) and participants who overlapped with the evaluators of the context-aware evaluations were not shown results from the Turing test before they finished all the evaluations.

In total, 15 participants evaluated a mix of human and CUBBITT translations (five professional translators, six MT researchers, and four other), 16 participants evaluated a mix of human and Google Translate translations (eight professional translators, five MT researchers, and three other). A total of 3081 sentences were evaluated by all participants of the test.

When measuring interannotator agreement, we computed the IAA Kappas (Supplementary Table 10) using our own script, treating the task as a simple binary classification. While in the previous types of evaluations, we computed the IAA Kappa scores using the script from WMT 201638, this was not possible in the Translation Turing test, which does not involve any ranking.

When carrying out statistical analysis, we computed the accuracy for each participant as the percentage of sentences with correctly identified MT or human translations (i.e., number of true positives + true negatives divided by the number of scored sentences) and the significance was assessed using the Fisher test on the contingency table. The resulting P-values were corrected for multiple testing with the Benjamini–Hochberg method using matlab function fdr_bh(pValues,0.05,‘dep’,‘yes’)39 and participants with the resulting Q-value below 0.05 were considered to have significantly distinguished between human and machine translations.

22 Block-BT and checkpoint averaging synergy

In this analysis, the four systems from Fig. 2a were compared: block-BT vs mix-BT, both with (Avg) vs without (noAvg) checkpoint averaging. All four systems were trained with a single iteration of backtranslation only, i.e., corresponding to the MT2 system in Supplementary Fig. 2. The WMT13 newstest (3000 sentences) was used to evaluate two properties of the systems over time: translation diversity and generation of novel translations by checkpoint averaging. These properties were analyzed over the time of the training (up to 1 million steps), during which checkpoints were saved every hour (up to 214 checkpoints).

23 Overall diversity and novel translation quantification

We first computed the overall diversity as the number of all the different translations produced by the 139 checkpoints between 350,000 and 1,000,000 steps. In particular, for every sentence in WMT13 newstest, the number of unique translations was computed in the hourly checkpoints, separately for block-BT-noAvg and mix-BT-noAvg. Comparing the two systems in every sentence, block-BT-noAvg produced more unique translations in 2334 (78%) sentences; mix-BT-noAvg produced more unique translations in 532 (18%) sentences; and the numbers of unique translations were equal in 134 (4%) sentences.

Next, in the same checkpoints and for every sentence, we compared translations produced by models with and without averaging and computed the number of checkpoints with a novelAvg∞ translation. These are defined as translations that were never produced by the same system without checkpoint averaging (by never we mean in none of the checkpoints between 350,000 and 1,000,000). In total, there were 1801 (60%) sentences with at least one checkpoint with novelAvg∞ translation in block-BT and 949 (32%) in mix-BT. When comparing the number of novelAvg∞ translations in block-BT vs mix-BT in individual sentences, there were 1644 (55%) sentences with more checkpoints with novelAvg∞ translations in block-BT, 184 (6%) in mix-BT, and 1172 (39%) with equal values.

24 Diversity and novel translations over time

First, we evaluated development of translation diversity over time using moving window of octuples of checkpoints in the two systems without checkpoint averaging. In particular, for every checkpoint and every sentence, we computed the number of different unique translations in the last eight checkpoints. The average across sentences is shown in Supplementary Fig. 16, separately for block-BT-noAvg and mix-BT-noAvg.

Second, we evaluated development of novel translations by checkpoint averaging over time. In particular, for every checkpoint and every sentence, we evaluated whether the Avg model created a novelAvg8 translation, i.e., whether the translation differed from all the translations of the last eight noAvg checkpoints. The percentage of sentences with a novelAvg8 translation in the given checkpoint is shown in Fig. 8a, separately for block-BT and mix-BT.

25 Effect of novel translations on evaluation by BLEU

We first identified the best model (checkpoint) for each of the systems according to BLEU: checkpoint 775178 in block-BT-Avg (BLEU 28.24), checkpoint 775178 in block-BT-NoAvg (BLEU 27.54), checkpoint 606797 in mix-BT-Avg (BLEU 27.18), and checkpoint 606797 in mix-BT-NoAvg (BLEU 26.92). We note that the Avg and NoAvg systems do not necessarily need to have the same checkpoint with the highest BLEU, however it was nevertheless the case in both block-BT and mix-BT systems here. We next identified which translations in block-BT-Avg and in mix-BT-Avg were novelAvg8 (i.e., not seen in the last eight NoAvg checkpoints). There were 988 novelAvg8 sentences in block-BT-Avg and 369 in mix-BT-Avg. Finally, we computed BLEU of Avg translations, in which either the novelAvg8 translations were replaced with the NoAvg versions (yellow bars in Fig. 8b), or vice versa (orange bars in Fig. 8b); separately for block-BT and mix-BT.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

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