Don’t Rank, Combine! Combining Machine Translation Hypotheses Using Quality Estimation (2024)

Abstract: Neural machine translation systems estimate probabilities of target sentences given source sentences, yet these estimates may not align with human preferences. This work introduces QE-fusion, a method that synthesizes translations using a quality estimation metric (QE), which correlates better with human judgments. QE-fusion leverages a pool of candidates sampled from a model and combines spans from different candidates using a QE metric such as COMETKIWI. We compare QE-fusion against beam search and recent reranking techniques, such as Minimum Bayes Risk decoding or QE-reranking. Our method consistently improves translation quality in terms of COMET and BLEURT scores when applied to large language models (LLMs) used for translation (PolyLM, XGLM, Llama2, Mistral, ALMA, and Tower) and to multilingual translation models (NLLB), over five language pairs. Notably, QE-fusion exhibits larger improvements for LLMs due to their ability to generate diverse outputs. We demonstrate that our approach generates novel translations in over half of the cases and consistently outperforms other methods across varying numbers of candidates (5–200). Furthermore, we empirically show that QE-fusion scales linearly with the number of candidates in the pool.

heading: 1 Introduction
text: Neural machine translation (NMT) models are probability estimators of translations given source sentences. Therefore, errors in NMT often arise due to the misalignment between the model’s probabilities and human preferences (Koehn and Knowles, 2017; Ott et al., 2018; Stahlberg and Byrne, 2019). In contrast, MT evaluation metrics have shown increasing correlation with human judgements (Mathur et al., 2020; Freitag et al., 2021, 2022b), making them valuable tools for selecting candidates generated by NMT models.
Reference-based evaluation metrics such as COMET (Rei et al., 2020) and BLEURT (Sellam et al., 2020) have been successfully employed for Minimum Bayes Risk (MBR) decoding (Fernandes et al., 2022; Freitag et al., 2022a). In MBR, these metrics serve as utility functions to select the candidate with the highest similarity to all other candidates (Kumar and Byrne, 2002, 2004). Additionally, quality estimation (QE) metrics such as COMET-QE (Rei et al., 2021), which do not need reference translations, have been used to rerank a pool of candidates based on their estimated quality (Fernandes et al., 2022; Farinhas et al., 2023). Such reranking approaches improve translation quality over standard beam search, particularly when measured with neural-based MT evaluation metrics.
However, reranking methods are challenged in situations where candidate translations exhibit complementary errors, with no candidate clearly improving over all others. Figure 1 illustrates this issue. The first candidate, Fire in French chemical plant, uses in instead of the more idiomatic at. The third candidate makes a better choice in this case but renders the verb as cleared instead of extinguished, which is incorrect here. Making the most of this pool of candidates is not possible without combining fragments from several ones.
To address this limitation, we propose QEfusion, an approach that leverages the potential complementarity of model-generated candidates to synthesize an improved translation, guided by a QE metric. QE-fusion starts by identifying divergent spans, i.e. spans that exhibit variations within the pool of candidates. Then, it traverses these divergent spans, selecting at each step the one that contributes to a higher score according to the QE metric. The chosen spans are integrated into the synthesized translation, which is thus a fusion of multiple candidates.
We demonstrate that QE-fusion is effective with pools of candidates obtained from high-performing
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multilingual NMT models such as NLLB (NLLB Team et al., 2022), as well as with candidates obtained using in-context learning with large language models (LLMs), which have recently shown comparable performance to NMT models (Garcia et al., 2023; Hendy et al., 2023; Zhu et al., 2023). Indeed, QE-fusion improves translation for several popular, open-source LLMs: PolyLM (Wei et al., 2023), XGLM (Lin et al., 2022), Llama2 (Touvron et al., 2023), Mistral (Jiang et al., 2023a), ALMA (Xu et al., 2024) and TowerBase (Alves et al., 2024).
Our contributions are the following:1
1. We introduce QE-fusion, a novel algorithm that leverages quality estimation metrics to create improved translations by combining spans from a pool of candidates.
2. We demonstrate the superior performance of QE-fusion compared to the recent QEreranking and MBR decoding methods, across various open-source LLMs and multilingual NMT models, in five language pairs.
3. We explain QE-fusion’s larger improvements for LLMs over NMT models by the greater diversity of candidates generated by LLMs.
4. We showcase the efficiency of our algorithm by empirically demonstrating that its runtime scales linearly with the number of candidates.
5. We show that QE-fusion effectively reduces hallucinations compared to QE-reranking and MBR, thus enhancing translation reliability.
1The code is available at https://github.com/ GeorgeVern/qe-fusion.

heading: 2 Related Work
text: We review in this section several approaches that aim to incorporate additional knowledge either during the decoding process or after it, in order to mitigate the misalignment between MT models and human preferences. We start with a brief reminder of MT evaluation metrics, which play a crucial role as a selection criterion.
MT evaluation metrics. Traditional overlapbased evaluation metrics for MT such as BLEU (Papineni et al., 2002) and ChrF (Popović, 2015) are known for their imperfect correlation with human judgments (Mathur et al., 2020; Kocmi et al., 2021; Freitag et al., 2021, 2022b). In response, researchers have shifted their attention towards metrics that use neural networks to score translation outputs, such as BERTScore (Zhang et al., 2020), Prism (Thompson and Post, 2020), COMET (Rei et al., 2020) and BLEURT (Sellam et al., 2020). To better emulate human assessment, these metrics are often fine-tuned to predict human scores based on annotations such as those provided by the WMT metrics tasks (Freitag et al., 2022b). In contrast to the reference-based metrics above, which have access to the reference translation, referencefree or quality estimation metrics solely rely on the source sentence for estimating the quality of a translation (Zerva et al., 2022). Recent QE metrics are COMET-QE (Rei et al., 2021), TransQuest (Ranasinghe et al., 2020) and COMETKIWI (Rei et al., 2022b).
Reranking candidate translations. One of the earliest proposals for reranking the outputs of NMT systems is the adaptation of the noisy channel model (Brown et al., 1993) to NMT systems (Yee et al., 2019; Bhosale et al., 2020). This approach combines scores from three components: a forward
translation model trained on the original direction, a backward model trained on the opposite direction, and a language model trained on the target language. By integrating these diverse components, noisy-channel reranking has significantly improved translation quality (Ng et al., 2019).
An alternative reranking approach uses Minimum Bayes Risk (Kumar and Byrne, 2002; Goel and Byrne, 2000), which selects the candidate with the highest utility from a pool of candidates. In MBR, the utility function measures the similarity between a hypothesis and a reference; however, at test time, when references are unknown, the same set of hypotheses serves both as the candidates and the pseudo-references. Possible utility functions include overlap-based (Eikema and Aziz, 2020) or state-of-the-art neural-based MT metrics (Eikema and Aziz, 2022; Fernandes et al., 2022; Freitag et al., 2022a). MBR has shown promising results, particularly when equipped with recent automatic MT metrics. However, its time complexity scales quadratically with the size of the candidate pool and depends on the cost of computing the utility function, which is considerable for neural metrics such as COMET.
A more direct strategy is using reference-free metrics to rerank generated outputs, known as bestof-n or QE-reranking. Initial findings suggested that this approach resulted in inferior translations compared to beam search (Freitag et al., 2022a; Fernandes et al., 2022), especially due to the insensitivity of such metrics to hallucinations (Guerreiro et al., 2023b). However, with advancements in reference-free metrics, QE-reranking has outperformed beam search (Gulcehre et al., 2023; Finkelstein et al., 2023). Beyond reranking, QE scores can also be used during the training phase: for data filtering (Finkelstein et al., 2023), curriculum construction (Gulcehre et al., 2023), or assigning quality-related tags to the outputs (Tomani et al., 2023). Notably, QE-reranking is substantially faster than MBR as its runtime scales linearly with the number of candidates. Yet, while reranking methods such as MBR decoding and QE-reranking effectively improve the performance of MT systems, they are ultimately constrained by the quality of the candidates in the pool.
Post-editing MT outputs. An alternative to reranking is editing the actual outputs of the LLM or MT system using trained post-editing models (Freitag et al., 2019; Voita et al., 2019; Welleck
et al., 2023). While this approach can improve results, it requires training an additional model with a considerable amount of data and comparable size to the original model. Recent works have explored the complementarity of outputs by training models to merge multiple candidates generated by LLMs (Jiang et al., 2023b; Vernikos et al., 2024). Farinhas et al. (2023) used an LLM instead of a trained model to merge the candidates. Their experiments demonstrated comparable performance to reranking approaches that use neural MT metrics.
Constructing translation candidates. A wide variety of scores have been used to construct candidate translation, including the model’s own future scores (Jinnai et al., 2023), lookahead heuristics (Lu et al., 2022), annd values predicted by separate models using Monte Carlo tree search (Leblond et al., 2021; Liu et al., 2023; Chaffin et al., 2022). However, these approaches require access to the model, which is not always guaranteed, and entail substantial computational overhead due to the number of candidates stored at each time step.

heading: 3 Definition of QE-fusion
text: QE-fusion leverages the complementary nature of a pool of translation candidates, combining their strongest fragments into an improved output. These candidates are generated either by an LLM with an appropriate prompt or by an encoder-decoder NMT model.

heading: 3.1 Candidate Generation
text: There are multiple ways to generate candidates from a model. Common approaches for LLMs include nucleus or top-p sampling (Holtzman et al., 2020), top-k, or sampling with a temperature. In our experiments, we adopt nucleus sampling with a temperature. The performance of LLMs can also be influenced by the number of samples and the prompt (Bawden and Yvon, 2023; Zhu et al., 2023). To optimize LLM performance, we follow the guidelines of Zhu et al. (2023) and use 8 examples for in-context learning in all our experiments.
For NMT models, beam search, while commonly used to return the top candidates in the beam, has been shown to lack diversity (Vijayakumar et al., 2018). Instead, we use epsilon sampling (Hewitt et al., 2022), which sets the probability of tokens below a certain threshold to zero and was recently shown to generate more diverse candidates compared to beam search (Freitag et al., 2023).
Algorithm 1 QE-fusion algorithm Input: candidate list Y , QE metricM, beam size b 1: hbase ← argmax
y∈Y M(y) ▷ select top-ranked candidate
2: hyps← {hbase} ▷ initialize beam 3: diffs ← find_diffs(hbase, Y) ▷ find divergent spans 4: for base_span, alter_spans in diffs.items() do 5: for h in hyps do 6: for span in alter_spans do 7: hnew ← h.replace(base_span, span) ▷ create new hypothesis 8: if hnew is not in hyps then 9: hyps← hyps ∪ {hnew} 10: end if 11: end for 12: end for 13: scores←M(hyps) 14: sorted_hyps← sorted(hyps, scores) ▷ sort hyps 15: hyps← sorted_hyps[: b] ▷ keep top b hyps 16: end for Output: hyps[0]

heading: 3.2 QE-fusion Algorithm
text: For each sentence translated by a model, the QEfusion algorithm (Algorithm 1) considers the topranked hypothesis by the QE metric as the base hypothesis, hbase (line 1). The rationale behind this choice is that this is already a high-quality translation which may require the fewest modifications. The algorithm then identifies divergent spans between hbase and other candidates generated by the model, using an off-the-shelf library2 that employs edit distance to spot the additions, deletions and replacements required to transform one sequence into another (line 3).
For each span where candidates diverge, the various alternatives are listed (line 4). The algorithm substitutes the initial span of hbase with each of the alternative spans (lines 6-11), synthesizing new hypotheses, {hnewi }i=1,2,.... A QE metric is used to compute scores for each hnewi (line 13). The hypotheses are then sorted based on their scores, and the top b candidates are retained, forming a beam (lines 14-15). This process is repeated for each span of hbase, progressively creating new hypotheses. Finally, the highest-scoring hypothesis is selected.
While this is a conceptual explanation of the algorithm, certain modifications are made for efficiency purposes such as batching the sentences and caching computed scores (see Appendix A.1).
2https://docs.python.org/3/library/difflib.html

heading: 4 Experimental Settings

heading: 4.1 Datasets and Evaluation Metrics
text: We assess performance across a spectrum of diverse language pairs. The selected languages include German, which is the most represented nonEnglish language in most models; Russian, a highresource language written in Cyrillic alphabet; Chinese, a high-resource language with a logographic script; and Icelandic, which is considered a lowresource language. We consider the translation of English into the first two languages, and from the latter two into English. Additionally, we consider a non-English-centric pair, German to French.
As we experiment with pre-trained models, we use only test data, which we take from WMT22 (Freitag et al., 2022b) and for is→en from WMT21 (Akhbardeh et al., 2021). We draw the few-shot examples for LLMs from the test sets of WMT21. Further details regarding dataset sizes and domains are presented in the Appendix A.2.
We report results in terms of two neural-based metrics: COMET-22 (Rei et al., 2022a) and BLEURT-20 (Sellam et al., 2020). Surface-based BLEU and ChrF scores are given in Appendix A.3.

heading: 4.2 Models and Parameters
text: We conduct an extensive evaluation using LLMs and encoder-decoder NMT models of various sizes. Specifically, we use popular LLMs such as PolyLM-1.7B (Wei et al., 2023), XGLM-2.9B (Lin et al., 2022), Mistral-7B (Jiang et al., 2023a), Llama2-7B (Touvron et al., 2023). We additionally use ALMA-7B (Xu et al., 2024) and TowerBase7B (Alves et al., 2024), two LLMs based on Llama2-7B that are fine-tuned for translation using both monolingual and parallel data. These LLMs have demonstrated impressive performance in MT (Xu et al., 2024), comparable to GPT-3.5 and NLLB-54B (NLLB Team et al., 2022) and represent intermediary stages between general LLMs and task-specific MT models. As for NMT systems, we use the multilingual NLLB-1.3B and 3.3B models (NLLB Team et al., 2022). Results for the 13B versions of Llama2 and ALMA are given in Appendix A.4.
For the LLMs, we adopt the hyper-parameters used by Touvron et al. (2023). We generate candidates using nucleus sampling with p = 0.9 and a temperature of 0.6. As a prompt for in-context learning, we follow Zhu et al. (2023) and use the instruction template: <X> = <Y> with 8 exam-
ples randomly sampled from the WMT21 data. For the NMT models, we follow Freitag et al. (2023) and use epsilon sampling (Hewitt et al., 2022) with ϵ = 0.02 and a temperature of 0.5. We study the impact of temperature in Section 6.3. We generate 5 candidates both for LLM and MT models for efficiency purposes, although we demonstrate in Section 6.1 that our approach also works with larger numbers of candidates.

heading: 4.3 Comparison Terms
text: We compare QE-fusion with standard decoding algorithms for MT, such as greedy decoding and beam search with a width of 5. We also compare our approach with three samplingbased algorithms: (1) random sampling from the pool, serving as a lower performance bound; (2) QE-reranking (Fernandes et al., 2022) using COMETKIWI (Rei et al., 2022b), the same QE metric employed in QE-fusion; and (3) MBR decoding (Eikema and Aziz, 2020), using either the surface-based BLEU or with the neural-based COMET-22 as the utility function. As COMET22 follows the same training pipeline and has the same number of parameters as COMETKIWI, this ensures a fair comparison of the models.

heading: 5 Results: Translation Performance

heading: 5.1 QE-fusion Applied to LLMs
text: Table 1 presents the results obtained across various language pairs and LLMs, in terms of COMET and BLEURT scores. Results with BLEU and ChrF scores, showing similar trends, are given in Appendix A.3. As expected, the translation performance of LLMs generally improves with scale, but also with recency. For instance, the more recent Mistral-7B significantly outperforms Llama27B, despite their similar sizes (7 billion parameters). ALMA-7B and Tower-7B emerge as the top-performing LLMs across all language pairs, confirming the merits of MT-specific fine-tuning of LLMs. Tower-7B has better performance than ALMA-7B in all pairs except is→en, where the latter dominates.3 We do not provide the is→en scores of smaller LLMs (PolyLM and XGLM) due to their poor capabilities in the low-resource Icelandic language.
3This is because is→en data was not used in the fine-tuning stages of Tower, contrary to ALMA, leading to catastrophic forgetting, as is visible when comparing the scores of Tower with those of its parent model, Llama2.
Regarding baselines, greedy decoding consistently lags behind beam search across all language pairs, an observation that contrasts with prior studies focused on zero-shot scenarios (Farinhas et al., 2023), likely due to our use of in-context examples. Unsurprisingly, random selection from the candidate pool emerges as the least effective baseline.
Among the reranking approaches, QE-reranking outperforms MBR with either BLEU or COMET as the utility function, particularly in terms of BLEURT scores. Among the two utility functions for MBR, COMET is superior while the use of BLEU often fails to outperform beam search. MBR with COMET as the utility function occasionally surpasses QE-reranking in terms of COMET scores. This may be due to a form of “reward hacking” (Gulcehre et al., 2023), i.e. employing the same metric for both candidate selection and evaluation, since the BLEURT scores are in the reverse order.
Our approach, QE-fusion, consistently outperforms all other methods, across all language pairs and LLMs, with 5 exceptions out of 56 comparisons. Two notable exceptions are where beam search achieves the best BLEURT scores, for PolyLM-1.7B (de→fr) and XGLM-2.9B (zh→en). In these cases, the candidate pool likely lacks highquality translations altogether. The other three exceptions correspond to very small differences in COMET scores (0.06, 0.02 and 0.01).
Moreover, QE-fusion also outperforms the other methods when combined with even larger LLMs, as confirmed by the results obtained with the Llama2 and ALMA models with 13 billion parameters presented in Appendix A.4, Tables 8 and 9, for COMET, BLEURT, BLEU and ChrF scores.
In Appendix A.5, Figure 6, we present a graphical synthesis of these comparisons using radar charts. The shapes corresponding to QE-fusion are always the outermost ones, regardless of variations due to the underlying LLM or language pair. In particular, our approach always outperforms QEreranking, confirming its superiority as a generalization of reranking approaches.

heading: 5.2 QE-fusion Applied to NMT Models
text: The COMET and BLEURT scores of our approach applied to multilingual NMT models, namely NLLB-1.3B and NLLB-3.3B, are presented in Table 2 (BLEU and ChrF scores are in Appendix A.3). We observe that NMT models have a slight edge over general-purpose LLMs (Llama2 and Mistral) while their MT-fine-tuned counterparts, ALMA and
Tower, achieve similar or better performance. Similar to the results with LLMs, our approach consistently outperforms beam search and reranking approaches. The gap between our approach and QE-reranking is slightly smaller in the case of NMT models, which we attribute to the lower diversity of the generated candidates. We test this hypothesis in Section 6.3.

heading: 6 Analysis of Results

heading: 6.1 Role of the Size of the Candidate Pool
text: In the above experiments, we generated five candidate translations for efficiency reasons. We now study the influence of the number of candidates on the scores of QE-fusion vs. those of the other
methods, using XGLM-2.9B for en→de translation. We progressively sample larger candidate pools, from 5 to 200 candidates, and present in Figure 2 the BLEURT scores of our approach compared to QE-reranking using COMETKIWI and to MBR using COMET as the utility function. Additionally, we compare with an oracle reranking approach that has access to the reference translation and uses COMET scores as the selection criterion. QE-fusion consistently outperforms reranking approaches across all sizes of candidate pools. Moreover, QE-fusion even matches the performance of the oracle for pool sizes of 5, 10 and 25 candidates.

heading: 6.2 Novelty of Outputs from QE-fusion
text: As the previous experiment may suggest that QEfusion has a similar effect as the use of larger candidate pools with reranking methods, we examine here the novelty of the synthesized candidates, by counting how many times the output of QE-fusion can be found in a larger pool. For a pool of p candidates given to QE-fusion, we measure how frequently an exact match of the output of QE-fusion can be found in larger pools of size q ≥ p, where p and q are in {5, 10, 25, 50, 100, 200}.
The results, presented in Figure 3, reveal that even with a small pool of 5 candidates, more than 50% of the outputs of QE-fusion would not have been generated by the LLM, even when sam-
pling 200 candidates (rightmost bar of the leftmost group). The percentage of identical (or non-novel) candidates decreases as the pool grows, due to more varied candidates present in larger pools.
When candidates generated by QE-fusion are present in the original pool, our method has the same effect as QE-reranking. The frequency of these cases is given by the leftmost bar of each group (pool size) in Figure 3. We observe that our approach defaults to QE-reranking less than 40% of the time for a pool of size 5 (leftmost bar) and this value drops to 20% for a pool of size 200.

heading: 6.3 Impact of Candidate Diversity on Quality
text: By construction, QE-fusion benefits from the diversity of candidates, as this allows for an increased number of divergent spans. We study here the effect of diversity on both QE-fusion and QE-reranking, for LLMs and NMT models.
To increase the diversity of the pool of candidate translations, we adjust the temperature parameter during decoding but keep constant all other generation parameters. A higher temperature results in token probability distributions that are more uniform, thus increasing the stochasticity of sampling and consequently the diversity of the candidate pool. Here, we measure this diversity by the number of unique 4-grams present in the candidate pool, averaged over all test sentences. Figure 4 displays in its lower part the diversity of the pool as a function of temperature for XGLM-2.9B and NLLB-1.3B on en→de translation, and in its upper part the BLEURT quality scores of these models with either QE-reranking or QE-fusion. Additional results with COMET scores and other diversity measures are given in Appendix A.6 and show similar trends.
Increasing the temperature leads to an expected rise in diversity. The rise is higher for XGLM-2.9B than for NLLB-1.3B, illustrating the fact that LLMs generate more diverse outputs, likely due to their general-domain language pretraining compared to
the task-specific training of NMT models. Nevertheless, generating too diverse candidates due to high temperatures results in a noticeable drop in performance (right side of the upper graph). The gap between QE-fusion and QE-reranking slightly widens as diversity increases, indicating the ability of our approach to leverage alternative spans. The optimal performance is achieved using a temperature in the [0.4, 0.6] interval.

heading: 6.4 Computation Time
text: In Section 6.1, Figure 2, we presented the scaling laws of QE-fusion vs. reranking in terms of performance when the size of the candidate pool varies. However, computation time is a crucial factor as the candidate pool grows. QE-reranking has the advantage of linear scaling with the number N of candidates, while MBR requires N(N − 1) model calls for each sentence. In contrast, QE-fusion has variable complexity, depending on the diversity of the pool and the presence of different spans.
To compare empirically the complexity of QEfusion with reranking methods, we measured their runtime for the en→de WMT22 test data with 2,037 sentences. All experiments were executed on a single Nvidia A40 GPU with 40 GB memory, using a batch size of 400 samples. Using a logarithmic scale, Figure 5 confirms that QE-reranking scales linearly with the candidate pool size, while MBR scales quadratically. Interestingly, QE-fusion also exhibits linear scaling with the number of candidates but with a constant factor of ×5 compared to QE-reranking. For 5 and 10 candidates, QEfusion has similar runtimes to MBR.
We have implemented specific optimizations, including score caching and input batching, to reduce
runtime (see Appendix A.1). These modifications were uniformly applied to all methods to ensure a fair comparison. We leave further optimizations such as pruning (Cheng and Vlachos, 2023) for future work.

heading: 6.5 Effect of QE-Fusion on Hallucinations
text: Following the approach of Guerreiro et al. (2023a), we define defect translations as those having an spBLEU score4 below 3, and compute their percentage. In our evaluation, unlike Guerreiro et al. (2023a), we do not perturb the source sentences, but focus on measuring the frequency of hallucinations during the translation of the original unperturbed source sentences.
The results presented in Table 3 indicate that QEreranking is more efficient in mitigating hallucinations compared to MBR with COMET, consistent with prior work (Farinhas et al., 2023). Remarkably, QE-fusion reduces hallucinations even further, outperforming all other methods across different models and language pairs, in nine out of ten cases.

heading: 6.6 Comparison to Post-editing Approaches
text: Due to the large scale and often restricted access of LLMs, novel approaches have emerged to enhance their predictions without access to their weights. These methods, similar to reranking, involve generating predictions from the LLM and subsequently refining them using a secondary, more compact model (Vernikos et al., 2024; Jiang et al., 2023b).
We compare QE-fusion with LMCor (Vernikos et al., 2024), a T5-base (Raffel et al., 2020) corrector model, which refines LLM-generated translations. LMCor is trained on the News Commentary
4We use spBLEU as implemented in SacreBLEU (Post, 2018): nrefs:1|case:mixed|eff:yes|tok:flores101| smooth:exp|version:2.3.1.
v16 corpus5 augmented with five translation candidates from XGLM-2.9B for each source sentence. During testing, it receives the source sentence and five translation candidates. We also include results from a T5-base model fine-tuned for MT without additional candidates.
Table 4 shows that LMCor outperforms finetuned T5 and in-context learning across all metrics. However, QE-fusion achieves significant improvements of 4 and 3 points in COMET and BLEURT, respectively, despite trailing in BLEU. This underscores the limitations of surface-based metrics and suggests that higher BLEU scores may be attained by models specifically trained for MT, which can mimic the translation style of the training data (see Appendix A.3).

heading: 7 Conclusion
text: In this paper, we introduced QE-fusion, a novel approach that combines fragments from diverse candidates to synthesize improved translations guided by quality estimation metrics. Our experiments across five language pairs involving both LLMs and NMT models demonstrate that QE-fusion consistently outperforms beam search, MBR decoding, and QE-reranking. QE-fusion is particularly beneficial to LLMs, capitalizing on their diverse outputs. Notably, QE-fusion maintains its superior performance even when the pool of candidates grows, while its runtime scales linearly with the number of candidates, highlighting its scalability.
By integrating external knowledge from quality estimation metrics, QE-fusion not only enhances translation quality but also tackles specific issues like hallucinations. This offers a promising avenue for addressing other phenomena such as contextspecific errors (Vernikos et al., 2022). Beyond translation, the versatility of QE-fusion extends to any text generation task where metrics or reward models (Ouyang et al., 2022) are available.
5www.statmt.org/wmt22/translation-task.html
Limitations
Human evaluation. While our work employs state-of-the-art MT evaluation metrics, we acknowledge the inherent limitations of automatic metrics. Human evaluation could offer additional, and possibly more reliable insights. At the time of writing, human evaluation is ongoing, starting with one language pair and four systems.
Choice of metrics. The QE metric used by QEfusion, COMETKIWI, shares some similarities with the COMET metric used for evaluation, as they originate from the same family of models. Consequently, using COMETKIWI as our criterion for merging spans might be considered as the reason why we get improvements in COMET scores. To address this concern, we confirm our findings with scores using three other metrics: BLEURT, BLEU and ChrF. Even with these alternate metrics, our approach consistently outperforms all other reranking techniques.

heading: Acknowledgments
text: We are grateful for their support to the Swiss National Science Foundation (DOMAT grant n. 175693, On-demand Knowledge for Documentlevel Machine Translation and EXOMAT grant n. 228494, External Knowledge for Low-resource Machine Translation), and to the Institute for ICT at HEIG-VD.

heading: A Appendix
text: A.1 Implementation Optimizations While Algorithm 1 outlines the concept of fusing candidates, we introduce specific modifications to enhance efficiency. Firstly, to mitigate the computationally expensive calls to the QE model, we parallelize the exploration of all sentences in the test set, resembling a batched beam search. By doing so, we reduce the overall number of calls to the model (which depends on the number of divergent spans) by utilizing a larger batch. Additionally, we implement a hash table to track previously generated candidates, ensuring that we do not compute scores for the same sentence twice. Lastly, we incorporate an early exit mechanism, removing sentences for which no pending pseudo-generation step exists. These optimizations significantly impact the time complexity of our algorithm, which we empirically demonstrate to scale linearly with the number of candidates in Section 6.4.
A.2 Datasets Table 5 presents information about the datasets used in our study, in terms of size and domain. More information is available in the synthesis articles from WMT22 (Freitag et al., 2022b) and WMT21 (Akhbardeh et al., 2021).
A.3 Results with Surface-based Metrics We provide the scores of the surface-based BLEU and ChrF metrics for LLMs in Table 6. The overall performance trends align with those of neuralbased metrics, indicating that larger models consistently achieve higher scores. Once again, QEfusion consistently surpasses reranking approaches.
However, regarding surface-based metrics, beam search or greedy decoding frequently emerge as the top-performing methods, with our approach securing the second position. Still, our approach outperforms all other sampling-based methods.
The outputs of beam search often exhibit predictability, while sampling introduces a layer of creativity to translations. Unfortunately, surfacebased metrics struggle to account for nuances like synonyms or significant restructuring, leading to potential penalties for such translations (a limitation which has contributed to a decline in their popularity).
Table 7 presents BLEU and ChrF scores for the NMT models. Firstly, we observe that the NMT models perform significantly better than the LLMs in terms of surface-based metrics, which is consistent with previous findings (Chowdhery et al., 2023; Hendy et al., 2023; Zhu et al., 2023). The trend differs slightly compared to LLMs, as methods like QE-reranking and MBR score higher in terms of surface-based metrics, particularly for the highresource pairs en→de and en→ru. This divergence can be attributed, once again, to the limited diversity of translations generated by MT models, while our approach favors more creative translations, potentially penalized by these metrics. Nevertheless, for pairs where MT models perform worse, such as is→en and de→fr, QE-fusion consistently outperforms reranking approaches and occasionally beam search.
A.4 Results using LLMs with 13B Parameters Tables 8 and 9 present the translation scores of the larger versions of Llama2 and ALMA with 13B parameters. The overall trend aligns with other LLMs: QE-fusion significantly outperforms reranking methods.
A.5 Graphical Comparison of Main Scores The BLEURT scores of various methods, LLMs and language pairs from Table 1 are represented as radar charts in Figure 6. The shapes corresponding to our proposal, QE-fusion, always extend outside the others (only beam search, MBR with COMET and QE-reranking are plotted, for simplicity), for all of the four LLMs represented: Llama2-7B, Mistral-7B, ALMA-7B, and TowerBase-7B. The latter two models, though fine-tuned for MT, have large differences for is→en and de→fr.
Figure 6 also shows the BLEURT scores for the two NMT models from Table 2, over the same
language pairs as above, excluding zh→en. Again, QE-fusion extends outside the other shapes for both NMT models.
A.6 Temperature and Diversity
In Figure 7, we present additional results regarding the impact of temperature on translation performance and pool diversity. We evaluate translation quality with COMET, demonstrating similar results to those in Section 6.3 with BLEURT. Higher temperatures enhance the results of both QE-reranking and QE-fusion but excessively high temperatures lead to a drop in performance.
To measure diversity, we consider here two additional metrics: the average number of unique candidates in the pool and the semantic diversity,
as defined by Farinhas et al. (2023), where u(x, y) is the utility function, in this case COMET, and yj , yi represent two different candidates from the pool:
1− 1 N(N − 1)
N∑
i,j=1 j ̸=i
u(yj , yi) (1)
The diversity metrics exhibit similar trends to our lexical diversity ones, with diversity increasing as the temperature rises. These results confirm that LLMs tend to produce more diverse outputs, a fact that contributes to explaining why QE-fusion is more effective on LLM outputs than on NMT ones.

heading: Future Work
text: We leave further optimizations such as pruning (Cheng and Vlachos, 2023) for future work