The Multi-Range Theory of Translation Quality Measurement: MQM scoring models and Statistical Quality Control (2024)

Abstract: The year 2024 marks the 10th anniversary of the Multidimensional Quality Metrics (MQM) framework for analytic translation quality evaluation. The MQM error typology has been widely used by practitioners in the translation and localization industry and has served as the basis for many derivative projects. The annual Conference on Machine Translation (WMT) shared tasks on both human and automatic translation quality evaluations used the MQM error typology. The metric stands on two pillars: error typology and the scoring model . The scoring model calculates the quality score from annotation data, detailing how to convert error type and severity counts into numeric scores to determine if the content meets specifications. Previously, only the raw scoring model had been published. This April, the MQM Council published the Linear Calibrated Scoring Model , officially presented herein, along with the Non-Linear Scoring Model , which had not been published

## introduction and background machine translation (mt) was one of the earliest artificial intelligence (ai) tasks when machine and intelligence was launched in the 1950s in the wake of wwii @xcite . mt has significantly influenced the translation industry since the statistical mt (smt) models started to produce editable automatic translations in the early 2010s, just before neural mt (nmt) came to the stage in the middle and second half-decade @xcite @xcite . but even today, when generative ai (genai) has captured the imagination of billions of people, both human and aibased translations may still contain errors. translation errors often carry risks. their consequences range from minor misunderstandings to serious legal, financial, reputational, or health-related outcomes for end users, translation providers, clients, and other stakeholders @xcite . risk mitigation requires evaluation to identify and quantify these risks. the multidimensional quality metrics (mqm) framework for analytic translation quality evaluation (tqe) was first proposed by @xcite just before the arrival of nmt, originally published as a deliverable of the eu-funded qtlaunchpad project. from the very beginning, it was designed for evaluation of both human translation (ht), and machine translation (mt), and it can now be applied to ai-generated translation. mqm has formalized and standardized the so-called analytic approach to translation quality measurement. this approach is typically based on evaluating a sample. it involves annotating translation errors by attributing them to predefined error types and severity levels to generate the data for deriving the translation quality score. mqm appeared as a major and fundamental standardization attempt to alleviate the then-widespread problems of practical translation evaluation, at a time when there was no single way to approach translation quality measurement. however, the lack of a sophisticated design of hierarchies and an adaptable scoring model also posed a bottleneck for its real-world application. the original eu-funded qtlaunchpad project deliverable, the mqm 1.0, published on the w3c project page, included only the raw scoring model, in which the score is calculated as a direct pro-portion of errors found in the evaluated sample, to the size of the sample. this approach has several drawbacks, specifically, a) such scores do not use human-readable scales, b) they have varying and non-intuitive error tolerance thresholds, and c) they produce non-comparable quality values across various content types and scenarios. all other score calculation models also had fixed, non-adaptable scoring systems, which confused the industry and led to numerous 'reinventions of the wheel'. subsequently, a few other human-centric evaluation metrics were proposed with a similar approach to mqm and these efforts were more simplified and easy to deploy, such as the hope metric by @xcite , which only includes eight initial error types and error severity levels. this approach was refined from industrial practice and designed specifically for machine-translation outputs. it also featured very different scoring models. nevertheless, the mqm framework has been picked up again by the leading mt shared task venue wmt since 2021 as the official human evaluation strategy to judge the submitted mt systems @xcite @xcite . there have been automatic evaluation designs that aim to mimic the mqm idea, such as comet-mqm reported from wmt2020 metrics shared task @xcite . in this paper, we introduce the latest developments of the mqm framework from the mqm council which comprises a voluntary, communitydriven research and standardization group composed of experts interested in translation quality evaluation, who have been developing the mqm since 2016. 1 these start with the discussion of sampling and low irr phenomena, followed with samplesizes, mqm2, projecting pi and formulas, and the introducing non-linearity. we leave the detailed mqm parameters into appendix for indexing. in recent years, the widely used dqf subset of mqm has been improved and updated to become mqm core. this error typology is better adapted to quality management systems with a clearer structure for devising improvement actions. the latest iteration of the framework includes the revised mqm core and mqm full error typology, a new linear scoring model with calibration, a process description with a sample scorecard, and now a non-linear mqm scoring model. (appendix 7). we further argue that different evaluation approaches have to be used for three ranges of sample sizes. for the first time in the history of the translation and localization industry, to the best of our knowledge, this paper presents a multi-range, versatile theory and technique of translation quality evaluation, making it possible for interested researchers to construct almost any analytic metrics derived from this approach. we also explained in this paper why segment-level scores cannot be accurate in principle, and explain the area of applicability of statistical quality control to translation quality evaluation. ## on sampling for any statistical approach to be applicable, it is critical to know what statistical distribution is valid before choosing the right distribution for further statistical analysis. such analysis is based on the notion that, ideally, (a) all errors are independent and (b) the probability of errors in the text is uniform. although these assumptions are always made, neither assumption is true concerning texts (and translation products) in general. practitioners in the language and translation industry know that translation errors are not, in general, uniformly distributed in content and, what is more, over time. furthermore, their significance and "weights" are also different in various parts of the material and/or types of material, and also vary according to other sometimes unpredictable factors. in addition, different types of errors may depend on each other. indeed, some errors only occur when triggered by other fundamental errors. there are about a dozen very important factors that can influence why error distribution in text is not, in fact, uniform. because of this, it is always recommended to revise, review, and evaluate the entire text. but no one has the resources to fully evaluate everything. that's why translation quality evaluation is typically based on evaluating samples (such as the work by @xcite from an industrial setting). sometimes this sampling is done by selecting full-text samples from a larger population, e.g. evaluating every tenth translation fully, or selecting complete shorter texts to arrive at the determined sample size. a typical approach in a traditional localization process is to select samples of medium sizes (500-5000 words) and then apply an analytical approach. however, smaller samples and larger samples are also possible, and it is important to consider the entire range of possible sample sizes, from one sentence to very large documents, which is the purpose of this paper. text is not the information itself; it is merely the conveyor of the expression of intended meaning. moreover, not only can we not know for sure the author's intended meaning, which leaves the text open to the reader's interpretation. this interpretation depends on the reader's cultural, educational, and professional background and experiences, as well as on their skills and the context of the communication act. additionally, language is highly ambiguous, offering numerous expression tools that allow a single sentence to be interpreted in many ways. this inherent ambiguity leads to significant uncertainty in any error annotation, which is a fundamental property of language rather than a flaw of human assessors @xcite . data scientists often make shallow conclusions from low irr, believing that automatic calculation of errors will resolve this problem. in recent years, many automatic metrics have been constructed, often claiming "human judgment" quality. recently, ai-based metrics have appeared, along with unverified and unproven claims that "genai seems capable of measuring translation quality" @xcite . in reality, however, genai does neither "think" nor "understand" anything and for this reason, the factual accuracy of genai generation remains a huge problem. no language model is turing complete foot_1 . language models are constrained by their architecture and the limitations of their training data and computational resources. language models are specialized tools designed for processing and generating text based on patterns learned from vast amounts of data. they are good at some tasks such as language generation, and summarization, but they are not capable of performing arbitrary computations or reasoning in the same way that a turing complete system can. because of this, language models are not considered general-purpose reasoners. they can provide useful responses and assist with many tasks within their scope of capabilities, but they cannot reason and compute in the general-purpose manner that a turing machine or turing complete system can. among other things, the factual accuracy of genai generation remains to be a huge problem. this affects both error annotation capability and accuracy on a secondary process level. genai may produce fluent text, but it performs worse on derivative tasks, such as error annotation tasks. in other words, genai misses factual errors when generating content, and of course, does not "see" errors during the annotation process, which also results in issues with the accuracy of this process. additionally, the better the genai output is, the more variable it becomes, which is similar (although different in nature) to the variability in human judgment. human judgment is variable because different people may have their own interpretation of the text. advanced genai behaves similarly, with its variable output becoming another interpretation. however, this interpretation is not verified or supported by human intelligence. and similar to human evaluation, the smaller the context window of the text, the more variable is the genai response. for all these important reasons, the smaller the evaluation sample, the greater the uncertainty of translation quality annotation. this is due to the intrinsic, fundamental variability in both human and genai-based error annotation that leads to the uncertainty of error evaluation. this means one simple thing: at the low end of the scale, sentence-level automatic scoring is so unreliable that it makes no sense, regardless of the method used to produce the score. furthermore, all automatic metrics must be supported by proper benchmarking and validation, which takes a lot of time and is very specific to the particular implementation setting and the specifications (language pair, subject matter area, task requirements, etc.). automatic metrics of any kind produce a single number with unknown reliability and confidence intervals. by definition, this number ignores the ambiguity of the text and therefore disregards other valid interpretations, which can be validated by human evaluators on larger samples. for all we know, various automatic and genai measurement results must be validated by analytic human evaluation on samples of sufficient sizes, which converges to higher irr (inter-rater reliability) in controlled settings with training and monitoring @xcite . training and continuous validation of evaluators' work contribute to improving irr over time. what ultimately matters for reliable evaluation is that a proper process allows for achieving statistically valid irr of human evaluation at the sample level, not necessarily at the segment level. ## three sample-size ranges -three very different methods the industrial era has developed a vast mathematical and methodological apparatus for measuring the quality of products by evaluating small samples from very large production lots, e.g. using student's t-distribution @xcite such as the recent work by @xcite . in a setting where decisions about the quality of a large lot are based on small samples, the uncertainty is so high that only sophisticated methods of statistical quality control can handle such a problem. they have been extensively developed and described by many researchers, such as @xcite , and have been long standardized by iso 3 . in a nutshell, errors always have a statistical nature, and this is yet another reason why segment-level quality scores do not make sense -not only the methods of producing them must be properly benchmarked and verified, but the fundamental uncertainty of individual error annotation is so high that it is not possible to get a "true" measurement except for very trivial mechanical spelling errors. when measuring errors on a very small sample, we need to apply the statistical quality control (sqc) method. these methods are extremely complex due to the underlying statistical and mathematical apparatus, which is why iso 2859-1 consists of 94 pages of tables. additionally, the conclusions drawn from applying these methods are not quality ratings but rather probabilities of the producer's and consumer's risks, which can be determined using such methods. in an earlier work by @xcite , it was demonstrated that for the translation quality rating to have low variability, the sample size should be greater than 200 sentences (3400 words). the authors discuss that if they go to smaller sample sizes, the confidence interval explodes. this means that even a 2000-word sample introduces significant uncertainty in the quality measurement result, and even more so with samples of 1000 words and especially 500 words. the lowest known credible metric is the ata certification model @xcite , where linguists are asked to translate one page (250 words). to address the uncertainty of evaluating such a small sample, two different reviewers assess the work, effectively duplicating the evaluation effort to mitigate the risks associated with the limited sample size. additionally, the ata certification requires linguists to translate two one-page samples to see how they handle the translation of different types of text, which also helps reduce the uncertainty of evaluating small samples. the methods of statistical quality control (sqc) are outside the scope of this paper. however, for this article, it is important to note that the translation quality of a sample smaller than 15-17 sentences (one page, 250 words) falls into the realm of sqc and cannot be measured by analytic quality evaluation methods unless the sample covers the entire text. for samples of approximately 300 words and above, the effects of statistical uncertainty and low inter-rater reliability cease to have a significant adverse effect, making methods of analytical quality evaluation applicable. for samples larger than ap-proximately 5000 words, other effects start to manifest, such as the priming effect of human perception. non-linearity starts to become apparent with larger samples. in this paper, we introduce a nonlinear calibration model that works for samples of both medium (customary) and large sizes. the three ranges of sample sizes are governed by entirely different mathematical apparatus. these ranges are shown in figure 8 (word counts: 0, 500, 5000+). ## mqm 2.0: the state of the art of analytical quality evaluation mqm is a framework for analytic translation quality evaluation (tqe). it can be used to evaluate human translation (ht), machine translation (mt), or ai-generated translation. mqm consists of two key components: the error typology and the scoring model. the mqm error typology is organized hierarchically with seven high-level error dimensions, subordinate error types, and associated severity levels. the scoring model features a system of weights and parameters assigned to the error types and severity levels, as well as a scoring formula used to calculate a numerical score that represents the quality of the evaluated translation according to agreed-upon specifications. the evaluated sample can comprise an entire document or a set of documents, or parts thereof. evaluators frequently work with samples in the range of 500 to 20,000 words, depending on the size of the project and the resources available for evaluation. ## on non-linearity this section describes the non-linear scoring model which solves the problem of the non-linearity of human perception concerning samples of medium to large size. all is well with linear scoring until the sample size is either too small (requiring methods of statistical quality control) or too large. many practitioners have observed that linear scoring defined for small to medium samples does not work for larger chunks of text. the reason that changing human perception fails a linear model is that the human mind is not a fixed state machine -we change our behaviour and our opinions with experience. this effect is known in cognitive science as "priming," where encountering certain features in the text makes readers more alert to them as they work their way through the text. priming works on errors too. when we see two errors on one page, then two errors on the next page, and three errors on the page thereafter, we get the impression that there are simply too many errors in the document. this is observed in real translation quality evaluation practice as follows (this is an actual quote from a very large buyer of translation services): once we started using our current methodology in 2020, we still asked the evaluators to indicate the cases where their actual feeling was different from what the score gave them. we very quickly realized that the main issue was that with very short samples the scoring was overly harsh and with very long samples it was too lenient. the reason for this is that when we evaluate holistically, the perception is not congruent with our scoring formula. for example, we might feel that if a translation sample is about one page, a single major mistranslation error is enough to say that it fails. however, if the sample is seven pages, we are not okay with allowing seven major mistranslation errors before it fails. instead, we would prefer to fail the sample already at three or four errors. this poses a problem for the linear scoring model which simply prorates the number of errors per page to a total number of pages in the sample." ## conclusion and future work in this paper we covered a wide scope of sample sizes and different approaches and scoring models. it can be said that this paper represents the unified theory of translation quality measurement which explains most use cases of translation quality mea-surement. the full mqm error typology with calibrated and non-linear scoring is a toolset which allows the reproduction of many different known proprietary metrics. we have also established the fact that human translation quality evaluation is more than ever the golden standard of measurement and benchmarking for quality measurement, since it is the only reliable way to validate any automatic translation quality evaluation. step calibrated quality score calculation formulas/values 1 establish parameters reference word count (rwc) 1000 max. quality score 100 passing threshold (pt) any number perceived as reasonable (e.g., 90) defined passing interval (dpi) 100 -dpt (e.g., 10) acceptable penalty points (app) for the reference word count any number perceived as reasonable 2 absolute penalty total (apt) 𝑖,𝑗 ∑ 𝐸𝑟𝑟𝑜𝑟 𝐶𝑜𝑢𝑛𝑡 𝑖𝑗 × 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 𝑗 × 𝐸𝑟𝑟𝑜𝑟 𝑇𝑦𝑝𝑒 𝑊𝑒𝑖𝑔ℎ𝑡 𝑖 where: @xmath0, @xmath1. 3 normed penalty total (npt) 𝐴𝑃𝑇×𝑅𝑊𝐶 𝐸𝑊𝐶 4 scaling factor (sf) 100-𝐷𝑃𝑇 𝐴𝑃𝑃 5 calibrated quality score (cqs) 100 -𝑁𝑃𝑇×𝑆𝐹 chine translation, pages 578-628, singapore. association for computational linguistics. attention is all you need. in conference on neural information processing system, pages 6000-6010.