Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR decoding using matrix completion techniques, focusing on a machine translation task. We formulate MBR decoding as a matrix completion problem, where the utility metric scores between candidate hypotheses and reference translations form a low-rank matrix. First we empirically show that the scores matrices indeed have a low-rank structure. Then we exploit this by only computing a random subset of the scores and efficiently recover the missing entries in the matrix by applying the Alternating Least Squares (ALS) algorithm, thereby enabling fast approximation of the MBR decoding process. Our experimental results on machine translation tasks demonstrate that the proposed method requires 1/16 utility metric computations compared to the vanilla MBR decoding while achieving equal translation quality measured by COMET on the WMT22 dataset (en<>de, en<>ru). We also benchmark our method against other approximation methods and we show significant gains in quality.

Recent work has shown that sample-based Minimum Bayes Risk (MBR) decoding outperforms beam search in text-to-text generation tasks, such as machine translation, text summarization, and image captioning. On the other hand, beam search is the current practice for speech-to-text tasks such as automatic speech recognition (ASR) and Speech Translation (ST). Given that MBR decoding is effective in text-to-text generation tasks, it is reasonable to expect it to also be effective for speech-to-text tasks. In this paper, we evaluate MBR decoding for ASR and ST tasks on English and Japanese using Whisper and its derivative models. We observe that the accuracy of MBR decoding outperforms that of beam search in most of the experimental settings we have evaluated. The results show that MBR decoding is a promising method for offline ASR and ST tasks that require high accuracy. The code is available at https://github.com/

First, we empirically show that the scores matrices indeed have a low-rank structure.

Minimum Bayes risk (MBR) decoding is a decision rule of text generation, which selects the hypothesis that maximizes the expected utility and robustly generates higher-quality texts than maximum a posteriori (MAP) decoding. However, it depends on sample texts drawn from the text generation model; thus, it is difficult to find a hypothesis that correctly captures the knowledge or information of out-of-domain. To tackle this issue, we propose case-based decision-theoretic (CBDT) decoding, another method to estimate the expected utility using examples of domain data. CBDT decoding not only generates higher-quality texts than MAP decoding, but also the combination of MBR and CBDT decoding outperformed MBR decoding in seven domain De--En and Ja$\leftrightarrow$En translation tasks and image captioning tasks on MSCOCO and nocaps datasets.

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR decoding using matrix completion techniques, focusing on a machine translation task. We formulate MBR decoding as a matrix completion problem, where the utility metric scores between candidate hypotheses and reference translations form a low-rank matrix. First we empirically show that the scores matrices indeed have a low-rank structure. Then we exploit this by only computing a random subset of the scores and efficiently recover the missing entries in the matrix by applying the Alternating Least Squares (ALS) algorithm, thereby enabling fast approximation of the MBR decoding process.

As automatic metrics become increasingly stronger and widely adopted, the risk of unintentionally "gaming the metric" during model development rises. This issue is caused by metric interference (Mint), i.e., the use of the same or related metrics for both model tuning and evaluation. Mint can misguide practitioners into being overoptimistic about the performance of their systems: as system outputs become a function of the interfering metric, their estimated quality loses correlation with human judgments. In this work, we analyze two common cases of Mint in machine translation-related tasks: filtering of training data, and decoding with quality signals. Importantly, we find that Mint strongly distorts instance-level metric scores, even when metrics are not directly optimized for -- questioning the common strategy of leveraging a different, yet related metric for evaluation that is not used for tuning. To address this problem, we propose MintAdjust, a method for more reliable evaluation under Mint. On the WMT24 MT shared task test set, MintAdjust ranks translations and systems more accurately than state-of-the-art-metrics across a majority of language pairs, especially for high-quality systems. Furthermore, MintAdjust outperforms AutoRank, the ensembling method used by the organizers.

Despite their outstanding performance in the majority of scenarios, contemporary language models still occasionally generate undesirable outputs, for example, hallucinated text. While such behaviors have previously been linked to uncertainty, there is a notable lack of methods that actively consider uncertainty during text generation. In this work, we show how Minimum Bayes Risk (MBR) decoding, which selects model generations according to an expected risk, can be generalized into a principled uncertainty-aware decoding method. In short, we account for model uncertainty during decoding by incorporating a posterior over model parameters into MBR's computation of expected risk. We show that this modified expected risk is useful for both choosing outputs and deciding when to abstain from generation and can provide improvements without incurring overhead. We benchmark different methods for learning posteriors and show that performance improves with prediction diversity. We release our code publicly.

Large language models (LLMs) are often equipped with multi-sample decoding strategies. An LLM implicitly defines an arithmetic code book, facilitating efficient and embarrassingly parallelizable \textbf{arithmetic sampling} to produce multiple samples using quasi-random codes. Traditional text generation methods, such as beam search and sampling-based techniques, have notable limitations: they lack parallelizability or diversity of sampled sequences. This study explores the potential of arithmetic sampling, contrasting it with ancestral sampling across two decoding tasks that employ multi-sample inference: chain-of-thought reasoning with self-consistency and machine translation with minimum Bayes risk decoding. Our results demonstrate that arithmetic sampling produces more diverse samples, significantly improving reasoning and translation performance as the sample size increases. We observe a $\mathbf{3\text{-}5\%}$ point increase in accuracy on the GSM8K dataset and a $\mathbf{0.45\text{-}0.89\%}$ point increment in COMET score for WMT19 tasks using arithmetic sampling without any significant computational overhead.

General-purpose LLM judges capable of human-level evaluation provide not only a scalable and accurate way of evaluating instruction-following LLMs but also new avenues for supervising and improving their performance. One promising way of leveraging LLM judges for supervision is through Minimum Bayes Risk (MBR) decoding, which uses a reference-based evaluator to select a high-quality output from amongst a set of candidate outputs. In the first part of this work, we explore using MBR decoding as a method for improving the test-time performance of instruction-following LLMs. We find that MBR decoding with reference-based LLM judges substantially improves over greedy decoding, best-of-N decoding with reference-free judges and MBR decoding with lexical and embedding-based metrics on AlpacaEval and MT-Bench. These gains are consistent across LLMs with up to 70B parameters, demonstrating that smaller LLM judges can be used to supervise much larger LLMs. Then, seeking to retain the improvements from MBR decoding while mitigating additional test-time costs, we explore iterative self-training on MBR-decoded outputs. We find that self-training using Direct Preference Optimisation leads to significant performance gains, such that the self-trained models with greedy decoding generally match and sometimes exceed the performance of their base models with MBR decoding.