# Linear-time Minimum Bayes Risk Decoding with Reference Aggregation

arXiv: https://arxiv.org/abs/2402.04251 · HTML: https://mlsanity.com/paper/2402.04251/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [A Call for Clarity in Reporting BLEU Scores](https://mlsanity.com/paper/1804.08771/) (2018)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [COMET: A Neural Framework for MT Evaluation](https://mlsanity.com/paper/2009.09025/) (2020)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [xCOMET: Transparent Machine Translation Evaluation through Fine-grained Error Detection](https://mlsanity.com/paper/2310.10482/) (2023)
- [Facebook FAIR's WMT19 News Translation Task Submission](https://mlsanity.com/paper/1907.06616/) (2019)
- [Is MAP Decoding All You Need? The Inadequacy of the Mode in Neural Machine Translation](https://mlsanity.com/paper/2005.10283/) (2020)
- [Truncation Sampling as Language Model Desmoothing](https://mlsanity.com/paper/2210.15191/) (2022)
- [High Quality Rather than High Model Probability: Minimum Bayes Risk Decoding with Neural Metrics](https://mlsanity.com/paper/2111.09388/) (2021)
- [Sampling-Based Approximations to Minimum Bayes Risk Decoding for Neural Machine Translation](https://mlsanity.com/paper/2108.04718/) (2021)
- [Epsilon Sampling Rocks: Investigating Sampling Strategies for Minimum Bayes Risk Decoding for Machine Translation](https://mlsanity.com/paper/2305.09860/) (2023)
- [Identifying Weaknesses in Machine Translation Metrics Through Minimum Bayes Risk Decoding: A Case Study for COMET](https://mlsanity.com/paper/2202.05148/) (2022)
- [Faster Minimum Bayes Risk Decoding with Confidence-based Pruning](https://mlsanity.com/paper/2311.14919/) (2023)
- [MBR and QE Finetuning: Training-time Distillation of the Best and Most Expensive Decoding Methods](https://mlsanity.com/paper/2309.10966/) (2023)
- [Direct Preference Optimization for Neural Machine Translation with Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2311.08380/) (2023)
- [Hyperparameter-Free Approach for Faster Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2401.02749/) (2024)

## Built on by (most cited first, 21 of 21)

- [Regularized Best-of-N Sampling with Minimum Bayes Risk Objective for Language Model Alignment](https://mlsanity.com/paper/2404.01054/) (2024)
- [Mitigating Metric Bias in Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2411.03524/) (2024)
- [Efficient Minimum Bayes Risk Decoding using Low-Rank Matrix Completion Algorithms](https://mlsanity.com/paper/2406.02832/) (2024)
- [Improving Minimum Bayes Risk Decoding with Multi-Prompt](https://mlsanity.com/paper/2407.15343/) (2024)
- [mbrs: A Library for Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2408.04167/) (2024)
- [Centroid-Based Efficient Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2402.11197/) (2024)
- [Uncertainty-Aware Decoding with Minimum Bayes Risk](https://mlsanity.com/paper/2503.05318/) (2025)
- [Introducing the NewsPaLM MBR and QE Dataset: LLM-Generated High-Quality Parallel Data Outperforms Traditional Web-Crawled Data](https://mlsanity.com/paper/2408.06537/) (2024)
- [Diversity Explains Inference Scaling Laws: Through a Case Study of Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2410.15021/) (2024)
- [Theoretical Guarantees for Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2502.12685/) (2025)
- [A Bayesian Optimization Approach to Machine Translation Reranking](https://mlsanity.com/paper/2411.09694/) (2024)
- [A Context-aware Framework for Translation-mediated Conversations](https://mlsanity.com/paper/2412.04205/) (2024)
- [Early-Exit and Instant Confidence Translation Quality Estimation](https://mlsanity.com/paper/2502.14429/) (2025)
- [Structure-Conditional Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2510.20700/) (2025)
- [Agreement-Constrained Probabilistic Minimum Bayes Risk Decoding](https://mlsanity.com/paper/2512.01316/) (2025)
- [Case-Based Decision-Theoretic Decoding with Quality Memories](https://mlsanity.com/paper/2509.12677/) (2025)
- [Minimum Bayes Risk Decoding for Error Span Detection in Reference-Free Automatic Machine Translation Evaluation](https://mlsanity.com/paper/2512.07540/) (2025)
- [Unveiling the Power of Source: Source-based Minimum Bayes Risk Decoding for Neural Machine Translation](https://mlsanity.com/paper/2406.11632/) (2024)
- [Multi-Hypothesis Distillation of Multilingual Neural Translation Models for Low-Resource Languages](https://mlsanity.com/paper/2507.21568/) (2025)
- [MLLP-VRAIN UPV system for the IWSLT 2026 Simultaneous Speech Translation task](https://mlsanity.com/paper/2606.17255/) (2026)
- [Quit While You're Ahead: Quit for Efficient Candidate Generation in Machine Translation Reranking](https://mlsanity.com/paper/2609.00588/) (2026)

## Abstract (arXiv)

Minimum Bayes Risk (MBR) decoding is a text generation technique that has been shown to improve the quality of machine translations, but is expensive, even if a sampling-based approximation is used. Besides requiring a large number of sampled sequences, it requires the pairwise calculation of a utility metric, which has quadratic complexity. In this paper, we propose to approximate pairwise metric scores with scores calculated against aggregated reference representations. This changes the complexity of utility estimation from O(n2) to O(n), while empirically preserving most of the quality gains of MBR decoding. We release our source code at https://github.com/ZurichNLP/mbr