Efficient Minimum Bayes Risk Decoding using Low-Rank Matrix Completion Algorithms

TL;DR

This paper introduces a low-rank matrix completion approach to approximate Minimum Bayes Risk decoding in machine translation, significantly reducing computation while maintaining translation quality.

Contribution

It formulates MBR decoding as a low-rank matrix completion problem and applies ALS to efficiently approximate scores, reducing computations by 16 times.

Findings

Achieves similar translation quality with 1/16th of the utility computations.

Empirically confirms the low-rank structure of score matrices.

Outperforms other approximation methods in quality benchmarks.

Abstract

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 the task of machine translation. We formulate MBR decoding as a matrix completion problem, where the utility metric scores between candidate hypotheses and pseudo-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 a 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 vanilla MBR decoding while achieving equal translation quality measured by COMET22 on the WMT22 dataset (en<>de and en<>ru). We also benchmark our method against other approximation methods and we show gains in quality when comparing to them.