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

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.