It’s MBR All the Way Down: Modern Generation Techniques Through the Lens of Minimum B ayes Risk (2023)

Abstract: Minimum Bayes Risk (MBR) decoding is a method for choosing the outputs of a machine learning system based not on the output with the highest probability, but the output with the lowest risk (expected error) among multiple candidates. It is a simple but powerful method: for an additional cost at inference time, MBR provides reliable several-point improvements across metrics for a wide variety of tasks without any additional data or training. Despite this, MBR is not frequently applied in NLP works, and knowledge of the method itself is limited. We first provide an introduction to the method and the recent literature. We show that several recent methods that do not reference MBR can be written as special cases of MBR; this reformulation provides additional theoretical justification for the performance of these methods, explaining some results that were previously only empirical. We provide theoretical and empirical results about the effectiveness of various MBR variants and make concrete recommendations for the application of MBR in NLP models, including future directions in this area.

## introduction while mbr is rarely applied by name in modern nlp, a number of methods with similar intuitions have gained popularity. in §4, we demonstrate that a number of generation techniques widely used with modern language models can be viewed as special instances of mbr: self-consistency @xcite and its extensions, range voting @xcite , output ensembling @xcite , and some types of density estimation @xcite . this view exposes connections between seemingly disparate methods and presents theoretical justifications for existing empirical results using these methods. we also discuss how insights from the mbr literature can inform the use of these other mbr-like methods. with the framing of mbr, the theoretical justification for the empirical performance of several methods becomes clear; the extension of selfconsistency to open-ended generations becomes trivial; and several promising modifications to selfconsistency and output ensembling are exposed. in particular, modern mbr-like methods often do not apply the insights from research on mbr, suggesting that these methods could be further improved. in §5, we show that some design choices, though seemingly intuitive to a practitioner accustomed to search-based decoding methods, should be avoided when applying mbr. ## formalization we begin with the basics of decoding and mbr. ## mbr as a frame for other methods self-consistency, output ensembling, density estimation, and range voting can all be viewed through the framing of mbr. this exposes unstated connections between the methods and provides some theoretical backing to the empirical success of these methods. we discuss each in turn. ## design decisions impact mbr performance although all the methods in section 4 are mbrlike, they make very different decisions about the four design choices in our mbr taxonomy. to demonstrate the importance of the method design, we consider empirically two cases where changing design impacts the performance of the method. ## mbr applications in nlp the use of minimum bayes risk decoding in nlp predates these mbr-like methods; mbr has been applied by name in nlp since the 1990s. historical context minimum bayes risk decoding has roots in bayesian decision theory, a field of study that dates as far back as the age of enlightenment @xcite . central to bayesian decision theory is the principle of risk minimization: in the face of uncertainty, an optimal decision maker should choose the option that minimizes the amount of error they can expect to suffer -or, in other terms, maximizes the amount of utility they can expect to enjoy @xcite . this is precisely the intuition encoded in mbr (i.e. equation 3 ). adoption in nlp mbr was adopted by the speech and nlp communities in the 1990s and early 2000s, finding applications in syntactical parsing @xcite , automatic speech recognition @xcite , and statistical machine translation @xcite @xcite . many nlp tasks during this time relied upon graph structures as inductive biases (i.e. parse trees or translation lattices/hypergraphs). as such, early mbr works often used these graphical models as hypothesis and evidence spaces. work on lattice mbr @xcite , for instance, treated the set of all hypotheses encoded in a word lattice, of which there are exponentially many, as both evidence and hypothesis sets. this is in contrast to most later mbr work, which operates on a relatively small list of text outputs obtained from a neural model. as a result, early work relied on rather involved dynamic programming algorithms ## conclusion minimum bayes risk decoding has declined in popularity, but the underlying concept of sampling a set from a distribution and choosing an output to minimize risk according to that set has remained. this concept now takes many surface forms-from self-consistency to range voting to output ensembles-and current research in these areas rarely draws connections to mbr. while rediscovery is a key part of science, so is recontextualizing new methods within a broader research narrative. this can often reveal new insights or cast findings in a different light. for instance, the empirical benefits of self-consistency can be justified through an mbr framing; work on extensions to self-consistency has rediscovered other properties of mbr; and work on ensembling has raised questions about how to weight mixtures of models that can be reasoned about within the framework of noisy estimates of global probability distributions. the adoption of newer terms for mbr-like methods may be a type of terminology drift. related phenomena have been studied in the philosophy of science literature, including pressures to coin new terms @xcite , potential negative consequences of divergent terminology @xcite , and decreased citation of older methods in nlp @xcite . for a more involved discussion of the literature on term coining and possible connections, see appendix b. language is not static, so some degree of terminology drift in scientific literature is unavoidable. however, recognizing the connections between modern techniques and older work is crucial to understanding why such methods are effective. we must not forget the lessons of the past as we search for the methods of the future.