Risk of an Output in Minimum Bayes Risk Decoding
In Minimum Bayes Risk (MBR) decoding, the risk associated with selecting a particular output y from a set of candidates Ω is defined as the expected cost over all possible reference outputs y_r. This is calculated by summing the product of the risk function R(y, y_r) and the probability of the reference output Pr(y_r|x) for every candidate in Ω. The formula is:
$\text{Risk}(y) = \mathbb{E}_{y_r \sim \Pr(y_r|\mathbf{x})} R(y, y_r) = \sum_{y_r \in \Omega} R(y, y_r) \cdot \Pr(y_r|\mathbf{x})$
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Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Computing Sciences
Foundations of Large Language Models Course
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Risk Function in Minimum Bayes Risk Decoding
Risk of an Output in Minimum Bayes Risk Decoding
A language model is prompted to solve the math problem 'What is 7 + 8?'. To improve reliability, the model generates five different outputs using a sampling strategy: [15, 14, 15, 15, 16]. A selection process is then used to choose the final answer by identifying the candidate that minimizes the expected disagreement with the other generated candidates. Which output will be selected?
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Risk of an Output in Minimum Bayes Risk Decoding
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y_Ais calculated by summing the pairwise costs betweeny_Aand every possible reference outputy_r, with each cost weighted by the probability of that reference output. The pairwise cost function is designed to be high for dissimilar outputs and low for similar outputs.Suppose you are calculating the expected cost for candidate
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