A language model processes an input prompt x and considers four potential output sequences: y1, y2, y3, and y4. The model calculates the conditional probability Pr(y|x) for each sequence as follows:

• Pr(y1|x) = 0.45
• Pr(y2|x) = 0.15
• Pr(y3|x) = 0.85
• Pr(y4|x) = 0.60

If the model employs a selection method that chooses the top 2 sequences that maximize this probability, which set of sequences will be the final output?

Interpreting the BoN Sampling Formula

In the mathematical formulation of a sampling method where the top N outputs are selected based on their likelihood given an input x, the expression argTopN_y [Pr(y|x)] returns the N highest conditional probability values.