1Cademy - Interpreting the BoN Sampling Formula

Learn Before

Mathematical Formulation of BoN Sampling

Short Answer

Interpreting the BoN Sampling Formula

Consider the formal definition for selecting a set of N output sequences based on an input sequence, x:

$\left\{\hat{\mathbf{y}}_1, ..., \hat{\mathbf{y}}_N\right\} = \underset{\mathbf{y}}{\text{argTopN}} [\text{Pr}(\mathbf{y}|\mathbf{x})]$

In your own words, explain what this mathematical expression represents. Specifically, describe the function of the Pr(y|x) component and the argTopN operation in this context.

Updated 2025-10-04

Contributors are:

Who are from:

Tags

Ch.5 Inference - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

Computing Sciences

Comprehension in Revised Bloom's Taxonomy

Cognitive Psychology

Psychology

Social Science

Empirical Science

Science

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.

Learn Before

Related