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Formula for Scoring Reasoning Paths by Counting Correct Steps

A simple method to score a reasoning path is to count the number of steps classified as 'correct'. This can be represented by the formula:

$r(\mathbf{x}, \mathbf{y}) = \sum_{k=1}^{n_s} \delta(\text{correct}, C(\mathbf{x}, \bar{\mathbf{y}}_{\le k}))$

where:

$r(\mathbf{x}, \mathbf{y})$ is the total reward for the reasoning path $\mathbf{y}$ given the input $\mathbf{x}$ .
$n_s$ is the total number of steps in the reasoning path.
$C(\mathbf{x}, \bar{\mathbf{y}}_{\le k})$ is the classification output for step $k$ , determined by selecting the label with the maximum probability.
$\delta(a, b)$ is the Kronecker delta function, which is ${}1$ if $a=b$ and ${}0$ otherwise. In this context, it equals ${}1$ if the classification for step $k$ is 'correct'.

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Updated 2026-05-03

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Gemini AI

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Google

References

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Ch.5 Inference - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

Computing Sciences

Ch.4 Alignment - Foundations of Large Language Models

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