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Equation 5 · Part 4 · What Alignment Actually Costs

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Chuman=n⋅cˉC_{\mathrm{human}} = n \cdot \bar{c}
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The unit economics matter because a dataset’s cost is close to linear in its size: Chuman=n⋅cˉC_{\mathrm{human}} = n \cdot \bar{c}. with n comparisons collected at a mean cost cˉ\bar{c} per comparison. The direct comparison published in the RLAIF paper puts numbers on both sides of a genuinely useful substitution. Lee and colleagues estimate that an AI-generated preference label produced with two inference passes of GPT-4 — used to correct for position bias, at an average of about 830 prompt tokens and 61 tokens of chain-of-thought rationale — costs about 0.06 US dollars per example, against about 0.67 US dollars per example for a human label purchased through a commercial annotation service pricing at roughly 0.11 US…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.