Equation 5 · What Alignment Actually Costs
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Symbol C_human
uman is part of the quantity the equation computes from the expression on the right.
Symbol barc
barc is one factor in the product that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
The unit economics matter because a dataset’s cost is close to linear in its size: . with n comparisons collected at a mean cost 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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The unit economics matter because a dataset’s cost is close to linear in its size: . with n comparisons collected at a mean cost 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 dollars per fifty words, applied to documents averaging 304 words [ 3 ] . That is better than a tenfold difference in , and it is the strongest documented economic argument for the shift toward AI feedback that labs including Anthropic and Google have made in various forms. It is not, on its own, evidence that AI feedback is a free substitute: RLAIF’s own comparison measures win rate and cost together and finds the two feedback sources broadly comparable on the tasks tested, not that the human signal was redundant. What the price gap buys is a change in n that a fixed budget can afford, not a change in what a labelled comparison actually measures.
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