Equation 3 · What Alignment Actually Costs
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
the compute spent training a policy against a reward model or a verifier, priced in GPU-hours and bounded by the same hardware capability development competes for. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol C_RL
the compute spent training a policy against a reward model or a verifier, priced in GPU-hours and bounded by the same hardware capability development competes for.
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.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
is the cost of collecting human feedback — demonstrations and preference comparisons, priced per label and bounded by how many people can be recruited and trained. is the compute spent training a policy against a reward model or a verifier, priced in GPU-hours and bounded by the same hardware capability development competes for. is the cost of adversarially testing the result, priced in expert-hours and bounded by how many domain specialists exist at all. Each term has published figures behind it. None of them is small in absolute terms. All of them are small relative to what they are meant to check.
For background, read the article’s source list.