Equation 27 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity
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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.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol C_train
rain is one of the signed contributions combined to compute the quantity on the left.
Symbol Q
Q is one of the signed contributions combined to compute the quantity on the left.
Symbol barc_inf
barnf is one of the signed contributions combined to compute 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
Which combination a provider chooses is not primarily a research question. Write total lifetime cost as . with Q requests over the model’s life. When Q is small — a research artefact, an internal tool — the training term dominates and compute-optimal allocation is the right target. When Q is very large, the second term dominates by orders of magnitude, and every technique that reduces pays back continuously while every technique that reduces pays back once.
Sources cited in the article section
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