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Equation 27 · Part 1 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

Symbol C_total

Ctotal=Ctrain+Q⋅cˉinf,C_{\mathrm{total}} = C_{\mathrm{train}} + Q \cdot \bar{c}_{\mathrm{inf}},
CtotalC_{\mathrm{total}}

What this part means

total lifetime cost.

Its job in the formula

CtC_total is part of the quantity the equation computes from the expression on the right.

Where the article explains it

Write total lifetime cost as CtotalC_{\mathrm{total}} = CtrainC_{\mathrm{train}} + Q ⋅\cdot cˉinf\bar{c}_{\mathrm{inf}}, with Q requests over the model’s life.

The passage around this formula

Which combination a provider chooses is not primarily a research question. Write total lifetime cost as Ctotal=Ctrain+Q⋅cˉinfC_{\mathrm{total}} = C_{\mathrm{train}} + Q \cdot \bar{c}_{\mathrm{inf}}. 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 cˉinf\bar{c}_{\mathrm{inf}} pays back continuously while every technique that reduces CtrainC_{\mathrm{train}} pays back once.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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