← All parts of this equation

Equation 27 · Part 2 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

Symbol C_train

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

What this part means

CtC_train is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

CtC_train is one of the signed contributions combined to compute the quantity on the left.

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.

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

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