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Published equation contexts

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

Why this formula appears here

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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CtrainC_{\mathrm{train}}

Symbol C_train

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

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cˉinf\bar{c}_{\mathrm{inf}}

Symbol barc_inf

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

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Published contexts (1)

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

Equation 27 · Foundation Models

Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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