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Equation 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute

What does this equation mean?

Ctotal=Cpre+Cpost+Q⋅cˉinf,C_{\mathrm{total}} = C_{\mathrm{pre}} + C_{\mathrm{post}} + Q \cdot \bar{c}_{\mathrm{inf}},

Add the one-time compute used to train and refine the model to the compute spent answering requests over its lifetime.

Read it piece by piece

CtotalC_{\mathrm{total}}

Total compute

All computation spent on this deployed model system over its lifetime.

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CpreC_{\mathrm{pre}}

Pretraining compute

The one-time computation used to learn from the initial training data.

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CpostC_{\mathrm{post}}

Post-training compute

The one-time computation used after pretraining to shape the model’s behavior.

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QQ

Number of requests

How many requests the system serves during the period being counted.

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cˉinf\bar{c}_{\mathrm{inf}}

Compute per request

The average computation used to answer one request. The bar means average.

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Q⋅cˉinfQ \cdot \bar{c}_{\mathrm{inf}}

Lifetime inference compute

Requests multiplied by average compute per request.

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How to interpret it

The last term grows with usage. Doubling the number of requests doubles that term if average compute per request stays the same. The equation is an accounting model, not a claim that every request costs the same.

Try the accounting model

Illustrative compute units. Change the request count to see how usage changes the total.

PretrainingPost-trainingRequests

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