Equation 20 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
What does this equation mean?
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 mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol C_total
otal is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
The third term in is now a control surface rather than a constant, and it obeys its own scaling behaviour.
Sources cited in the article section
- [9] Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters ↗
- [1] GPT-5 System Card ↗
These citations give research context. Read each source to check which claims it supports.
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