Equation 27 · Part 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
Symbol p_k
What this part means
only achievable if something can identify the successful attempt.
Its job in the formula
is part of the quantity the equation computes from the expression on the right.
Full expression→Symbol p_k→Article meaning
Where the article explains it
Attempts from one model on one prompt are strongly correlated, so realised gains fall well below this bound; and is only achievable if something can identify the successful attempt.
The passage around this formula
…formula]. which is concave in k and saturates quickly. Two caveats destroy any naive extrapolation from it. Attempts from one model on one prompt are strongly correlated, so realised gains fall well below this bound; and is only achievable if something can identify the successful attempt. Without a verifier, extra samples buy candidates, not answers. This is precisely why the reasoning-effort control and the availability of parallel test-time compute are architectural facts about a product rather than mere…
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 surrounding passage
These citations provide research context; check each source for the exact claim it supports.