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Equation 2 · Part 1 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

Symbol p

p(x1:T)=∏t=1Tp(xt∣x<t).p(x_{1:T})=\prod_{t=1}^{T}p(x_t\mid x_{<t}).
pp

What this part means

p is part of the quantity the equation computes from the expression on the right.

Its job in the formula

p is part of the quantity the equation computes from the expression on the right.

The passage around this formula

An autoregressive model factorizes a sequence as p(x1:T)=∏t=1Tp(xt∣x<t)p(x_{1:T})=\prod_{t=1}^{T}p(x_t\mid x_{<t}). Source code can be placed in this representation alongside natural language. The model is not executing the program in this equation. It learns statistical structure over token sequences.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

Sources cited in the article section

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