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Equation 2 · Part 3 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

Symbol t

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

What this part means

t appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

t appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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