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Equation 2 · Part 8 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 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 →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.