Equation 2 · Part 10 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex
Starting index or lower bound: t=1
What this part means
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Its job in the formula
t=1 appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: t=1→Article meaning
The passage around this formula
An autoregressive model factorizes a sequence as . 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.
Learn the underlying idea
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Open the illustrated sums and products: repeat an operation over an index guide →
Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.