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Equation 1 · Part 3 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Symbol w_2

P(w1,w2,…,wT)=∏t=1TP(wt∣w1,…,wt−1).P(w_1, w_2, \ldots, w_T) = \prod_{t=1}^{T} P(w_t \mid w_1, \ldots, w_{t-1}).
w2w_2

What this part means

w2w_2 is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

w2w_2 is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

First, the object of study became prediction . A model of language is a probability assignment over what comes next. The chain rule makes this exact for any sequence of tokens: P(w1,w2,…,wT)=∏t=1TP(wt∣w1,…,wt−1)P(w_1, w_2, \ldots, w_T) = \prod_{t=1}^{T} P(w_t \mid w_1, \ldots, w_{t-1}). Second, quality became measurable without a task . Cross-entropy on held-out text is a number, and a lower number is unambiguously better. That gave the field a scalar to descend for the next seventy years, long before anyone knew what descending it would buy. Brown and colleagues later made the benchmark concrete, estimating an upper bound of 1.75 bits per character for English from a word trigram model measured against a balanced sample, and proposing a common corpus as a standard against which…

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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.

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Sources cited in the surrounding passage

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