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Equation 1 · Part 8 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Symbol w_t-1

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}).
wt−1w_{t-1}

What this part means

wtw_t-1 is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

wtw_t-1 is one of the signed contributions combined to compute the quantity on the left.

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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