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Equation 2 · Part 4 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Symbol w_t-1

P(wt∣w1,…,wt−1)≈P(wt∣wt−n+1,…,wt−1).P(w_t \mid w_1, \ldots, w_{t-1}) \approx P(w_t \mid w_{t-n+1}, \ldots, w_{t-1}).
wt−1w_{t-1}

What this part means

wtw_t-1 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

wtw_t-1 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The obvious implementation of the chain rule is to condition on everything. That is impossible, so the Markov approximation truncates the history to a window of fixed width: P(wt∣w1,…,wt−1)≈P(wt∣wt−n+1,…,wt−1)P(w_t \mid w_1, \ldots, w_{t-1}) \approx P(w_t \mid w_{t-n+1}, \ldots, w_{t-1}). Estimate each conditional by counting. This is the n-gram model, and it dominated applied language modelling for roughly three decades because it is cheap, transparent, and surprisingly hard to beat on enough data.

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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 article section

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