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Equation 5 · Part 2 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Symbol j

ci=∑j=1Txαijhj,αij=exp⁡(eij)∑k=1Txexp⁡(eik).c_i = \sum_{j=1}^{T_x} \alpha_{ij} h_j, \qquad \alpha_{ij} = \frac{\exp(e_{ij})}{\sum_{k=1}^{T_x} \exp(e_{ik})}.
jj

What this part means

j occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

j occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Bahdanau, Cho and Bengio proposed letting the decoder search the source for the parts relevant to each output word, rather than reading from a single compressed vector [ 9 ] . The decoder computes, at each output step i , a context vector as a weighted sum of all encoder states: ci=∑j=1Txαijhj,αij=exp⁡(eij)∑k=1Txexp⁡(eik)c_i = \sum_{j=1}^{T_x} \alpha_{ij} h_j, \qquad \alpha_{ij} = \frac{\exp(e_{ij})}{\sum_{k=1}^{T_x} \exp(e_{ik})}. The capacity of the intermediate representation now grows with the input rather than being fixed in advance. They further reported that the learned alignments corresponded well with human linguistic intuition — an interpretability result that arrived free with a performance fix, which is rare.

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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