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Equation 5 · Part 10 · From n-Grams to Reasoning Models: A Technical History of the Language Model

fraction

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})}.
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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