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Equation 5 · Part 18 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Ending index or upper bound: T_x

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})}.
TxT_x

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

TxT_x occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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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Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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