← All parts of this equation

Equation 5 · Part 17 · From n-Grams to Reasoning Models: A Technical History of the Language Model

Starting index or lower bound: k=1

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})}.
k=1k=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

k=1 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.

Read this part in the article →

Learn the underlying idea

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

Open the illustrated sums and products: repeat an operation over an index guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.