Given a document $D$ with $T$ words, the formal model of the neural e2e-coref algorithm considers all of the $\frac{T(T-1)}{2}$ possible text spans in $D$. The task is to assign to each span $i$ an antecedent $y_i$, which is a random variable ranging over the values $\{1, ..., i - 1, \epsilon\}$ (representing each previous span and a special dummy token $\epsilon$). When the dummy token $\epsilon$ is chosen, it indicates that the span does not have an antecedent. For each pair of spans $i$ and $j$, the system assigns a score for the coreference link between span $i$ and span $j$: $s(i, j) = m(i) + m(j) + c(i, j)$, where $m$ is the mention score and $c$ is the antecedent score.