Given a document $D$ with $T$ words, the model considers all of the $\frac{T(T-1)}{2}$ text spans in $D$. The task is to assign to each span $i$ an antecedent $y_i$, a random variable ranging over the values ${1, ..., i - 1, \epsilon}$; each previous span and a special dummy token $\epsilon$. When the dummy token is chosen, it means 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.

The Neural e2e-coref Algorithm's Formal Model

This is a mention-ranking algorithm that considers all possible spans of text in the document, assigns a mention-score to each span, prunes the mentions based on this score, then assigns coreference links to the remaining mentions.

University of Michigan - Ann Arbor

Supervised neural machine learning systems are used to model coreference, mainly used coreference architectures are 

 - The Mention-Pair Architecture
 - The Mention-Rank Architecture
  - Entity-based Models


Architectures for Coreference Algorithms

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

This is a classifier which does a binary classification whether a candidate anaphor and a candidate antecedent is co referring or not.

The Mention-Pair Architecture

The mention ranking model directly compares candidate antecedents to each other, choosing the highest-scoring antecedent for each anaphor.

The Mention-Rank Architecture

Entity-based models link each mention to a previous discourse entity (rather than previous mentions). 

Learn Before

Related

Learn After