Centering theory is a theory of both discourse salience and discourse coherence. As a model of discourse salience, it suggests that at any given point in the discourse, one of the entities in the discourse model is salient; As a model of discourse coherence, it proposes that discourses in which adjacent sentences continue to maintain the same salient entity are more coherent than those which shift back and forth between multiple entities.

Centering Theory

Entity grid model is an alternative way to capture entity-based coherence: instead of having a top-down theory, the entity-grid model using machine learning to induce the patterns of entity mentioning that make a discourse more coherent.

Entity Grid Model

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

San Jose State University

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

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.

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