Discourse Coherence

25.3 Centering and entity-based coherence

1. What is the central intuition of Centering Theory?
   At any point one entity is salient (“centered”), and discourses that CONTINUE to keep the same entity salient are more coherent than those that SHIFT between entities. “John went to his music store… He had frequented the store… He was excited…” is better than alternating “It was a store John had frequented… It was closing just as John arrived.”
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, pp. 578–579
2. Define Cb, Cf and Cp in Centering Theory.
   The backward-looking center \(C_b(U_n)\) is the salient entity being focused on after \(U_n\). The forward-looking centers \(C_f(U_n)\) are the entities evoked by \(U_n\), ranked by salience and grammatical role (subject > object > others). The preferred center \(C_p\) is the highest-ranked \(C_f\): a prediction of what comes next.
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 579
3. What are the four Centering transitions (Brennan et al. 1987)?

   	same \(C_b\)	new \(C_b\)
   \(C_b = C_p\)	Continue	Smooth-Shift
   \(C_b \neq C_p\)	Retain	Rough-Shift

   “Same \(C_b\)”: \(C_b(U_{n+1}) = C_b(U_n)\) or \(C_b(U_n)\) undefined; the rows compare \(C_b(U_{n+1})\) with \(C_p(U_{n+1})\).
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 579
4. State Centering’s Rule 1 and Rule 2.
   Rule 1: if any element of \(C_f(U_n)\) is realized by a pronoun in \(U_{n+1}\), then \(C_b(U_{n+1})\) must be realized as a pronoun too. Rule 2: Continue is preferred to Retain, to Smooth-Shift, to Rough-Shift.
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 579
5. What does a Retain transition signal about the speaker?
   The speaker keeps the current entity as \(C_b\) but places it lower in \(C_f\), intending to shift to a new entity in a future utterance.
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, pp. 579–580
6. Apply Centering to U1 “John went to his favorite music store to buy a piano.” and U2 “He was excited that he could finally buy a piano.”
   \(C_f(U_1)\) = {John, music store, piano}, \(C_p\) = John, \(C_b\) undefined. \(C_f(U_2)\) = {John, piano}, \(C_p\) = John, \(C_b\) = John. Since \(C_b(U_2) = C_p(U_2)\) and \(C_b(U_1)\) is undefined: Continue.
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 580
7. How does the entity grid model differ from Centering Theory?
   Instead of a top-down theory, it uses machine learning to induce which patterns of entity mentions make a discourse coherent (Barzilay and Lapata 2008).
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 580
8. What is an entity grid?
   A 2-D array with a row per sentence and a column per discourse entity (after coreference); cells give the entity’s highest grammatical role there: subject S, object O, neither X, absent –. (1) [The committee]S approved [the budget]O. (2) [It]S includes [funds]O for [schools]X. (3) [The committee]S will publish [it]O.

   	committee	budget	funds	schools
   1	S	O	–	–
   2	–	S	O	X
   3	S	O	–	–

   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, pp. 580–581
9. How does the entity grid become a feature vector for coherence?
   Count local entity transitions, sequences in \(\{S, O, X, -\}^n\) read down each column (e.g. [S –], [O S]), and use the probability of each transition type as features of the document. Coherent texts have some dense columns (main entities, often subjects) and many sparse ones.
   • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 581
10. What are the two ways of evaluating entity-based and neural coherence models?
    Predicting human coherence ratings (best when there is an end task, like essay grading), or self-supervision: natural documents vs pseudo-documents with changed sentence order, which are less coherent.
    • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 582
11. Describe the three self-supervised coherence tasks.
    Sentence order discrimination: rank the original above a random permutation. Sentence insertion: remove a sentence and find its original position among all positions (harder, documents differ by one sentence). Sentence order reconstruction: put shuffled sentences back in order (hardest).
    • Jurafsky & Martin, Speech and Language Processing, 3rd ed. draft, ch. 25, §25.3, p. 582