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A tree interpretation of arc standard dependency derivation

Zihao Huang, Ai Ka Lee, Jungyeul Park

Abstract

We show that arc-standard derivations for projective dependency trees determine a unique ordered tree representation with surface-contiguous yields and stable lexical anchoring. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting hierarchical object uniquely determines the original dependency arcs. We further show that this representation characterizes projectivity: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is derivational rather than convertive. It interprets arc-standard transition sequences directly as ordered tree construction, rather than transforming a completed dependency graph into a phrase-structure output. For non-projective inputs, the same interpretation can be used in practice via pseudo-projective lifting before derivation and inverse decoding after recovery. A proof-of-concept implementation in a standard neural transition-based parser shows that the mapped derivations are executable and support stable dependency recovery.

A tree interpretation of arc standard dependency derivation

Abstract

We show that arc-standard derivations for projective dependency trees determine a unique ordered tree representation with surface-contiguous yields and stable lexical anchoring. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting hierarchical object uniquely determines the original dependency arcs. We further show that this representation characterizes projectivity: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is derivational rather than convertive. It interprets arc-standard transition sequences directly as ordered tree construction, rather than transforming a completed dependency graph into a phrase-structure output. For non-projective inputs, the same interpretation can be used in practice via pseudo-projective lifting before derivation and inverse decoding after recovery. A proof-of-concept implementation in a standard neural transition-based parser shows that the mapped derivations are executable and support stable dependency recovery.

Paper Structure

This paper contains 13 sections, 3 theorems, 5 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and related work
  3. Transition-based parsing and projectivity
  4. Conversion versus derivational interpretation
  5. Ordered tree interpretation of arc-standard derivations
  6. Dependency trees and ordered tree representations
  7. Mapped configurations and transition correspondence
  8. shift
  9. leftarc
  10. rightarc
  11. Feasibility of the derivational mapping
  12. Discussion
  13. Conclusion

Key Result

Theorem 1

A single-headed dependency tree admits a rooted ordered representation of the kind defined above, with leaves in surface order and every subtree spanning a contiguous substring, if and only if the dependency tree is projective.

Figures (1)

  • Figure 1: A dependency tree and its ordered dependency tree representation

Theorems & Definitions (6)

  • Theorem 1: Projective characterization
  • proof : Proof sketch
  • Theorem 2: Transition correspondence
  • proof : Proof sketch
  • Theorem 3: Recoverability
  • proof : Proof sketch