Non-Projective Parse

The defining feature of a non-projective parse is the presence of crossing dependency arcs when the sentence is drawn linearly above the text. In a projective tree, no arcs intersect; in a non-projective tree, at least one arc crosses another. This occurs when a word and its syntactic head are separated by words that do not depend on either of them, violating the adjacency constraint of projective structures.

Non-projective structures are the primary mechanism for encoding long-distance dependencies, where a syntactic relation spans across intervening clause boundaries. Classic examples include:

• Wh-movement: 'What did you say that John bought?' — 'what' depends on 'bought' across multiple clauses.
• Topicalization: 'Beans, I don't like.' — 'beans' is the object of 'like' but appears at the sentence periphery.
• Relative clauses: 'The report that the manager filed yesterday was approved.' — 'report' governs 'filed' across a clause boundary.

Languages with morphologically rich case-marking systems frequently exhibit non-projective structures because word order is not rigidly fixed by grammatical function. In languages like Czech, German, Latin, Turkish, and Hindi, constituents can be scrambled for discourse emphasis, creating crossing arcs. For example, in German subordinate clauses, the finite verb appears at the end, while its arguments may be fronted, producing systematic non-projectivity that projective parsers cannot capture.

Handling non-projective parses requires specialized decoding algorithms beyond simple shift-reduce or arc-eager strategies:

• Chu-Liu/Edmonds Algorithm: Finds the maximum spanning tree in a directed graph, enabling global decoding of non-projective structures in graph-based parsing.
• Swap-based transition systems: Extend shift-reduce parsing with a SWAP action that reorders the buffer to handle crossing arcs.
• Pseudo-projective parsing: A preprocessing approach that lifts non-projective arcs to higher nodes, converting the tree to a projective form with encoded labels, then restores crossings in postprocessing.

Non-projective dependencies disproportionately affect parser evaluation. The Labeled Attachment Score (LAS) often drops significantly on non-projective arcs compared to projective ones. State-of-the-art parsers using biaffine attention and deep contextualized embeddings from models like XLM-RoBERTa have narrowed this gap, but non-projective accuracy remains a key differentiator. The Universal Dependencies framework explicitly marks non-projective relations, enabling targeted evaluation on these challenging linguistic phenomena.

Non-projective parses are not merely syntactic curiosities—they are essential for accurate semantic interpretation. In Abstract Meaning Representation (AMR) and semantic dependency parsing, crossing arcs frequently represent:

• Control structures: 'John promised Mary to leave.' — 'John' is the implicit subject of 'leave'.
• Predicative complements: 'They considered him brilliant.' — 'him' and 'brilliant' share a non-projective relation.
• Coordination with ellipsis: 'Kim bought apples and Sandy pears.' — 'bought' governs 'pears' across the conjunction. Without non-projective capacity, these meaning-bearing relations are lost.

The property of a dependency tree where no arcs cross when drawn above a sentence in linear order. A projective parse can be planar, meaning all dependencies are nested. Non-projective parses violate this constraint, requiring arcs to intersect. Projectivity is a simplifying assumption that holds for English but fails for morphologically rich languages with free word order, such as Czech, Turkish, and Latin.

The task of training a dependency parser on one or more source languages and applying it to a target language with little to no annotated data. Non-projective structures pose a significant challenge because languages vary widely in word order freedom. Modern approaches leverage multilingual BERT or XLM-RoBERTa representations to transfer syntactic knowledge across languages, enabling zero-shot parsing of non-projective phenomena like wh-movement and scrambling without target-language treebanks.

An extended representation in Universal Dependencies that augments basic syntactic trees with additional arcs to capture implicit predicates, shared arguments, and control relationships. While basic UD trees are constrained to be projective for practical annotation, enhanced dependencies can introduce crossing arcs to represent semantic phenomena like:

• Control structures: 'She wants to leave' adds an arc from 'leave' to 'She'
• Relative clauses: Explicitly linking the relativizer to its antecedent
• Gapping: Connecting elided material to its overt antecedent

The task of identifying predicate-argument structures that capture the meaning of a sentence, often abstracting away from surface syntax. Unlike syntactic dependency parsing, semantic graphs are inherently non-projective because they represent logical relations that frequently cross syntactic boundaries. For example, in 'The book that John wrote sold well,' the semantic relation between 'book' and 'sold' crosses the syntactic dependency between 'book' and 'wrote.'

A semantic formalism that encodes sentence meaning as a rooted, directed, acyclic graph where nodes are concepts and edges are semantic roles. AMR graphs are fundamentally non-projective, abstracting away from word order entirely to represent who did what to whom. Unlike dependency trees, AMR does not anchor nodes to surface tokens, allowing it to represent phenomena like:

• Implicit arguments: 'The cake was eaten' includes an implicit agent
• Coreference: Merging multiple mentions into a single concept node
• Reentrancy: A single concept participating in multiple relations