  An interesting and frequent type of multi-word expression (MWE) is the
headless MWE, for which there are no true internal syntactic dominance
relations; examples include many named entities ("Wells Fargo") and dates
("July 5, 2020") as well as certain productive constructions ("blow for blow",
"day after day"). Despite their special status and prevalence, current
dependency-annotation schemes require treating such flat structures as if they
had internal syntactic heads, and most current parsers handle them in the same
fashion as headed constructions. Meanwhile, outside the context of parsing,
taggers are typically used for identifying MWEs, but taggers might benefit from
structural information. We empirically compare these two common
strategies--parsing and tagging--for predicting flat MWEs. Additionally, we
propose an efficient joint decoding algorithm that combines scores from both
strategies. Experimental results on the MWE-Aware English Dependency Corpus and
on six non-English dependency treebanks with frequent flat structures show
that: (1) tagging is more accurate than parsing for identifying flat-structure
MWEs, (2) our joint decoder reconciles the two different views and, for
non-BERT features, leads to higher accuracies, and (3) most of the gains result
from feature sharing between the parsers and taggers.
