  The phrase grounding task aims to ground each entity mention in a given
caption of an image to a corresponding region in that image. Although there are
clear dependencies between how different mentions of the same caption should be
grounded, previous structured prediction methods that aim to capture such
dependencies need to resort to approximate inference or non-differentiable
losses. In this paper, we formulate phrase grounding as a sequence labeling
task where we treat candidate regions as potential labels, and use neural chain
Conditional Random Fields (CRFs) to model dependencies among regions for
adjacent mentions. In contrast to standard sequence labeling tasks, the phrase
grounding task is defined such that there may be multiple correct candidate
regions. To address this multiplicity of gold labels, we define so-called
Soft-Label Chain CRFs, and present an algorithm that enables convenient
end-to-end training. Our method establishes a new state-of-the-art on phrase
grounding on the Flickr30k Entities dataset. Analysis shows that our model
benefits both from the entity dependencies captured by the CRF and from the
soft-label training regime. Our code is available at
\url{github.com/liujch1998/SoftLabelCCRF}
