  Recognizing named entities (NEs) is commonly conducted as a classification
problem that predicts a class tag for a word or a NE candidate in a sentence.
In shallow structures, categorized features are weighted to support the
prediction. Recent developments in neural networks have adopted deep structures
that map categorized features into continuous representations. This approach
unfolds a dense space saturated with high-order abstract semantic information,
where the prediction is based on distributed feature representations. In this
paper, positions of NEs in a sentence are represented as continuous values.
Then, a regression operation is introduced to regress boundaries of NEs in a
sentence. Based on boundary regression, we design a boundary regression model
to support nested NE recognition. It is a multiobjective learning framework,
which simultaneously predicts the classification score of a NE candidate and
refine its spatial location in a sentence. It has the advantage to resolve
nested NEs and support boundary regression for locating NEs in a sntence. By
sharing parameters for predicting and locating, this model enables more potent
nonlinear function approximators to enhance model discriminability. Experiments
demonstrate state-of-the-art performance for nested NE recognition\footnote{Our
codes to implement the BR model are available at:
\url{https://github.com/wuyuefei3/BR}.}.
