Recognizing named entities (NEs) is commonly conducted as a classification problem that predicts a class tag for an 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, the regression operation is introduced to locate NEs in a sentence. In this approach, a deep network is first designed to transform an input sentence into recurrent feature maps. Bounding boxes are generated from the feature maps, where a box is an abstract representation of an NE candidate. In addition to the class tag, each bounding box has two parameters denoting the start position and the length of an NE candidate. In the training process, the location offset between a bounding box and a true NE are learned to minimize the location loss. Based on this motivation, a multiobjective learning framework is designed to simultaneously locate entities and predict the class probability. By sharing parameters for locating and predicting, the framework can take full advantage of annotated data and enable more potent nonlinear function approximators to enhance model discriminability. Experiments demonstrate state-of-the-art performance for nested named entitiesfootnote{Our codes will be available at: url{https://github.com/wuyuefei3/BR}}.
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