Span extraction is an essential problem in machine reading comprehension. Most of the existing algorithms predict the start and end positions of an answer span in the given corresponding context by generating two probability vectors. In this paper, we propose a novel approach that extends the probability vector to a probability matrix. Such a matrix can cover more start-end position pairs. Precisely, to each possible start index, the method always generates an end probability vector. Besides, we propose a sampling-based training strategy to address the computational cost and memory issue in the matrix training phase. We evaluate our method on SQuAD 1.1 and three other question answering benchmarks. Leveraging the most competitive models BERT and BiDAF as the backbone, our proposed approach can get consistent improvements in all datasets, demonstrating the effectiveness of the proposed method.
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