Implicit discourse relation recognition aims to understand and annotate the latent relations between two discourse arguments, such as temporal, comparison, etc. Most previous methods encode two discourse arguments separately, the ones considering pair specific clues ignore the bidirectional interactions between two arguments and the sparsity of pair patterns. In this paper, we propose a novel neural Tensor network framework with Interactive Attention and Sparse Learning (TIASL) for implicit discourse relation recognition. (1) We mine the most correlated word pairs from two discourse arguments to model pair specific clues, and integrate them as interactive attention into argument representations produced by the bidirectional long short-term memory network. Meanwhile, (2) the neural tensor network with sparse constraint is proposed to explore the deeper and the more important pair patterns so as to fully recognize discourse relations. The experimental results on PDTB show that our proposed TIASL framework is effective.