Submodularity is desirable for a variety of objectives in content selection where the current neural encoder-decoder framework is inadequate. However, it has so far not been explored in the neural encoder-decoder system for text generation. In this work, we define diminishing attentions with submodular functions and in turn, prove the submodularity of the effective neural coverage. The greedy algorithm approximating the solution to the submodular maximization problem is not suited to attention score optimization in auto-regressive generation. Therefore instead of following how submodular function has been widely used, we propose a simplified yet principled solution. The resulting attention module offers an architecturally simple and empirically effective method to improve the coverage of neural text generation. We run experiments on three directed text generation tasks with different levels of recovering rate, across two modalities, three different neural model architectures and two training strategy variations. The results and analyses demonstrate that our method generalizes well across these settings, produces texts of good quality and outperforms state-of-the-art baselines.
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