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Modern neural networks are often augmented with an attention mechanism, whichtells the network where to focus within the input. We propose in this paper anew framework for sparse and structured attention, building upon a smoothed maxoperator. We show that the gradient of this operator defines a mapping fromreal values to probabilities, suitable as an attention mechanism. Our frameworkincludes softmax and a slight generalization of the recently-proposed sparsemaxas special cases. However, we also show how our framework can incorporatemodern structured penalties, resulting in more interpretable attentionmechanisms, that focus on entire segments or groups of an input. We deriveefficient algorithms to compute the forward and backward passes of ourattention mechanisms, enabling their use in a neural network trained withbackpropagation. To showcase their potential as a drop-in replacement forexisting ones, we evaluate our attention mechanisms on three large-scale tasks:textual entailment, machine translation, and sentence summarization. Ourattention mechanisms improve interpretability without sacrificing performance;notably, on textual entailment and summarization, we outperform the standardattention mechanisms based on softmax and sparsemax.

A Regularized Framework for Sparse and Structured Neural Attention