Modern neural architectures critically rely on attention for mapping structured inputs to sequences. In this paper we show that prevalent attention architectures do not adequately model the dependence among the attention and output variables along the length of a predicted sequence... We present an alternative architecture called Posterior Attention Models that relying on a principled factorization of the full joint distribution of the attention and output variables propose two major changes. First, the position where attention is marginalized is changed from the input to the output. Second, the attention propagated to the next decoding stage is a posterior attention distribution conditioned on the output. Empirically on five translation and two morphological inflection tasks the proposed posterior attention models yield better predictions and alignment accuracy than existing attention models. (read more)