  Sequence-to-sequence (encoder-decoder) models with attention constitute a
cornerstone of deep learning research, as they have enabled unprecedented
sequential data modeling capabilities. This effectiveness largely stems from
the capacity of these models to infer salient temporal dynamics over long
horizons; these are encoded into the obtained neural attention (NA)
distributions. However, existing NA formulations essentially constitute
point-wise selection mechanisms over the observed source sequences; that is,
attention weights computation relies on the assumption that each source
sequence element is independent of the rest. Unfortunately, although
convenient, this assumption fails to account for higher-order dependencies
which might be prevalent in real-world data. This paper addresses these
limitations by leveraging Quantum-Statistical modeling arguments. Specifically,
our work broadens the notion of NA, by attempting to account for the case that
the NA model becomes inherently incapable of discerning between individual
source elements; this is assumed to be the case due to higher-order temporal
dynamics. On the contrary, we postulate that in some cases selection may be
feasible only at the level of pairs of source sequence elements. To this end,
we cast NA into inference of an attention density matrix (ADM) approximation.
We derive effective training and inference algorithms, and evaluate our
approach in the context of a machine translation (MT) application. We perform
experiments with challenging benchmark datasets. As we show, our approach
yields favorable outcomes in terms of several evaluation metrics.
