  The Fisher information metric is an important foundation of information
geometry, wherein it allows us to approximate the local geometry of a
probability distribution. Recurrent neural networks such as the
Sequence-to-Sequence (Seq2Seq) networks that have lately been used to yield
state-of-the-art performance on speech translation or image captioning have so
far ignored the geometry of the latent embedding, that they iteratively learn.
We propose the information geometric Seq2Seq (GeoSeq2Seq) network which
abridges the gap between deep recurrent neural networks and information
geometry. Specifically, the latent embedding offered by a recurrent network is
encoded as a Fisher kernel of a parametric Gaussian Mixture Model, a formalism
common in computer vision. We utilise such a network to predict the shortest
routes between two nodes of a graph by learning the adjacency matrix using the
GeoSeq2Seq formalism; our results show that for such a problem the
probabilistic representation of the latent embedding supersedes the
non-probabilistic embedding by 10-15\%.
