The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold.

Work completed at the University of Washington. Work completed at Microsoft Research.

We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets.

Recent accelerations in multi-modal applications have been made possible with the plethora of image and text data available online.

We wish to thank all of the reviewers for their time and thorough reading of our paper! We appreciate the reviewer's suggestions regarding clarity. We have added the suggested summary sentence "the key We started with binary sentiment classification, but are actively working on more tasks. RNN hidden states onto the top two PCs for two different input sequences that differ only by two tokens (replacing ' The trajectories start out the same as the initial tokens are identical. We have added a footnote noting this in the main text.