While writing a full blog post about this is beyond my late-night ability at this hour. I have to say I consider this to be ground-breaking work. To summarize, I would say this is a stepping stone in the unification and reconciliation of the “model zoo” in machine learning. In plain words, this K-Stereographic model seems to me, after all the research I have done for Envisage, Knosis, Enten and the other partner companies, the most promising work in providing a bedrock from a common “internal language” across various machine learning models.
You can think of this as the ABC of the machine-equivalent of the proto-language our thoughts are whispered in.
On a personal note I would add that I am proud to have had one of the co-authors, Octavian Ganea, as a teaching assistant for the Numerical Methods course in my second year at the Polytechnic. By any metric, I was in no way a model student; but then again, we were both a lot younger back then.
Without further ado…
the κ-Stereographic Model, that harnesses the formalism of gyrovector spaces in order to capture all three geometries of constant curvature (hyperbolic, Euclidean and spherical) at once. Furthermore, the presented model also allows to smoothly interpolate between the geometries of constant curvature and thus provides a way to learn the curvature of spaces jointly with the embeddings.http://hyperbolicdeeplearning.com/k-stereographic-model/