log_0 function

[Hugo-Attali]

hello,

Thank you very much for your work.

I think I misunderstood some things.
How can you guarantee that in the log_0 function, tanh^-1(sqrt(c) | y |) does not give an infinite result if sqrt(c) | y |>1 ?
Moreover I understood that hyperbolic space is defined by its negative curvature but in your work c > 0. What exactly is c?

Thank you very much !

[octavian-ganea]

sqrt(c) | y | is always smaller than 1 as that is our definition of the Poincare disk (see our paper). The curvature is just -c, please check the notations in our paper or http://proceedings.mlr.press/v119/bachmann20a/bachmann20a.pdf .