Question about poincare distance

[ttgump]

Hi,
In the manifolds.poincare.py, the square distance is defined as (line 26-32):

`

sqrt_c = c ** 0.5
dist_c = artanh(
    sqrt_c * self.mobius_add(-p1, p2, c, dim=-1).norm(dim=-1, p=2, keepdim=False)
)
dist = dist_c * 2 / sqrt_c
return dist ** 2

`

But according to the equation (2) in the paper, the square distance in Poincare ball should be like this
`

sqrt_c = c ** 0.5
sq_norms_p1 = torch.sum(p1**2, dim=-1)
sq_norms_p2 = torch.sum(p2**2, dim=-1)
sq_d = torch.sum((p1-yp2)**2, dim=-1)
dist_c = arcosh(
    1 + 2*c*sq_d/(1+c*sq_norms_p1)/1+c*sq_norms_p2)
)
dist = dist_c / sqrt_c
return dist ** 2

`

[junhocho]

Hi, we used code related to hyperbolic space referring to HGCN.
checkout, https://github.com/HazyResearch/hgcn/blob/a526385744da25fc880f3da346e17d0fe33817f8/manifolds/poincare.py#L25

Also, check this out another implementation, https://github.com/leymir/hyperbolic-image-embeddings/blob/9e84d35497598a1ba99a3c38ea79bfaf47f8d076/hyptorch/pmath.py#L205

I guess the mobius addition make both equation equivalent.