def _log_det_jacobian(self, x, y):
r = F.sqrt(functions.clamp(functions.lorentzian_product(x, x), eps))
d = x / r[..., None]
dim = d.shape[-1]
logdet = (dim - 2) * F.log(F.sinh(r) / r)
return logdet
def pseudo_polar_projection(x):
r = F.sqrt(F.sum(F.square(x), axis=-1, keepdims=True))
d = x / F.broadcast_to(clamp(r, eps), x.shape)
r_proj = F.cosh(r)
d_proj = F.broadcast_to(F.sinh(r), d.shape) * d
x_proj = F.concat((r_proj, d_proj), axis=-1)
return x_proj
def forward(self, x):
y1 = F.sinh(x)
return y1
def exponential_map(x, v):
vnorm = F.sqrt(clamp(lorentzian_product(v, keepdims=True), eps))
return F.cosh(vnorm) * x + F.sinh(vnorm) * v / vnorm
def sinh(self, x):
return F.sinh(x)