utils/manifolds.py

"""Copyright (c) Meta Platforms, Inc. and affiliates."""

import math
import torch
from geoopt.manifolds import Sphere as geoopt_Sphere


class Sphere(geoopt_Sphere):
    def transp(self, x, y, v):
        denom = 1 + self.inner(x, x, y, keepdim=True)
        res = v - self.inner(x, y, v, keepdim=True) / denom * (x + y)
        cond = denom.gt(1e-3)
        return torch.where(cond, res, -v)

    def uniform_logprob(self, x):
        dim = x.shape[-1]
        return torch.full_like(
            x[..., 0],
            math.lgamma(dim / 2) - (math.log(2) + (dim / 2) * math.log(math.pi)),
        )

    def random_base(self, *args, **kwargs):
        return self.random_uniform(*args, **kwargs)

    def base_logprob(self, *args, **kwargs):
        return self.uniform_logprob(*args, **kwargs)


def geodesic(manifold, start_point, end_point):
    shooting_tangent_vec = manifold.logmap(start_point, end_point)

    def path(t):
        """Generate parameterized function for geodesic curve.
        Parameters
        ----------
        t : array-like, shape=[n_points,]
            Times at which to compute points of the geodesics.
        """
        tangent_vecs = torch.einsum("i,...k->...ik", t, shooting_tangent_vec)
        points_at_time_t = manifold.expmap(start_point.unsqueeze(-2), tangent_vecs)
        return points_at_time_t

    return path