nlgm.manifolds Module

class nlgm.manifolds.BasicManifold(dimension: int, curvature: float, base_point: Tensor = None)

A base class for manifolds, providing a common interface for dimension, curvature, and base point.

Args:

dimension (int): The dimension of the manifold. curvature (float): The curvature of the manifold. base_point (torch.Tensor): The origin point of the tangent space.

distance(tangent_vector: Tensor) → Tensor

Computes the geodesic distance between two points.

Args:

point_x (torch.Tensor): The first point. point_y (torch.Tensor): The second point.

Returns:

torch.Tensor: The Euclidean distance between the two points.

exponential_map(tangent_vector: Tensor) → Tensor

Applies the exponential map to the given tangent vector in Euclidean space.

Args:

tangent_vector (torch.Tensor): The tangent vector to be mapped.

Returns:

torch.Tensor: The result of applying the exponential map to the tangent vector.

class nlgm.manifolds.EuclideanManifold(dimension: int, curvature: float, base_point: Tensor = None)

distance(point_x: Tensor, point_y: Tensor) → Tensor

Computes the geodesic distance between two points in Euclidean space.

Args:

point_x (torch.Tensor): The first point. point_y (torch.Tensor): The second point.

Returns:

torch.Tensor: The Euclidean distance between the two points.

exponential_map(tangent_vector: Tensor) → Tensor

Applies the exponential map to the given tangent vector in Euclidean space.

Args:

tangent_vector (torch.Tensor): The tangent vector to be mapped.

Returns:

torch.Tensor: The result of applying the exponential map to the tangent vector.

class nlgm.manifolds.HyperbolicManifold(dimension: int, curvature: float, base_point: Tensor = None)

distance(point_x: Tensor, point_y: Tensor) → Tensor

Computes the geodesic distance between two points in Hyperbolic space.

Args:

point_x (torch.Tensor): The first point. point_y (torch.Tensor): The second point.

Returns:

torch.Tensor: The geodesic distance between the two points.

exponential_map(tangent_vector: Tensor) → Tensor

Applies the exponential map to the given tangent vector in Hyperbolic space.

Args:

tangent_vector (torch.Tensor): The tangent vector to be mapped.

Returns:

torch.Tensor: The result of applying the exponential map to the tangent vector.

class nlgm.manifolds.ProductManifold(curvatures: List[float])

Represents a product manifold constructed from multiple manifold components, each characterized by its dimension and curvature.

Args:

curvatures (List[float]): A list containing the curvatures of component manifolds.

Attributes:

manifolds (List[BasicManifold]): A list of manifold objects representing the components of the product manifold. dimensions (List[int]): A list of dimensions of each component manifold.

Note: dimension of each component manifold is assumed to be 2.

distance(point_x: Tensor, point_y: Tensor) → Tensor

Computes the distance between two points in the product manifold space.

Args:

point_x (torch.Tensor): The first point in the product manifold space. point_y (torch.Tensor): The second point in the product manifold space.

Returns:

torch.Tensor: The distance between the two points in the product manifold space.

exponential_map(latent_vector: Tensor) → Tensor

Applies the exponential map of each component manifold to the corresponding segment of the input latent vector and returns a concatenated tensor representing the projection into the product manifold space.

Args:

latent_vector (torch.Tensor): A latent vector in Euclidean space to be mapped to the product manifold space.

Its dimension should match the sum of the dimensions of the component manifolds.

Returns:

torch.Tensor: A tensor representing the projection of the input latent vector into the product manifold space,

preserving the differentiability for gradient-based optimization.

class nlgm.manifolds.SphericalManifold(dimension: int, curvature: float, base_point: Tensor = None)

distance(point_x: Tensor, point_y: Tensor) → Tensor

Computes the geodesic distance between two points in Spherical space.

Args:

point_x (torch.Tensor): The first point. point_y (torch.Tensor): The second point.

Returns:

torch.Tensor: The geodesic distance between the two points.

exponential_map(tangent_vector: Tensor) → Tensor

Applies the exponential map to the given tangent vector in Spherical space.

Args:

tangent_vector (torch.Tensor): The tangent vector to be mapped.

Returns:

torch.Tensor: The result of applying the exponential map to the tangent vector.