hypll.manifolds.poincare_ball.math.stats

Functions

d2arcosh(x)

darcosh(x)

frechet_ball_backward(X, y, grad, K)

Args X (tensor): point of shape [..., points, dim] y (tensor): mean point of shape [..., dim] grad (tensor): gradient K (float): curvature (must be negative)

frechet_ball_forward(X[, K, max_iter, rtol, ...])

Args X (tensor): point of shape [..., points, dim] K (float): curvature (must be negative)

frechet_mean(x, c[, vec_dim, batch_dim, keepdim])

frechet_variance(x, c[, mu, vec_dim, ...])

Args x (tensor): points of shape [..., points, dim] mu (tensor): mean of shape [..., dim]

grad_var(X, y, K)

Args X (tensor): point of shape [..., points, dim] y (tensor): mean point of shape [..., dim] K (float): curvature (must be negative)

inverse_hessian(X, y, K)

Args X (tensor): point of shape [..., points, dim] y (tensor): mean point of shape [..., dim] K (float): curvature (must be negative)

l_prime(y)

midpoint(x, c[, man_dim, batch_dim, w, keepdim])

Classes

FrechetMean

This implementation is copied mostly from:
class hypll.manifolds.poincare_ball.math.stats.FrechetMean
This implementation is copied mostly from:

https://github.com/CUVL/Differentiable-Frechet-Mean.git

which is itself based on the paper:

https://arxiv.org/abs/2003.00335

Both by Aaron Lou (et al.)

static forward(ctx, x, c, vec_dim, batch_dim, keepdim)

Define the forward of the custom autograd Function.

This function is to be overridden by all subclasses. There are two ways to define forward:

Usage 1 (Combined forward and ctx):

@staticmethod
def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
    pass

  • It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

  • See combining-forward-context for more details

Usage 2 (Separate forward and ctx):

@staticmethod
def forward(*args: Any, **kwargs: Any) -> Any:
    pass

@staticmethod
def setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) -> None:
    pass

  • The forward no longer accepts a ctx argument.

  • Instead, you must also override the torch.autograd.Function.setup_context() staticmethod to handle setting up the ctx object. output is the output of the forward, inputs are a Tuple of inputs to the forward.

  • See extending-autograd for more details

The context can be used to store arbitrary data that can be then retrieved during the backward pass. Tensors should not be stored directly on ctx (though this is not currently enforced for backward compatibility). Instead, tensors should be saved either with ctx.save_for_backward() if they are intended to be used in backward (equivalently, vjp) or ctx.save_for_forward() if they are intended to be used for in jvp.

static backward(ctx, grad_output)

Define a formula for differentiating the operation with backward mode automatic differentiation.

This function is to be overridden by all subclasses. (Defining this function is equivalent to defining the vjp function.)

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computed w.r.t. the output.

hypll.manifolds.poincare_ball.math.stats.frechet_mean(x: Tensor, c: Tensor, vec_dim: int = -1, batch_dim: int | list[int] = 0, keepdim: bool = False) → Tensor
hypll.manifolds.poincare_ball.math.stats.midpoint(x: Tensor, c: Tensor, man_dim: int = -1, batch_dim: int | list[int] = 0, w: Tensor | None = None, keepdim: bool = False) → Tensor
hypll.manifolds.poincare_ball.math.stats.frechet_variance(x: Tensor, c: Tensor, mu: Tensor | None = None, vec_dim: int = -1, batch_dim: int | list[int] = 0, keepdim: bool = False) → Tensor

Args

x (tensor): points of shape […, points, dim] mu (tensor): mean of shape […, dim]

where the … of the three variables match

Returns

tensor of shape […]

hypll.manifolds.poincare_ball.math.stats.l_prime(y: Tensor) → Tensor
hypll.manifolds.poincare_ball.math.stats.frechet_ball_forward(X: Tensor, K: Tensor = tensor([1.]), max_iter: int = 1000, rtol: float = 1e-06, atol: float = 1e-06) → Tensor

Args

X (tensor): point of shape […, points, dim] K (float): curvature (must be negative)

Returns

frechet mean (tensor): shape […, dim]

hypll.manifolds.poincare_ball.math.stats.darcosh(x)
hypll.manifolds.poincare_ball.math.stats.d2arcosh(x)
hypll.manifolds.poincare_ball.math.stats.grad_var(X: Tensor, y: Tensor, K: Tensor) → Tensor

Args

X (tensor): point of shape […, points, dim] y (tensor): mean point of shape […, dim] K (float): curvature (must be negative)

Returns

grad (tensor): gradient of variance […, dim]

hypll.manifolds.poincare_ball.math.stats.inverse_hessian(X: Tensor, y: Tensor, K: Tensor) → Tensor

Args

X (tensor): point of shape […, points, dim] y (tensor): mean point of shape […, dim] K (float): curvature (must be negative)

Returns

inv_hess (tensor): inverse hessian of […, points, dim, dim]

hypll.manifolds.poincare_ball.math.stats.frechet_ball_backward(X: Tensor, y: Tensor, grad: Tensor, K: Tensor) → tuple[Tensor]

Args

X (tensor): point of shape […, points, dim] y (tensor): mean point of shape […, dim] grad (tensor): gradient K (float): curvature (must be negative)

Returns

gradients (tensor, tensor, tensor):

gradient of X […, points, dim], curvature []