tfep.nn.transformers.moebius.MoebiusTransformer

class tfep.nn.transformers.moebius.MoebiusTransformer(dimension: int, max_radius: float = 0.99, unit_sphere: bool = False)

Bases: MAFTransformer

Moebius transformer.

This implements a generalization of the Moebius transformation proposed in [1, 2] to non-unit spheres. The transformer will expand/contract the distribution on the sphere of radius \(r\), where \(r\) is the norm of the input vector.

The transformation has the form

\(y = \frac{||x||^2 - ||w||^2}{||x - w||^2} (x - w) - w\)

where \(y, x, w\) are all dimension-dimensional vectors and \(||w|| < ||x||\). The function automatically rescales the w argument following the same strategy as in [2] to satisfy the condition on the norm. Consequently, ``w``s of any norm can be passed.

The implementation of the transformation on the unit sphere is slightly more efficient and can be toggled with the unit_sphere argument.

References

[1] Kato S, McCullagh P. Moebius transformation and a Cauchy family

on the sphere. arXiv preprint arXiv:1510.07679. 2015 Oct 26.

[2] Rezende DJ, Papamakarios G, Racanière S, Albergo MS, Kanwar G,

Shanahan PE, Cranmer K. Normalizing Flows on Tori and Spheres. arXiv preprint arXiv:2002.02428. 2020 Feb 6.

__init__(dimension: int, max_radius: float = 0.99, unit_sphere: bool = False)

Constructor.

Parameters:

• dimension (int) – The dimensionality of the vectors in x and w.

• max_radius (float) – Must be stringly less than 1. Rescaling of the w vectors will be performed so that its maximum norm will be max_radius * |x|.

• unit_sphere (bool) – If True, the input vectors x are assumed to be on the unit sphere, which makes the implementation slightly faster.

Methods

__init__(dimension[, max_radius, unit_sphere])	Constructor.
add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Set the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(x, parameters)	Apply the transformation.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_degrees_out(degrees_in)	Returns the degrees associated to the conditioner's output.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_identity_parameters(n_features)	Return the value of the parameters that makes this the identity function.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
half()	Casts all floating point parameters and buffers to half datatype.
inverse(y, parameters)	Reverse the transformation.
ipu([device])	Move all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules()	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Return an iterator over module parameters.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module)	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

Attributes

T_destination
call_super_init
dump_patches
training

forward(x: Tensor, parameters: Tensor) → tuple[Tensor]

Apply the transformation.

Parameters:

• x (torch.Tensor) – Shape (batch_size, n_vectors*dimension). Contiguous elements of x are interpreted as vectors (i.e., the first and second input vectors are x[:dimension] and x[dimension:2*dimension].

• parameters (torch.Tensor) – Shape (batch_size, n_vectors*dimension). The transformation parameters. These parameter vectors are automatically rescaled so that |w| < |x|.

Returns:

• y (torch.Tensor) – Shape (batch_size, n_vectors*dimension). The transformed vectors.

• log_det_J (torch.Tensor) – Shape (batch_size,). The logarithm of the absolute value of the Jacobian determinant dy / dx.

get_degrees_out(degrees_in: Tensor) → Tensor

Returns the degrees associated to the conditioner’s output.

Parameters:

degrees_in (torch.Tensor) – Shape (n_transformed_features,). The autoregressive degrees associated to the features provided as input to the transformer.

Returns:

degrees_out – Shape (n_parameters,). The autoregressive degrees associated to each output of the conditioner that will be fed to the transformer as parameters.

Return type:

torch.Tensor

get_identity_parameters(n_features: int) → Tensor

Return the value of the parameters that makes this the identity function.

This can be used to initialize the normalizing flow to perform the identity transformation.

Parameters:

n_features (int) – The dimension of the input vector passed to the transformer.

Returns:

parameters – A tensor of shape (n_features,) representing the parameter vector to perform the identity function with a Moebius transformer.

Return type:

torch.Tensor

inverse(y: Tensor, parameters: Tensor) → tuple[Tensor]

Reverse the transformation.

Parameters:

• y (torch.Tensor) – Shape (batch_size, n_vectors*dimension). Contiguous elements of y are interpreted as vectors (i.e., the first and second input vectors are y[:dimension] and y[dimension:2*dimension].

• parameters (torch.Tensor) – Shape (batch_size, n_vectors*dimension). The transformation parameters. These parameter vectors are automatically rescaled so that |w| < |y|.

Returns:

• x (torch.Tensor) – Shape (batch_size, n_vectors*dimension). The transformed vectors.

• log_det_J (torch.Tensor) – Shape (batch_size,). The logarithm of the absolute value of the Jacobian determinant dx / dy.