tfep.nn.transformers.sos.SOSPolynomialTransformer

class tfep.nn.transformers.sos.SOSPolynomialTransformer(n_polynomials=2)

Bases: MAFTransformer

Sum-of-squares polynomial transformer module for autoregressive normalizing flows.

This is an implementation of the polynomial transformer proposed in [1].

:math:`y_i = a_0 + int_0^{x_i} sum_{k=1}^K left( sum_{l=0}^L a_{kl} z^l

ight)^2 dz`

where \(K\) and \(L\) are the total number and degree of the polynomials respectively, and \(a_X\) represent the parameters of the transformer.

Only sums of squared first-degree polynomials (i.e., L=1) are currently supported as they are the only one with an analytic inverse and sum of zeroth degree polynomials (i.e., L=0) are equivalent to affine transformer.

nets.functions.transformer.sos_polynomial_transformer

[1] Jaini P, Selby KA, Yu Y. Sum-of-Squares Polynomial Flow. arXiv

preprint arXiv:1905.02325. 2019 May 7.

__init__(n_polynomials=2)

Constructor.

Parameters:

n_polynomials (int) – The functional form of this transformer is a sum of squared polynomials. This is the number of such polynomials, which must be greater than 1. The more polynomials, the greater the number of parameters. Default is 2.

Methods

__init__([n_polynomials])	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 to the input.
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)	Currently not implemented.
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
degree_polynomials	The degree of each squared polynomial.
dump_patches
n_parameters_per_feature	Number of parameters needed by the transformer for each input dimension.
parameters_per_polynomial	Numer of parameters needed by the transformer for each squared polynomial.
training

property degree_polynomials

The degree of each squared polynomial.

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

Apply the transformation to the input.

Parameters:

• x (torch.Tensor) – Shape (batch_size, n_features). Input tensor.

• parameters (torch.Tensor) – Shape (batch_size, (1 + K*L)*n_features). The coefficients of the squared polynomials obtained from the conditioner. The coefficients are ordered by polynomial so that parameters[:,0] is \(a_0\) followed by \(a_{10}, a_{11}, ..., a_{K0}, a_{K1}\).

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 of the transformer.

Returns:

parameters – Shape (1+K*L, n_features) where K and L are the number and degree of the polynomials.

Return type:

torch.Tensor

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

Currently not implemented.

property n_parameters_per_feature

Number of parameters needed by the transformer for each input dimension.

property parameters_per_polynomial

Numer of parameters needed by the transformer for each squared polynomial.