tfep.nn.flows.maf.MAF

class tfep.nn.flows.maf.MAF(degrees_in: Sequence[int], transformer: Module | None = None, hidden_layers: int | Sequence[int] | Sequence[Sequence[int]] = 2, embedding: MAFEmbedding | None = None, weight_norm: bool = True, initialize_identity: bool = True)

Bases: AutoregressiveFlow

Masked Autoregressive Flow.

This implements an autoregressive flow in which the tfep.nn.conditioners.MADE [1] network is used for the conditioner. The class supports arbitrary transformers.

When the transformer is the AffineTransformer, this is equivalent to MAF and IAF [2-3]. These two differ only in the direction of the conditional dependence, effectively determining which between forward and inverse evaluation is faster.

See also

tfep.nn.conditioners.MADE

The autoregressive layer used as conditioner.

References

[1] Germain M, Gregor K, Murray I, Larochelle H. Made: Masked autoencoder

for distribution estimation. In International Conference on Machine Learning 2015 Jun 1 (pp. 881-889).

[2] Kingma DP, Salimans T, Jozefowicz R, Chen X, Sutskever I, Welling M.

Improved variational inference with inverse autoregressive flow. In Advances in neural information processing systems 2016 (pp. 4743-4751).

[3] Papamakarios G, Pavlakou T, Murray I. Masked autoregressive flow for

density estimation. In Advances in Neural Information Processing Systems 2017 (pp. 2338-2347).

Examples

A masked autoregressive flow using a linear transformer. This uses two MAF layers inverting the dependencies between inputs. This is a standard strategy in autoregressive flows to ensure every output depends on every input.

>>> from tfep.nn.conditioners.made import generate_degrees
>>> flow = torch.nn.Sequential(
...     MAF(degrees_in=generate_degrees(n_features=5, order='ascending')),
...     MAF(degrees_in=generate_degrees(n_features=5, order='descending')),
... )

Multiple inputs can be assigned the same degree. Further, it is possible to specify “conditioning” inputs (in this case, the first 3) which affect all outputs but that are not mapped by assigning them degree -1.

>>> maf = MAF(degrees_in=[-1, -1, -1, 0, 0, 1, 2])

__init__(degrees_in: Sequence[int], transformer: Module | None = None, hidden_layers: int | Sequence[int] | Sequence[Sequence[int]] = 2, embedding: MAFEmbedding | None = None, weight_norm: bool = True, initialize_identity: bool = True)

Constructor.

Parameters:

• degrees_in (Sequence[int]) – Shape: (n_inputs,). degrees_in[i] is the degree assigned to the i-th input. The degrees must assume consecutive values starting from 0 or -1. Input features assigned a -1 degree are labeled as “conditioning” and affect the output without being mapped.

• transformer (torch.nn.Module or None, optional) – The transformer used to map the input features. By default, the tfep.nn.transformers.affine.AffineTransformer is used.

• hidden_layers (Union[int, Sequence[int], Sequence[Sequence[int]]], optional) – If an integer, this is the number of hidden layers. In this case, the number of nodes in each layer is set to max(n_inputs, ceil((n_inputs * n_outputs)**0.5)) where n_inputs is the number of input features that affect the output, and n_outputs is the number of output features.

  If a sequence of integers, hidden_layers[l] is the number of nodes in the l-th hidden layer. The degrees of each node are assigned in a round-robin fashion by tiling degrees_in until the requested number of nodes is covered.

  Otherwise, degrees_hidden[l][i] is the degree assigned to the i-th node of the l-th hidden layer.

  Default is 2.

• embedding (torch.nn.Module, optional) – If present, the conditioner input features are first passed to this layer whose output is then fed to the conditioner.

• weight_norm (bool, optional) – If True, weight normalization is applied to the masked linear modules. Default is True.

• initialize_identity (bool, optional) – If True, the parameters are initialized in such a way that the flow initially performs the identity function.

Methods

__init__(degrees_in[, transformer, ...])	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)	Push forward.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
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.
get_transformer_parameters(x)	Compute the parameters for the transformer.
half()	Casts all floating point parameters and buffers to half datatype.
inverse(y)	Inverse.
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.
n_parameters()	The total number of (unmasked) parameters.
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
has_fixed_indices	True if some of the features are not transformed by the flow.
training

forward(x: Tensor) → Tensor

Push forward.

Parameters:

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

Returns:

• y (torch.Tensor) – Shape (batch_size, n_features). Mapped features.

• log_det_J (torch.Tensor) – Shape (batch_size,). The log absolute value of the Jacobian of the transformation.

get_transformer_parameters(x: Tensor) → Tensor

Compute the parameters for the transformer.

Parameters:

x (torch.Tensor) – Shape (batch_size, n_features). The input tensor.

Returns:

Parameters – Shape (batch_size, n_parameters). The transformer parameters.

Return type:

torch.Tensor

property has_fixed_indices

True if some of the features are not transformed by the flow.

Type:

bool

inverse(y: Tensor) → Tensor

Inverse.

This is in general slower than the forward pass as it may require multiple passes (see ref. [1] for the algorithm).

Parameters:

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

Returns:

• x (torch.Tensor) – Shape (batch_size, n_features). Mapped features.

• log_det_J (torch.Tensor) – Shape (batch_size,). The log absolute value of the Jacobian of the transformation.

n_parameters() → int

The total number of (unmasked) parameters.