def register_parametrization(
module: Module,
tensor_name: str,
parametrization: Module,
*,
unsafe: bool = False,
) -> Module:
r"""Adds a parametrization to a tensor in a module.
Assume that ``tensor_name="weight"`` for simplicity. When accessing ``module.weight``,
the module will return the parametrized version ``parametrization(module.weight)``.
If the original tensor requires a gradient, the backward pass will differentiate
through :attr:`parametrization`, and the optimizer will update the tensor accordingly.
The first time that a module registers a parametrization, this function will add an attribute
``parametrizations`` to the module of type :class:`~ParametrizationList`.
The list of parametrizations on the tensor ``weight`` will be accessible under
``module.parametrizations.weight``.
The original tensor will be accessible under
``module.parametrizations.weight.original``.
Parametrizations may be concatenated by registering several parametrizations
on the same attribute.
The training mode of a registered parametrization is updated on registration
to match the training mode of the host module
Parametrized parameters and buffers have an inbuilt caching system that can be activated
using the context manager :func:`cached`.
A :attr:`parametrization` may optionally implement a method with signature
.. code-block:: python
def right_inverse(self, X: Tensor) -> Union[Tensor, Sequence[Tensor]]
This method is called on the unparametrized tensor when the first parametrization
is registered to compute the initial value of the original tensor.
If this method is not implemented, the original tensor will be just the unparametrized tensor.
If all the parametrizations registered on a tensor implement `right_inverse` it is possible
to initialize a parametrized tensor by assigning to it, as shown in the example below.
It is possible for the first parametrization to depend on several inputs.
This may be implemented returning a tuple of tensors from ``right_inverse``
(see the example implementation of a ``RankOne`` parametrization below).
In this case, the unconstrained tensors are also located under ``module.parametrizations.weight``
with names ``original0``, ``original1``,...
.. note::
If unsafe=False (default) both the forward and right_inverse methods will be called
once to perform a number of consistency checks.
If unsafe=True, then right_inverse will be called if the tensor is not parametrized,
and nothing will be called otherwise.
.. note::
In most situations, ``right_inverse`` will be a function such that
``forward(right_inverse(X)) == X`` (see
`right inverse <https://en.wikipedia.org/wiki/Inverse_function#Right_inverses>`_).
Sometimes, when the parametrization is not surjective, it may be reasonable
to relax this.
.. warning::
If a parametrization depends on several inputs, :func:`~register_parametrization`
will register a number of new parameters. If such parametrization is registered
after the optimizer is created, these new parameters will need to be added manually
to the optimizer. See :meth:`torch.Optimizer.add_param_group`.
Args:
module (nn.Module): module on which to register the parametrization
tensor_name (str): name of the parameter or buffer on which to register
the parametrization
parametrization (nn.Module): the parametrization to register
Keyword args:
unsafe (bool): a boolean flag that denotes whether the parametrization
may change the dtype and shape of the tensor. Default: `False`
Warning: the parametrization is not checked for consistency upon registration.
Enable this flag at your own risk.
Raises:
ValueError: if the module does not have a parameter or a buffer named :attr:`tensor_name`
Examples:
>>> import torch
>>> import torch.nn as nn
>>> import torch.nn.utils.parametrize as P
>>>
>>> class Symmetric(nn.Module):
>>> def forward(self, X):
>>> return X.triu() + X.triu(1).T # Return a symmetric matrix
>>>
>>> def right_inverse(self, A):
>>> return A.triu()
>>>
>>> m = nn.Linear(5, 5)
>>> P.register_parametrization(m, "weight", Symmetric())
>>> print(torch.allclose(m.weight, m.weight.T)) # m.weight is now symmetric
True
>>> A = torch.rand(5, 5)
>>> A = A + A.T # A is now symmetric
>>> m.weight = A # Initialize the weight to be the symmetric matrix A
>>> print(torch.allclose(m.weight, A))
True
>>> class RankOne(nn.Module):
>>> def forward(self, x, y):
>>> # Form a rank 1 matrix multiplying two vectors
>>> return x.unsqueeze(-1) @ y.unsqueeze(-2)
>>>
>>> def right_inverse(self, Z):
>>> # Project Z onto the rank 1 matrices
>>> U, S, Vh = torch.linalg.svd(Z, full_matrices=False)
>>> # Return rescaled singular vectors
>>> s0_sqrt = S[0].sqrt().unsqueeze(-1)
>>> return U[..., :, 0] * s0_sqrt, Vh[..., 0, :] * s0_sqrt
>>>
>>> linear_rank_one = P.register_parametrization(nn.Linear(4, 4), "weight", RankOne())
>>> print(torch.linalg.matrix_rank(linear_rank_one.weight).item())
1
"""
parametrization.train(module.training)
if is_parametrized(module, tensor_name):
# Correctness checks.
# If A is the space of tensors with shape and dtype equal to module.weight
# we check that parametrization.forward and parametrization.right_inverse are
# functions from A to A
if not unsafe:
Y = getattr(module, tensor_name)
X = parametrization(Y)
if not isinstance(X, Tensor):
raise ValueError(
f"A parametrization must return a tensor. Got {type(X).__name__}."
)
if X.dtype != Y.dtype:
raise ValueError(
"Registering a parametrization may not change the dtype of the tensor, unless the `unsafe` flag is enabled.\n"
f"module.{tensor_name}.dtype: {Y.dtype}\n"
f"parametrization(module.{tensor_name}).dtype: {X.dtype}"
)
if X.shape != Y.shape:
raise ValueError(
"Registering a parametrization may not change the shape of the tensor, unless the `unsafe` flag is enabled.\n"
f"module.{tensor_name}.shape: {Y.shape}\n"
f"parametrization(module.{tensor_name}).shape: {X.shape}"
)
if hasattr(parametrization, "right_inverse"):
try:
Z = parametrization.right_inverse(X) # type: ignore[operator]
except NotImplementedError:
pass
else:
if not isinstance(Z, Tensor):
raise ValueError(
f"parametrization.right_inverse must return a tensor. Got: {type(Z).__name__}"
)
if Z.dtype != Y.dtype:
raise ValueError(
"The tensor returned by parametrization.right_inverse must have the same dtype "
f"as module.{tensor_name}, unless the `unsafe` flag is enabled.\n"
f"module.{tensor_name}.dtype: {Y.dtype}\n"
f"returned dtype: {Z.dtype}"
)
if Z.shape != Y.shape:
raise ValueError(
"The tensor returned by parametrization.right_inverse must have the same shape "
f"as module.{tensor_name}, unless the `unsafe` flag is enabled.\n"
f"module.{tensor_name}.shape: {Y.shape}\n"
f"returned shape: {Z.shape}"
)
# else right_inverse is assumed to be the identity
# add the new parametrization to the parametrization list
assert isinstance(module.parametrizations, ModuleDict) # Make mypy happy
module.parametrizations[tensor_name].append(parametrization)
# If unsafe was True in previous parametrization, keep it enabled
module.parametrizations[tensor_name].unsafe |= unsafe # type: ignore[index, union-attr]
elif tensor_name in module._buffers or tensor_name in module._parameters:
# Set the parametrization mechanism
# Fetch the original buffer or parameter
original = getattr(module, tensor_name)
# We create this early to check for possible errors
parametrizations = ParametrizationList(
[parametrization], original, unsafe=unsafe
)
# Delete the previous parameter or buffer
delattr(module, tensor_name)
# If this is the first parametrization registered on the module,
# we prepare the module to inject the property
if not is_parametrized(module):
# Change the class
_inject_new_class(module)
# Inject a ``ModuleDict`` into the instance under module.parametrizations
module.parametrizations = ModuleDict()
# Add a property into the class
_inject_property(module, tensor_name)
# Add a ParametrizationList
assert isinstance(module.parametrizations, ModuleDict) # Make mypy happy
module.parametrizations[tensor_name] = parametrizations
else:
raise ValueError(
f"Module '{module}' does not have a parameter, a buffer, or a "
f"parametrized element with name '{tensor_name}'"
)
return module
def register_parametrization(module: Module, tensor_name: str,
parametrization: Module) -> Module:
r"""Adds a parametrization to a tensor in a module.
Assume that ``tensor_name="weight"`` for simplicity. When accessing ``module.weight``,
the module will return the parametrized version ``parametrization(module.weight)``.
If the original tensor requires a gradient, the backward pass will differentiate
through the :attr:`parametrization`, and the optimizer will update the tensor accordingly.
The first time that a module registers a parametrization, this function will add an attribute
``parametrizations`` to the module of type :class:`~ParametrizationList`.
The list of parametrizations on a tensor will be accessible under
``module.parametrizations.weight``.
The original tensor will be accessible under
``module.parametrizations.weight.original``.
Parametrizations may be concatenated by registering several parametrizations
on the same attribute.
Parametrized parameters and buffers have an inbuilt caching system that can be activated
using the context manager :func:`cached`.
A :attr:`parametrization` may optionally implement a method with signature
.. code-block:: python
def right_inverse(self, X: Tensor) -> Tensor
If :attr:`parametrization` implements this method, it will be possible to assign
to the parametrized tensor. This may be used to initialize the tensor, as shown in the example.
In most situations, ``right_inverse`` will be a function such that
``forward(right_inverse(X)) == X`` (see
`right inverse <https://en.wikipedia.org/wiki/Inverse_function#Right_inverses>`_).
Sometimes, when the parametrization is not surjective, it may be reasonable
to relax this, as shown in the example below.
Args:
module (nn.Module): module on which to register the parametrization
tensor_name (str): name of the parameter or buffer on which to register
the parametrization
parametrization (nn.Module): the parametrization to register
Returns:
Module: module
Raises:
ValueError: if the module does not have a parameter or a buffer named :attr:`tensor_name`
Examples:
>>> import torch
>>> import torch.nn.utils.parametrize as P
>>>
>>> class Symmetric(torch.nn.Module):
>>> def forward(self, X):
>>> return X.triu() + X.triu(1).T # Return a symmetric matrix
>>>
>>> def right_inverse(self, A):
>>> return A.triu()
>>>
>>> m = torch.nn.Linear(5, 5)
>>> P.register_parametrization(m, "weight", Symmetric())
>>> print(torch.allclose(m.weight, m.weight.T)) # m.weight is now symmetric
True
>>> A = torch.rand(5, 5)
>>> A = A + A.T # A is now symmetric
>>> m.weight = A # Initialize the weight to be the symmetric matrix A
>>> print(torch.allclose(m.weight, A))
True
"""
if is_parametrized(module, tensor_name):
# Just add the new parametrization to the parametrization list
module.parametrizations[tensor_name].append(
parametrization) # type: ignore
elif tensor_name in module._buffers or tensor_name in module._parameters:
# Set the parametrization mechanism
# Fetch the original buffer or parameter
original = getattr(module, tensor_name)
# Delete the previous parameter or buffer
delattr(module, tensor_name)
# If this is the first parametrization registered on the module,
# we prepare the module to inject the property
if not is_parametrized(module):
# Change the class
_inject_new_class(module)
# Inject the a ``ModuleDict`` into the instance under module.parametrizations
module.parametrizations = ModuleDict()
# Add a property into the class
_inject_property(module, tensor_name)
# Add a ParametrizationList
module.parametrizations[
tensor_name] = ParametrizationList( # type: ignore
[parametrization], original)
else:
raise ValueError(
"Module '{}' does not have a parameter, a buffer, or a "
"parametrized element with name '{}'".format(module, tensor_name))
return module