tfep.nn.transformers.sos.SOSPolynomialTransformerFunc

class tfep.nn.transformers.sos.SOSPolynomialTransformerFunc(*args, **kwargs)[source]

Bases: Function

Implement the sum-of-squares polynomial transformer for triangular maps.

This provides a functional API for the SOSPolynomialTransformer layer. It implements the polynomial transformer proposed in [1].

\(y_i = a_0 + \int_0^{x_i} \sum_{k=1}^K \left( \sum_{l=0}^L a_{kl} z^l \right)^2 dz\)

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

The function returns the transformed feature as a Tensor of shape (batch_size, n_features) and the log absolute determinant of its Jacobian as a Tensor of shape (batch_size,).

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.

Parameters:

x (torch.Tensor) – Shape (batch_size, n_features). Input tensor x.
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) – Output tensor of shape (batch_size, n_features).
log_det_J (torch.Tensor) – The logarithm of the absolute value of the determinant of the Jacobian of the transformation with shape (batch_size,).

References

[1] Jaini P, Selby KA, Yu Y. Sum-of-Squares Polynomial Flow. arXiv: preprint arXiv:1905.02325. 2019 May 7.

__init__(*args, **kwargs)

Methods

`__init__`(args, *kwargs)
`apply`(args, *kwargs)
`backward`(ctx, grad_y, grad_log_det_J)	Define a formula for differentiating the operation with backward mode automatic differentiation.
`forward`(ctx, x, parameters)	Define the forward of the custom autograd Function.
`get_sos_poly_coefficients`(parameters)	Compute the coefficient of the SOS polynomial.
`jvp`(ctx, *grad_inputs)	Define a formula for differentiating the operation with forward mode automatic differentiation.
`mark_dirty`(*args)	Mark given tensors as modified in an in-place operation.
`mark_non_differentiable`(*args)	Mark outputs as non-differentiable.
`mark_shared_storage`(*pairs)
`maybe_clear_saved_tensors`
`name`
`register_hook`
`register_prehook`
`save_for_backward`(*tensors)	Save given tensors for a future call to `backward()`.
`save_for_forward`(*tensors)	Save given tensors for a future call to `jvp()`.
`set_materialize_grads`(value)	Set whether to materialize grad tensors.
`setup_context`(ctx, inputs, output)	There are two ways to define the forward pass of an autograd.Function.
`vjp`(ctx, *grad_outputs)	Define a formula for differentiating the operation with backward mode automatic differentiation.
`vmap`(info, in_dims, *args)	Define the behavior for this autograd.Function underneath `torch.vmap()`.

Attributes

`dirty_tensors`
`generate_vmap_rule`
`materialize_grads`
`metadata`
`needs_input_grad`
`next_functions`
`non_differentiable`
`requires_grad`
`saved_for_forward`
`saved_tensors`
`saved_variables`
`to_save`

static backward(ctx, grad_y, grad_log_det_J)[source]

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.

static forward(ctx, x, parameters)[source]

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 get_sos_poly_coefficients(parameters)[source]

Compute the coefficient of the SOS polynomial.

Parameters:: parameters (torch.Tensor) – The coefficients of the squared polynomials obtained from the conditioner. Each Tensor has shape (batch_size, 1+K*L, n_features). The coefficients are ordered by polynomial so that parameters[:,0] is \(a_0\) followed by \(a_{10}, a_{11}, ..., a_{K0}, a_{K1}\).
Returns:: sos_poly_coefficients – sos_poly_coefficients[i] is a tensor of shape (batch_size, n_features) with the coefficients of the term of the SOS polynomial of degree i.
Return type:: List[torch.Tensor]

static jvp(ctx: Any, *grad_inputs: Any) → Any

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

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

You can use the ctx object to pass any value from the forward to this functions.

mark_dirty(*args: Tensor)

Mark given tensors as modified in an in-place operation.

This should be called at most once, in either the setup_context() or forward() methods, and all arguments should be inputs.

Every tensor that’s been modified in-place in a call to forward() should be given to this function, to ensure correctness of our checks. It doesn’t matter whether the function is called before or after modification.

Examples::

>>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
>>> class Inplace(Function):
>>>     @staticmethod
>>>     def forward(ctx, x):
>>>         x_npy = x.numpy() # x_npy shares storage with x
>>>         x_npy += 1
>>>         ctx.mark_dirty(x)
>>>         return x
>>>
>>>     @staticmethod
>>>     @once_differentiable
>>>     def backward(ctx, grad_output):
>>>         return grad_output
>>>
>>> a = torch.tensor(1., requires_grad=True, dtype=torch.double).clone()
>>> b = a * a
>>> Inplace.apply(a)  # This would lead to wrong gradients!
>>>                   # but the engine would not know unless we mark_dirty
>>> # xdoctest: +SKIP
>>> b.backward() # RuntimeError: one of the variables needed for gradient
>>>              # computation has been modified by an inplace operation

mark_non_differentiable(*args: Tensor)

Mark outputs as non-differentiable.

This should be called at most once, in either the setup_context() or forward() methods, and all arguments should be tensor outputs.

This will mark outputs as not requiring gradients, increasing the efficiency of backward computation. You still need to accept a gradient for each output in backward(), but it’s always going to be a zero tensor with the same shape as the shape of a corresponding output.

This is used e.g. for indices returned from a sort. See example::

>>> class Func(Function):
>>>     @staticmethod
>>>     def forward(ctx, x):
>>>         sorted, idx = x.sort()
>>>         ctx.mark_non_differentiable(idx)
>>>         ctx.save_for_backward(x, idx)
>>>         return sorted, idx
>>>
>>>     @staticmethod
>>>     @once_differentiable
>>>     def backward(ctx, g1, g2):  # still need to accept g2
>>>         x, idx = ctx.saved_tensors
>>>         grad_input = torch.zeros_like(x)
>>>         grad_input.index_add_(0, idx, g1)
>>>         return grad_input

save_for_backward(*tensors: Tensor)

Save given tensors for a future call to backward().

save_for_backward should be called at most once, in either the setup_context() or forward() methods, and only with tensors.

All tensors intended to be used in the backward pass should be saved with save_for_backward (as opposed to directly on ctx) to prevent incorrect gradients and memory leaks, and enable the application of saved tensor hooks. See torch.autograd.graph.saved_tensors_hooks.

Note that if intermediary tensors, tensors that are neither inputs nor outputs of forward(), are saved for backward, your custom Function may not support double backward. Custom Functions that do not support double backward should decorate their backward() method with @once_differentiable so that performing double backward raises an error. If you’d like to support double backward, you can either recompute intermediaries based on the inputs during backward or return the intermediaries as the outputs of the custom Function. See the double backward tutorial for more details.

In backward(), saved tensors can be accessed through the saved_tensors attribute. Before returning them to the user, a check is made to ensure they weren’t used in any in-place operation that modified their content.

Arguments can also be None. This is a no-op.

See extending-autograd for more details on how to use this method.

Example::

>>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
>>> class Func(Function):
>>>     @staticmethod
>>>     def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
>>>         w = x * z
>>>         out = x * y + y * z + w * y
>>>         ctx.save_for_backward(x, y, w, out)
>>>         ctx.z = z  # z is not a tensor
>>>         return out
>>>
>>>     @staticmethod
>>>     @once_differentiable
>>>     def backward(ctx, grad_out):
>>>         x, y, w, out = ctx.saved_tensors
>>>         z = ctx.z
>>>         gx = grad_out * (y + y * z)
>>>         gy = grad_out * (x + z + w)
>>>         gz = None
>>>         return gx, gy, gz
>>>
>>> a = torch.tensor(1., requires_grad=True, dtype=torch.double)
>>> b = torch.tensor(2., requires_grad=True, dtype=torch.double)
>>> c = 4
>>> d = Func.apply(a, b, c)

save_for_forward(*tensors: Tensor)

Save given tensors for a future call to jvp().

save_for_forward should be called at most once, in either the setup_context() or forward() methods, and all arguments should be tensors.

In jvp(), saved objects can be accessed through the saved_tensors attribute.

Arguments can also be None. This is a no-op.

See extending-autograd for more details on how to use this method.

Example::

>>> # xdoctest: +SKIP
>>> class Func(torch.autograd.Function):
>>>     @staticmethod
>>>     def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
>>>         ctx.save_for_backward(x, y)
>>>         ctx.save_for_forward(x, y)
>>>         ctx.z = z
>>>         return x * y * z
>>>
>>>     @staticmethod
>>>     def jvp(ctx, x_t, y_t, _):
>>>         x, y = ctx.saved_tensors
>>>         z = ctx.z
>>>         return z * (y * x_t + x * y_t)
>>>
>>>     @staticmethod
>>>     def vjp(ctx, grad_out):
>>>         x, y = ctx.saved_tensors
>>>         z = ctx.z
>>>         return z * grad_out * y, z * grad_out * x, None
>>>
>>>     a = torch.tensor(1., requires_grad=True, dtype=torch.double)
>>>     t = torch.tensor(1., dtype=torch.double)
>>>     b = torch.tensor(2., requires_grad=True, dtype=torch.double)
>>>     c = 4
>>>
>>>     with fwAD.dual_level():
>>>         a_dual = fwAD.make_dual(a, t)
>>>         d = Func.apply(a_dual, b, c)

set_materialize_grads(value: bool)

Set whether to materialize grad tensors. Default is True.

This should be called only from either the setup_context() or forward() methods.

If True, undefined grad tensors will be expanded to tensors full of zeros prior to calling the backward() and jvp() methods.

Example::

>>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
>>> class SimpleFunc(Function):
>>>     @staticmethod
>>>     def forward(ctx, x):
>>>         return x.clone(), x.clone()
>>>
>>>     @staticmethod
>>>     @once_differentiable
>>>     def backward(ctx, g1, g2):
>>>         return g1 + g2  # No check for None necessary
>>>
>>> # We modify SimpleFunc to handle non-materialized grad outputs
>>> class Func(Function):
>>>     @staticmethod
>>>     def forward(ctx, x):
>>>         ctx.set_materialize_grads(False)
>>>         ctx.save_for_backward(x)
>>>         return x.clone(), x.clone()
>>>
>>>     @staticmethod
>>>     @once_differentiable
>>>     def backward(ctx, g1, g2):
>>>         x, = ctx.saved_tensors
>>>         grad_input = torch.zeros_like(x)
>>>         if g1 is not None:  # We must check for None now
>>>             grad_input += g1
>>>         if g2 is not None:
>>>             grad_input += g2
>>>         return grad_input
>>>
>>> a = torch.tensor(1., requires_grad=True)
>>> b, _ = Func.apply(a)  # induces g2 to be undefined

static setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) → Any

There are two ways to define the forward pass of an autograd.Function.

Either:

Override forward with the signature forward(ctx, *args, **kwargs). setup_context is not overridden. Setting up the ctx for backward happens inside the forward.
Override forward with the signature forward(*args, **kwargs) and override setup_context. Setting up the ctx for backward happens inside setup_context (as opposed to inside the forward)

See torch.autograd.Function.forward() and extending-autograd for more details.

static vjp(ctx: Any, *grad_outputs: Any) → Any

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.

static vmap(info, in_dims, *args)

Define the behavior for this autograd.Function underneath torch.vmap().

For a torch.autograd.Function() to support torch.vmap(), you must either override this static method, or set generate_vmap_rule to True (you may not do both).

If you choose to override this staticmethod: it must accept

an info object as the first argument. info.batch_size specifies the size of the dimension being vmapped over, while info.randomness is the randomness option passed to torch.vmap().
an in_dims tuple as the second argument. For each arg in args, in_dims has a corresponding Optional[int]. It is None if the arg is not a Tensor or if the arg is not being vmapped over, otherwise, it is an integer specifying what dimension of the Tensor is being vmapped over.
*args, which is the same as the args to forward().

The return of the vmap staticmethod is a tuple of (output, out_dims). Similar to in_dims, out_dims should be of the same structure as output and contain one out_dim per output that specifies if the output has the vmapped dimension and what index it is in.

Please see func-autograd-function for more details.