def Gradient(inputs, f, name=None):
r"""Computes the gradient function for function f via backpropagation.
Args:
inputs: A list of tensors of size N + M.
f: The function we want to compute the gradient for.
The function 'f' must be a numerical function which takes N inputs and
produces M outputs. Its gradient function 'g', which is a function
taking N + M inputs and produces N outputs.
I.e. if we have
(y1, y2, ..., yM) = f(x1, x2, ..., xN),
then, g is
(dL/dx1, dL/dx2, ..., dL/dxN) = g(x1, x2, ..., xN,
dL/dy1, dL/dy2, ..., dL/dyM),
where L is a scalar-value function of (x1, x2, ..., xN) (e.g., the
loss function). dL/dxi is the partial derivative of L with respect
to xi.
name: A name for the operation (optional).
Returns:
A list of tensors of size N.
"""
# TODO(zhifengc): Pretty-print the above spec in latex.
# TODO(zhfiengc): Needs some math expert to say the comment above better.
tlist = [_.type for _ in f.definition.signature.input_arg]
return symbolic_gradient(input=inputs, Tout=tlist, f=f, name=name)
def Gradient(inputs, f, name=None):
r"""Computes the gradient function for function f via backpropagation.
Args:
inputs: A list of tensors of size N + M.
f: The function we want to compute the gradient for.
The function 'f' must be a numerical function which takes N inputs and
produces M outputs. Its gradient function 'g', which is a function
taking N + M inputs and produces N outputs.
I.e. if we have
(y1, y2, ..., yM) = f(x1, x2, ..., xN),
then, g is
(dL/dx1, dL/dx2, ..., dL/dxN) = g(x1, x2, ..., xN,
dL/dy1, dL/dy2, ..., dL/dyM),
where L is a scalar-value function of (x1, x2, ..., xN) (e.g., the
loss function). dL/dxi is the partial derivative of L with respect
to xi.
name: A name for the operation (optional).
Returns:
A list of tensors of size N.
"""
# TODO(zhifengc): Pretty-print the above spec in latex.
# TODO(zhfiengc): Needs some math expert to say the comment above better.
tlist = [_.type for _ in f.definition.signature.input_arg]
return symbolic_gradient(input=inputs, Tout=tlist, f=f, name=name)
