Function hessians

tensorflow/python/ops/gradients_impl.py:333–396

Constructs the Hessian of sum of `ys` with respect to `x` in `xs`. `hessians()` adds ops to the graph to output the Hessian matrix of `ys` with respect to `xs`. It returns a list of `Tensor` of length `len(xs)` where each tensor is the Hessian of `sum(ys)`. The Hessian is a matrix of seco

(ys,
             xs,
             name="hessians",
             colocate_gradients_with_ops=False,
             gate_gradients=False,
             aggregation_method=None)

@tf_export(v1=["hessians"])
def hessians(ys,
             xs,
             name="hessians",
             colocate_gradients_with_ops=False,
             gate_gradients=False,
             aggregation_method=None):
  """Constructs the Hessian of sum of `ys` with respect to `x` in `xs`.

  `hessians()` adds ops to the graph to output the Hessian matrix of `ys`
  with respect to `xs`.  It returns a list of `Tensor` of length `len(xs)`
  where each tensor is the Hessian of `sum(ys)`.

  The Hessian is a matrix of second-order partial derivatives of a scalar
  tensor (see https://en.wikipedia.org/wiki/Hessian_matrix for more details).

  Args:
    ys: A `Tensor` or list of tensors to be differentiated.
    xs: A `Tensor` or list of tensors to be used for differentiation.
    name: Optional name to use for grouping all the gradient ops together.
      defaults to 'hessians'.
    colocate_gradients_with_ops: See `gradients()` documentation for details.
    gate_gradients: See `gradients()` documentation for details.
    aggregation_method: See `gradients()` documentation for details.

  Returns:
    A list of Hessian matrices of `sum(ys)` for each `x` in `xs`.

  Raises:
    LookupError: if one of the operations between `xs` and `ys` does not
      have a registered gradient function.
  """
  xs = gradients_util._AsList(xs)  # pylint: disable=protected-access
  kwargs = {
      "colocate_gradients_with_ops": colocate_gradients_with_ops,
      "gate_gradients": gate_gradients,
      "aggregation_method": aggregation_method
  }
  # Compute first-order derivatives and iterate for each x in xs.
  hessians = []
  _gradients = gradients(ys, xs, **kwargs)
  for gradient, x in zip(_gradients, xs):
    # change shape to one-dimension without graph branching
    gradient = array_ops.reshape(gradient, [-1])

    # Declare an iterator and tensor array loop variables for the gradients.
    n = array_ops.size(x)
    loop_vars = [
        array_ops.constant(0, dtypes.int32),
        tensor_array_ops.TensorArray(x.dtype, n)
    ]
    # Iterate over all elements of the gradient and compute second order
    # derivatives.
    _, hessian = control_flow_ops.while_loop(
        lambda j, _: j < n,
        lambda j, result: (j + 1,
                           result.write(j, gradients(gradient[j], x)[0])),
        loop_vars
    )