tensorplay.autograd.functional.hessian

tensorplay.autograd.functional.hessian(func, inputs, create_graph=False, strict=False, vectorize=False, outer_jacobian_strategy='reverse-mode')[source]

Compute the Hessian of a given scalar function.

Parameters:

• func (function) – a Python function that takes Tensor inputs and returns a Tensor with a single element.

• inputs (tuple of Tensors or Tensor) – inputs to the function func.

• create_graph (bool, optional) – If True, the Hessian will be computed in a differentiable manner. Note that when strict is False, the result can not require gradients or be disconnected from the inputs. Defaults to False.

• strict (bool, optional) – If True, an error will be raised when we detect that there exists an input such that all the outputs are independent of it. If False, we return a Tensor of zeros as the hessian for said inputs, which is the expected mathematical value. Defaults to False.

• vectorize (bool, optional) – Not supported by this engine yet; passing True raises NotImplementedError.

• outer_jacobian_strategy (str, optional) – Only "reverse-mode" is supported; forward-mode AD raises NotImplementedError.

Returns:

if there is a single input, this will be a single Tensor containing the Hessian for the input. If it is a tuple, then the Hessian will be a tuple of tuples where Hessian[i][j] will contain the Hessian of the ith input and jth input with size the sum of the size of the ith input plus the size of the jth input. Hessian[i][j] will have the same dtype and device as the corresponding ith input.

Return type:

Hessian (Tensor or a tuple of tuple of Tensors)

Example

>>> def pow_reducer(x):
...     return x.pow(3).sum()
>>> inputs = tensorplay.rand(2, 2)
>>> hessian(pow_reducer, inputs)
tensor([[[[5.2265, 0.0000],
          [0.0000, 0.0000]],
         [[0.0000, 4.8221],
          [0.0000, 0.0000]]],
        [[[0.0000, 0.0000],
          [1.9456, 0.0000]],
         [[0.0000, 0.0000],
          [0.0000, 3.2550]]]])