vhp(func, inputs, v=None, create_graph=False, strict=False)¶
Function that computes the dot product between a vector
vand the Hessian of a given scalar function at the point given by the inputs.
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
v (tuple of Tensors or Tensor) – The vector for which the vector Hessian product is computed. Must be the same size as the input of
func. This argument is optional when
func’s input contains a single element and (if it is not provided) will be set as a Tensor containing a single
create_graph (bool, optional) – If
True, both the output and result will be computed in a differentiable way. Note that when
False, the result can not require gradients or be disconnected from the inputs. Defaults to
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 vhp for said inputs, which is the expected mathematical value. Defaults to
- tuple with:
func_output (tuple of Tensors or Tensor): output of
vhp (tuple of Tensors or Tensor): result of the dot product with the same shape as the inputs.
- Return type
>>> def pow_reducer(x): ... return x.pow(3).sum() >>> inputs = torch.rand(2, 2) >>> v = torch.ones(2, 2) >>> vhp(pow_reducer, inputs, v) (tensor(0.5591), tensor([[1.0689, 1.2431], [3.0989, 4.4456]])) >>> vhp(pow_reducer, inputs, v, create_graph=True) (tensor(0.5591, grad_fn=<SumBackward0>), tensor([[1.0689, 1.2431], [3.0989, 4.4456]], grad_fn=<MulBackward0>)) >>> def pow_adder_reducer(x, y): ... return (2 * x.pow(2) + 3 * y.pow(2)).sum() >>> inputs = (torch.rand(2), torch.rand(2)) >>> v = (torch.zeros(2), torch.ones(2)) >>> vhp(pow_adder_reducer, inputs, v) (tensor(4.8053), (tensor([0., 0.]), tensor([6., 6.])))